Deck 10: Hypothesis Testing: Two Sample Tests

Question 1

When the sample sizes are equal,the pooled variance of the two groups is the average of the two sample variances.

Answer 1

True

Question 2

When you test for differences between the means of two independent populations,you can only use a two-tailed test.

Answer 2

False

Question 3

A researcher is curious about the effect of sleep on students' test performances.He chooses 60 students and gives each two tests: one given after two hours of sleep and one after eight hours of sleep.The test the researcher should use would be a related samples test.

Answer 3

True

Question 4

Given the following information,calculate the degrees of freedom that should be used in the pooled-variance t test. S₁² = 4 S₂² = 6
N₁ = 16 n₂ = 25

A)df = 16
B)df = 41
C)df = 25
D)df = 39

Question 5

The t test for the difference between the means of two independent populations assumes that the respective

A)sample sizes are equal.
B)populations are approximately normal.
C)sample variances are equal.
D)All of the above.

Question 6

A Marine drill instructor recorded the time in which each of 11 recruits completed an obstacle course both before and after basic training.To test whether any improvement occurred,the instructor would use a t-distribution with 11 degrees of freedom.

Question 7

In testing for differences between the means of two related populations,the null hypothesis is

A)H₀: μ_D < 0.
B)H₀: μ_D = 0.
C)H₀: μ_D = 2.
D)H₀: μ_D > 0.

Question 8

In testing for differences between the means of two independent populations where the variances in each population are unknown but assumed equal,the degrees of freedom are

A)n₁ + n₂ - 2.
B)n₁ + n₂ - 1.
C)n - 2.
D)n - 1.

Question 9

If you are testing for the difference between the means of two independent populations presuming equal variances with samples of n₁ = 20 and n₂ = 20,the number of degrees of freedom is equal to

A)39.
B)19.
C)18.
D)38.

Question 10

The sample size in each independent sample must be the same if we are to test for differences between the means of two independent populations.

Question 11

Repeated measurements from the same individuals are an example of data collected from two related populations.

Question 12

In testing for differences between the means of two independent populations,the null hypothesis is

A)H₀: μ₁ - μ₂ = 0.
B)H₀: μ₁ - μ₂ < 2.
C)H₀: μ₁ - μ₂ > 0.
D)H₀: μ₁ - μ₂ = 2.

Question 13

In testing for differences between the means of two related populations where the variance of the differences is unknown,the degrees of freedom are

A)n₁ + n₂ - 1.
B)n - 1.
C)n₁ + n₂ - 2.
D)n - 2.

Question 14

When testing for differences between the means of two related populations,you can use either a one-tailed or two-tailed test.

Question 15

A business statistics lecturer wanted to test whether the grades on a business statistics test were the same for upper and lower students.The lecturer took a random sample of size 10 from each,conducted a test and found out that the variances were equal.For this situation,the lecturer should use a t test with related samples.

Question 16

If you are testing for the difference between the means of two independent populations with samples of n₁ = 20 and n₂ = 20,the number of degrees of freedom is equal to

A)19.
B)39.
C)38.
D)18.

Question 17

In what type of test is the variable of interest the difference between the values of the observations rather than the observations themselves?

A)A test for the difference between the means of two independent populations.
B)A test for the equality of variances from two independent populations.
C)A test for the difference between the means of two related populations.
D)All of the above.

Question 18

A business statistics lecturer wanted to test whether the grades on a business statistics test were the same for upper and lower students.The lecturer took a random sample of size 10 from each,conducted a test and found out that the variances were equal.For this situation,the lecturer should use a t test with independent samples.

Question 19

A Marine drill instructor recorded the time in which each of 11 recruits completed an obstacle course both before and after basic training.To test whether any improvement occurred,the instructor would use a t-distribution with 10 degrees of freedom.

Question 20

The t test for the mean difference between two related populations assumes that the

A)population sizes are equal.
B)population of differences is approximately normal or sample sizes are large enough.
C)sample variances are equal.
D)All of the above.

Question 21

Instruction 10-4
A real estate company is interested in testing whether the mean time that families in Gotham have been living in their current homes is less than families in Metropolis.Assume that the two population variances are equal.A random sample of 100 families from Gotham and a random sample of 150 families in Metropolis yield the following data on length of residence in current homes.
Gotham: $\quad \bar { X } _ { \mathrm { G } } = 35$ months, $\quad S _ { \mathrm { G } } ^ { }² = 900$
Metropolis: $\quad \bar { X } _ { M } = 50$ months, $\quad S _ { M ^ { 2 } } = 1,050$

-Referring to Instruction 10-4,what is the standardised value of the estimate of the mean of the sampling distribution of the difference between sample means?

A)-3.69
B)-1.96
C)-2.33
D)-8.75

Question 22

Instruction 10-2
A researcher randomly sampled 30 graduates of an MBA program and recorded data concerning their starting salaries.Of primary interest to the researcher was the effect of gender on starting salaries.The result of the pooled-variance t test of the mean salaries of the females (Population 1)and males (Population 2)in the sample is given below.
$$\begin{array}{l}\begin{array} { |l | l| } \hline \text {Hypothesised Difference }&0\\\hline \text {Level of Significance }&0.05\\\hline \text {Population 1 Sample }&\\\hline \text {Sample Size }&18\\\hline \text {Sample Mean }&48266.7\\\hline \text {Sample Standard Deviation }&13577.63\\\hline \text { Population 2 Sample}&\\\hline \text {Sample Size }&12\\\hline \text { Sample Mean}&55000\\\hline \text {Sample Standard Deviation }&11741.29\\\hline \text {Difference in Sample Means }&-6733.3\\\hline \text {-Test Statistic }&-1.40193\\\hline \text {Lower-Tail Test }&\\\hline \text {Lower Critical Value }&-1.70113\\\hline \text { \( p \)-Value}&0.085962\\\hline\end{array}\end{array}$$

-Referring to Instruction 10-2,the researcher was attempting to show statistically that the female MBA graduates have a significantly lower mean starting salary than the male MBA graduates.What assumptions were necessary to conduct this hypothesis test?

A)The samples were randomly and independently selected.
B)The population variances are approximately equal.
C)Both populations of salaries (male and female)must have approximate normal distributions.
D)All of the above assumptions were necessary.

Question 23

Instruction 10-4
A real estate company is interested in testing whether the mean time that families in Gotham have been living in their current homes is less than families in Metropolis.Assume that the two population variances are equal.A random sample of 100 families from Gotham and a random sample of 150 families in Metropolis yield the following data on length of residence in current homes.
Gotham: $\quad \bar { X } _ { \mathrm { G } } = 35$ months, $\quad S _ { \mathrm { G } } ^ { }² = 900$
Metropolis: $\quad \bar { X } _ { M } = 50$ months, $\quad S _ { M ^ { 2 } } = 1,050$

-Referring to Instruction 10-4,suppose ? = 0.10.Which of the following represents the correct conclusion?

A)There is not enough evidence that the mean amount of time families in Gotham have been living in their current homes is less than families in Metropolis.
B)There is enough evidence that the mean amount of time families in Gotham have been living in their current homes is less than families in Metropolis.
C)There is not enough evidence that the mean amount of time families in Gotham have been living in their current homes is not less than families in Metropolis.
D)There is enough evidence that the mean amount of time families in Gotham have been living in their current homes is not less than families in Metropolis.

Question 24

Instruction 10-2
A researcher randomly sampled 30 graduates of an MBA program and recorded data concerning their starting salaries.Of primary interest to the researcher was the effect of gender on starting salaries.The result of the pooled-variance t test of the mean salaries of the females (Population 1)and males (Population 2)in the sample is given below.
$$\begin{array}{l}\begin{array} { |l | l| } \hline \text {Hypothesised Difference }&0\\\hline \text {Level of Significance }&0.05\\\hline \text {Population 1 Sample }&\\\hline \text {Sample Size }&18\\\hline \text {Sample Mean }&48266.7\\\hline \text {Sample Standard Deviation }&13577.63\\\hline \text { Population 2 Sample}&\\\hline \text {Sample Size }&12\\\hline \text { Sample Mean}&55000\\\hline \text {Sample Standard Deviation }&11741.29\\\hline \text {Difference in Sample Means }&-6733.3\\\hline \text {-Test Statistic }&-1.40193\\\hline \text {Lower-Tail Test }&\\\hline \text {Lower Critical Value }&-1.70113\\\hline \text { \( p \)-Value}&0.085962\\\hline\end{array}\end{array}$$

-Referring to Instruction 10-2,the researcher was attempting to show statistically that the female MBA graduates have a significantly lower mean starting salary than the male MBA graduates.From the analysis in Instruction 10-2,the correct test statistic is

A)-1.4019.
B)0.0860.
C)-6,733.33.
D)-1.7011.

Question 25

Instruction 10-4
A real estate company is interested in testing whether the mean time that families in Gotham have been living in their current homes is less than families in Metropolis.Assume that the two population variances are equal.A random sample of 100 families from Gotham and a random sample of 150 families in Metropolis yield the following data on length of residence in current homes.
Gotham: $\quad \bar { X } _ { \mathrm { G } } = 35$ months, $\quad S _ { \mathrm { G } } ^ { }² = 900$
Metropolis: $\quad \bar { X } _ { M } = 50$ months, $\quad S _ { M ^ { 2 } } = 1,050$

-Referring to Instruction 10-4,what is the estimated standard error of the difference between the two sample means?

A)4.06
B)8.01
C)16.00
D)5.61

Question 26

Instruction 10-2
A researcher randomly sampled 30 graduates of an MBA program and recorded data concerning their starting salaries.Of primary interest to the researcher was the effect of gender on starting salaries.The result of the pooled-variance t test of the mean salaries of the females (Population 1)and males (Population 2)in the sample is given below.

Referring to Instruction 10-2,what is the 99% confidence interval estimate for the difference between two means?

Question 27

Instruction 10-4
A real estate company is interested in testing whether the mean time that families in Gotham have been living in their current homes is less than families in Metropolis.Assume that the two population variances are equal.A random sample of 100 families from Gotham and a random sample of 150 families in Metropolis yield the following data on length of residence in current homes.
Gotham: $\quad \bar { X } _ { \mathrm { G } } = 35$ months, $\quad S _ { \mathrm { G } } ^ { }² = 900$
Metropolis: $\quad \bar { X } _ { M } = 50$ months, $\quad S _ { M ^ { 2 } } = 1,050$

-Referring to Instruction 10-4,what is a point estimate for the mean of the sampling distribution of the difference between the two sample means?

A)-10
B)0
C)-22
D)-15

Question 28

Instruction 10-2
A researcher randomly sampled 30 graduates of an MBA program and recorded data concerning their starting salaries.Of primary interest to the researcher was the effect of gender on starting salaries.The result of the pooled-variance t test of the mean salaries of the females (Population 1)and males (Population 2)in the sample is given below.
$$\begin{array}{l}\begin{array} { |l | l| } \hline \text {Hypothesised Difference }&0\\\hline \text {Level of Significance }&0.05\\\hline \text {Population 1 Sample }&\\\hline \text {Sample Size }&18\\\hline \text {Sample Mean }&48266.7\\\hline \text {Sample Standard Deviation }&13577.63\\\hline \text { Population 2 Sample}&\\\hline \text {Sample Size }&12\\\hline \text { Sample Mean}&55000\\\hline \text {Sample Standard Deviation }&11741.29\\\hline \text {Difference in Sample Means }&-6733.3\\\hline \text {-Test Statistic }&-1.40193\\\hline \text {Lower-Tail Test }&\\\hline \text {Lower Critical Value }&-1.70113\\\hline \text { \( p \)-Value}&0.085962\\\hline\end{array}\end{array}$$

-Referring to Instruction 10-2,the researcher was attempting to show statistically that the female MBA graduates have a significantly lower mean starting salary than the male MBA graduates.What is the proper conclusion for this test?

A)At the ? = 0.10 level,there is sufficient evidence to indicate a difference in the mean starting salaries of male and female MBA graduates.
B)At the ? = 0.10 level,there is sufficient evidence to indicate that females have a higher mean starting salary than male MBA graduates.
C)At the ? = 0.10 level,there is sufficient evidence to indicate that females have a lower mean starting salary than male MBA graduates.
D)At the ? = 0.10 level,there is insufficient evidence to indicate any difference in the mean starting salaries of male and female MBA graduates.

Question 29

Instruction 10-4
A real estate company is interested in testing whether the mean time that families in Gotham have been living in their current homes is less than families in Metropolis.Assume that the two population variances are equal.A random sample of 100 families from Gotham and a random sample of 150 families in Metropolis yield the following data on length of residence in current homes.
Gotham: $\quad \bar { X } _ { \mathrm { G } } = 35$ months, $\quad S _ { \mathrm { G } } ^ { }² = 900$
Metropolis: $\quad \bar { X } _ { M } = 50$ months, $\quad S _ { M ^ { 2 } } = 1,050$

-Referring to Instruction 10-4,what is(are)the critical value(s)of the relevant hypothesis test if the level of significance is 0.01?

A)t ? Z = -1.96
B)t ? Z = -2.080
C)t ? Z = -2.33
D)t ? Z = ± 1.96

Question 30

Instruction 10-2
A researcher randomly sampled 30 graduates of an MBA program and recorded data concerning their starting salaries.Of primary interest to the researcher was the effect of gender on starting salaries.The result of the pooled-variance t test of the mean salaries of the females (Population 1)and males (Population 2)in the sample is given below.
$$\begin{array}{l}\begin{array} { |l | l| } \hline \text {Hypothesised Difference }&0\\\hline \text {Level of Significance }&0.05\\\hline \text {Population 1 Sample }&\\\hline \text {Sample Size }&18\\\hline \text {Sample Mean }&48266.7\\\hline \text {Sample Standard Deviation }&13577.63\\\hline \text { Population 2 Sample}&\\\hline \text {Sample Size }&12\\\hline \text { Sample Mean}&55000\\\hline \text {Sample Standard Deviation }&11741.29\\\hline \text {Difference in Sample Means }&-6733.3\\\hline \text {-Test Statistic }&-1.40193\\\hline \text {Lower-Tail Test }&\\\hline \text {Lower Critical Value }&-1.70113\\\hline \text { \( p \)-Value}&0.085962\\\hline\end{array}\end{array}$$

-Referring to Instruction 10-2,the researcher was attempting to show statistically that the female MBA graduates have a significantly lower mean starting salary than the male MBA graduates.According to the test run,which of the following is an appropriate alternative hypothesis?

A)H₁: ?_females = ?_males
B)H₁: ?_females > ?_males
C)H₁: ?_females < ?_males
D)H₁: ?_females ? ?_males

Question 31

Instruction 10-1
Are Chinese managers more motivated than Australian managers? A randomly selected group of each were administered the Sarnoff Survey of Attitudes Toward Life (SSATL),which measures motivation for upward mobility.The SSATL scores are summarised below.
$$\begin{array} { | l | l | l | } \hline & \text { Australian } & \text { Chinese } \\\hline \text { Sample Size } & 211 & 100 \\\hline \text { Mean SSATL Score } & 65.75 & 79.83 \\\hline \text { Population Std. Dev. } & 11.07 & 6.41 \\\hline\end{array}$$

-Referring to Instruction 10-1,what is the value of the test statistic?

A)96.4471
B)-14.08
C)-1.9677
D)-11.8092

Question 32

Instruction 10-4
A real estate company is interested in testing whether the mean time that families in Gotham have been living in their current homes is less than families in Metropolis.Assume that the two population variances are equal.A random sample of 100 families from Gotham and a random sample of 150 families in Metropolis yield the following data on length of residence in current homes.
Gotham: $\quad \bar { X } _ { \mathrm { G } } = 35$ months, $\quad S _ { \mathrm { G } } ^ { }² = 900$
Metropolis: $\quad \bar { X } _ { M } = 50$ months, $\quad S _ { M ^ { 2 } } = 1,050$

-Referring to Instruction 10-4,suppose ? = 0.10.Which of the following represents the result of the relevant hypothesis test?

A)The alternative hypothesis is rejected.
B)The null hypothesis is rejected.
C)The null hypothesis is not rejected.
D)Insufficient information exists on which to make a decision.

Question 33

Instruction 10-2
A researcher randomly sampled 30 graduates of an MBA program and recorded data concerning their starting salaries.Of primary interest to the researcher was the effect of gender on starting salaries.The result of the pooled-variance t test of the mean salaries of the females (Population 1)and males (Population 2)in the sample is given below.

Referring to Instruction 10-2,what is the 95% confidence interval estimate for the difference between two means?

Question 34

Instruction 10-1
Are Chinese managers more motivated than Australian managers? A randomly selected group of each were administered the Sarnoff Survey of Attitudes Toward Life (SSATL),which measures motivation for upward mobility.The SSATL scores are summarised below.
$$\begin{array} { | l | l | l | } \hline & \text { Australian } & \text { Chinese } \\\hline \text { Sample Size } & 211 & 100 \\\hline \text { Mean SSATL Score } & 65.75 & 79.83 \\\hline \text { Population Std. Dev. } & 11.07 & 6.41 \\\hline\end{array}$$

-Referring to Instruction 10-1,judging from the way the data were collected,which test would likely be most appropriate to employ?

A)Z test for the mean difference between two proportions.
B)Pooled-variance t test for the difference between two means.
C)Test for the ratio between two variances.
D)Paired t test.

Question 35

Instruction 10-4
A real estate company is interested in testing whether the mean time that families in Gotham have been living in their current homes is less than families in Metropolis.Assume that the two population variances are equal.A random sample of 100 families from Gotham and a random sample of 150 families in Metropolis yield the following data on length of residence in current homes.
Gotham: $\quad \bar { X } _ { \mathrm { G } } = 35$ months, $\quad S _ { \mathrm { G } } ^ { }² = 900$
Metropolis: $\quad \bar { X } _ { M } = 50$ months, $\quad S _ { M ^ { 2 } } = 1,050$

-Referring to Instruction 10-4,what is(are)the critical value(s)of the relevant hypothesis test if the level of significance is 0.05?

A)t ? Z = -1.645
B)t ? Z = -1.96
C)t ? Z = -2.080
D)t ? Z = ± 1.96

Question 36

Instruction 10-4
A real estate company is interested in testing whether the mean time that families in Gotham have been living in their current homes is less than families in Metropolis.Assume that the two population variances are equal.A random sample of 100 families from Gotham and a random sample of 150 families in Metropolis yield the following data on length of residence in current homes.
Gotham: $\quad \bar { X } _ { \mathrm { G } } = 35$ months, $\quad S _ { \mathrm { G } } ^ { }² = 900$
Metropolis: $\quad \bar { X } _ { M } = 50$ months, $\quad S _ { M ^ { 2 } } = 1,050$

-Referring to Instruction 10-4,suppose ? = 0.01.Which of the following represents the result of the relevant hypothesis test?

A)The alternative hypothesis is rejected.
B)The null hypothesis is rejected.
C)The null hypothesis is not rejected.
D)Insufficient information exists on which to make a decision.

Question 37

Instruction 10-1
Are Chinese managers more motivated than Australian managers? A randomly selected group of each were administered the Sarnoff Survey of Attitudes Toward Life (SSATL),which measures motivation for upward mobility.The SSATL scores are summarised below.
$$\begin{array} { | l | l | l | } \hline & \text { Australian } & \text { Chinese } \\\hline \text { Sample Size } & 211 & 100 \\\hline \text { Mean SSATL Score } & 65.75 & 79.83 \\\hline \text { Population Std. Dev. } & 11.07 & 6.41 \\\hline\end{array}$$

-Referring to Instruction 10-1,suppose that the test statistic is Z = 2.45.Find the p-value if we assume that the alternative hypothesis was a two-tailed test (H₁: ?_A - ?_J ? 0).

A)0.0142
B)0.4929
C)0.9858
D)0.0071

Question 38

Given the following information,calculate S_p²,the pooled sample variance that should be used in the pooled-variance t test. S₁² = 4 S₂² = 6
N₁ = 16 n₂ = 25

A)S_p² = 6
B)S_p² = 5
C)S_p² = 4
D)S_p² = 5.23

Question 39

Instruction 10-4
A real estate company is interested in testing whether the mean time that families in Gotham have been living in their current homes is less than families in Metropolis.Assume that the two population variances are equal.A random sample of 100 families from Gotham and a random sample of 150 families in Metropolis yield the following data on length of residence in current homes.
Gotham: $\quad \bar { X } _ { \mathrm { G } } = 35$ months, $\quad S _ { \mathrm { G } } ^ { }² = 900$
Metropolis: $\quad \bar { X } _ { M } = 50$ months, $\quad S _ { M ^ { 2 } } = 1,050$

-Referring to Instruction 10-4,suppose ? = 0.05.Which of the following represents the result of the relevant hypothesis test?

A)The alternative hypothesis is rejected.
B)The null hypothesis is rejected.
C)The null hypothesis is not rejected.
D)Insufficient information exists on which to make a decision.

Question 40

Instruction 10-4
A real estate company is interested in testing whether the mean time that families in Gotham have been living in their current homes is less than families in Metropolis.Assume that the two population variances are equal.A random sample of 100 families from Gotham and a random sample of 150 families in Metropolis yield the following data on length of residence in current homes.
Gotham: $\quad \bar { X } _ { \mathrm { G } } = 35$ months, $\quad S _ { \mathrm { G } } ^ { }² = 900$
Metropolis: $\quad \bar { X } _ { M } = 50$ months, $\quad S _ { M ^ { 2 } } = 1,050$

-Referring to Instruction 10-4,suppose ? = 0.05.Which of the following represents the correct conclusion?

A)There is not enough evidence that the mean amount of time families in Gotham have been living in their current homes is less than families in Metropolis.
B)There is enough evidence that the mean amount of time families in Gotham have been living in their current homes is less than families in Metropolis.
C)There is not enough evidence that the mean amount of time families in Gotham have been living in their current homes is not less than families in Metropolis.
D)There is enough evidence that the mean amount of time families in Gotham have been living in their current homes is not less than families in Metropolis.

Question 41

Instruction 10-4
A real estate company is interested in testing whether the mean time that families in Gotham have been living in their current homes is less than families in Metropolis.Assume that the two population variances are equal.A random sample of 100 families from Gotham and a random sample of 150 families in Metropolis yield the following data on length of residence in current homes.

Referring to Instruction 10-4,what is the 95% confidence interval estimate for the difference in the two means?

Question 42

Instruction 10-5
To test the effectiveness of a business school preparation course,8 students took a general business test before and after the course.The results are given below.
$$\begin{array} { c c c } \text { Student } & \begin{array} { c } \text { Exam Score } \\\text { Before Course (1) }\end{array} & \begin{array} { c } \text { Exam Score } \\\text { After Course (2) }\end{array} \\\hline { 3 - 3 } 2 & 530 & 670 \\2 & 690 & 770 \\3 & 910 & 1,000 \\4 & 700 & 710 \\5 & 450 & 550 \\6 & 820 & 870 \\7 & 820 & 770 \\8 & 630 & 610\end{array}$$

-Referring to Instruction 10-5,one must assume that the population of difference scores is normally distributed.

Question 43

Instruction 10-5
To test the effectiveness of a business school preparation course,8 students took a general business test before and after the course.The results are given below.
$$\begin{array} { c c c } \text { Student } & \begin{array} { c } \text { Exam Score } \\\text { Before Course (1) }\end{array} & \begin{array} { c } \text { Exam Score } \\\text { After Course (2) }\end{array} \\\hline { 3 - 3 } 2 & 530 & 670 \\2 & 690 & 770 \\3 & 910 & 1,000 \\4 & 700 & 710 \\5 & 450 & 550 \\6 & 820 & 870 \\7 & 820 & 770 \\8 & 630 & 610\end{array}$$

-Referring to Instruction 10-5,at the 0.05 level of significance,the conclusion for this hypothesis test is that there is sufficient evidence that

A)the business school preparation course does not improve exam score.
B)the business school preparation course does improve exam score.
C)the business school preparation course has no impact on exam score.
D)No conclusion can be drawn from the information given.

Question 44

Instruction 10-5
To test the effectiveness of a business school preparation course,8 students took a general business test before and after the course.The results are given below.

Referring to Instruction 10-5,the calculated value of the test statistic is ________.

Question 45

Instruction 10-4
A real estate company is interested in testing whether the mean time that families in Gotham have been living in their current homes is less than families in Metropolis.Assume that the two population variances are equal.A random sample of 100 families from Gotham and a random sample of 150 families in Metropolis yield the following data on length of residence in current homes.

Referring to Instruction 10-4,what is the 99% confidence interval estimate for the difference in the two means?

Question 46

Instruction 10-6
A buyer for a manufacturing plant suspects that his primary supplier of raw materials is overcharging.In order to determine if his suspicion is correct,he contacts a second supplier and asks for the prices on similar various materials.He wants to compare these prices with those of his primary supplier.The data collected is presented in the table below,with some summary statistics presented (all of these might not be necessary to answer the questions which follow).The buyer believes that the differences are normally distributed and will use this sample to perform an appropriate test at a level of significance of 0.01.

Referring to Instruction 10-6,the calculated value of the test statistic is ________.

Question 47

Instruction 10-5
To test the effectiveness of a business school preparation course,8 students took a general business test before and after the course.The results are given below.
$$\begin{array} { c c c } \text { Student } & \begin{array} { c } \text { Exam Score } \\\text { Before Course (1) }\end{array} & \begin{array} { c } \text { Exam Score } \\\text { After Course (2) }\end{array} \\\hline { 3 - 3 } 2 & 530 & 670 \\2 & 690 & 770 \\3 & 910 & 1,000 \\4 & 700 & 710 \\5 & 450 & 550 \\6 & 820 & 870 \\7 & 820 & 770 \\8 & 630 & 610\end{array}$$

-Referring to Instruction 10-5,in examining the differences between related samples you are essentially sampling from an underlying population of difference "scores".

Question 48

Instruction 10-6
A buyer for a manufacturing plant suspects that his primary supplier of raw materials is overcharging.In order to determine if his suspicion is correct,he contacts a second supplier and asks for the prices on similar various materials.He wants to compare these prices with those of his primary supplier.The data collected is presented in the table below,with some summary statistics presented (all of these might not be necessary to answer the questions which follow).The buyer believes that the differences are normally distributed and will use this sample to perform an appropriate test at a level of significance of 0.01.
$$\begin{array} { c c c r } \text { Material } & \begin{array} { c } \text { Primary } \\\text { Supplier }\end{array} & \begin{array} { c } \text { Secondary } \\\text { Supplier }\end{array} & \text { Difference } \\\hline 1& \$ 55 & \$ 45 & \$ 10 \\2 & \$ 48 & \$ 47 & \$ 1 \\3 & \$ 31 & \$ 32 & - \$ 1 \\4 & \$ 83 & \$ 77 & \$ 6 \\5 & \$ 37 & \$ 37 & \$ 0 \\6& \$ 55 & \$ 54 & \$ 1 \\\hline \hline \text { Sum: } &\$309&\$292&\$17\\\text { Sum of Squares. } & \$ 17,573 & \$ 15,472 & \$ 139\end{array}$$

-Referring to Instruction 10-6,the buyer should decide that the primary supplier is

A)not overcharging because there is strong evidence to prove otherwise.
B)not overcharging because there is insufficient evidence to prove otherwise.
C)overcharging because there is strong evidence that this is the case.
D)overcharging because there is insufficient evidence to prove otherwise.

Question 49

Instruction 10-6
A buyer for a manufacturing plant suspects that his primary supplier of raw materials is overcharging.In order to determine if his suspicion is correct,he contacts a second supplier and asks for the prices on similar various materials.He wants to compare these prices with those of his primary supplier.The data collected is presented in the table below,with some summary statistics presented (all of these might not be necessary to answer the questions which follow).The buyer believes that the differences are normally distributed and will use this sample to perform an appropriate test at a level of significance of 0.01.
$$\begin{array} { c c c r } \text { Material } & \begin{array} { c } \text { Primary } \\\text { Supplier }\end{array} & \begin{array} { c } \text { Secondary } \\\text { Supplier }\end{array} & \text { Difference } \\\hline 1& \$ 55 & \$ 45 & \$ 10 \\2 & \$ 48 & \$ 47 & \$ 1 \\3 & \$ 31 & \$ 32 & - \$ 1 \\4 & \$ 83 & \$ 77 & \$ 6 \\5 & \$ 37 & \$ 37 & \$ 0 \\6& \$ 55 & \$ 54 & \$ 1 \\\hline \hline \text { Sum: } &\$309&\$292&\$17\\\text { Sum of Squares. } & \$ 17,573 & \$ 15,472 & \$ 139\end{array}$$

-Referring to Instruction 10-6,the test to perform is a

A)paired t test for the mean difference.
B)Z test for the difference between two means.
C)separate-variance t test for differences between two means.
D)pooled-variance t test for differences between two means.

Question 50

Instruction 10-5
To test the effectiveness of a business school preparation course,8 students took a general business test before and after the course.The results are given below.
$$\begin{array} { c c c } \text { Student } & \begin{array} { c } \text { Exam Score } \\\text { Before Course (1) }\end{array} & \begin{array} { c } \text { Exam Score } \\\text { After Course (2) }\end{array} \\\hline { 3 - 3 } 2 & 530 & 670 \\2 & 690 & 770 \\3 & 910 & 1,000 \\4 & 700 & 710 \\5 & 450 & 550 \\6 & 820 & 870 \\7 & 820 & 770 \\8 & 630 & 610\end{array}$$

-Referring to Instruction 10-5,the value of the standard error of the difference scores is

A)60.828.
B)14.696.
C)22.991.
D)65.027.

Question 51

Instruction 10-5
To test the effectiveness of a business school preparation course,8 students took a general business test before and after the course.The results are given below.
$$\begin{array} { c c c } \text { Student } & \begin{array} { c } \text { Exam Score } \\\text { Before Course (1) }\end{array} & \begin{array} { c } \text { Exam Score } \\\text { After Course (2) }\end{array} \\\hline { 3 - 3 } 2 & 530 & 670 \\2 & 690 & 770 \\3 & 910 & 1,000 \\4 & 700 & 710 \\5 & 450 & 550 \\6 & 820 & 870 \\7 & 820 & 770 \\8 & 630 & 610\end{array}$$

-Referring to Instruction 10-5,at the 0.05 level of significance,the decision for this hypothesis test would be

A)reject the null hypothesis.
B)reject the alternative hypothesis.
C)do not reject the null hypothesis.
D)It cannot be determined from the information given.

Question 52

Instruction 10-6
A buyer for a manufacturing plant suspects that his primary supplier of raw materials is overcharging.In order to determine if his suspicion is correct,he contacts a second supplier and asks for the prices on similar various materials.He wants to compare these prices with those of his primary supplier.The data collected is presented in the table below,with some summary statistics presented (all of these might not be necessary to answer the questions which follow).The buyer believes that the differences are normally distributed and will use this sample to perform an appropriate test at a level of significance of 0.01.

Referring to Instruction 10-6,the hypotheses that the buyer should test are a null hypothesis that ________ versus an alternative hypothesis that ________.

Question 53

Instruction 10-4
A real estate company is interested in testing whether the mean time that families in Gotham have been living in their current homes is less than families in Metropolis.Assume that the two population variances are equal.A random sample of 100 families from Gotham and a random sample of 150 families in Metropolis yield the following data on length of residence in current homes.
Gotham: $\quad \bar { X } _ { \mathrm { G } } = 35$ months, $\quad S _ { \mathrm { G } } ^ { }² = 900$
Metropolis: $\quad \bar { X } _ { M } = 50$ months, $\quad S _ { M ^ { 2 } } = 1,050$

-Referring to Instruction 10-4,suppose ? = 0.01.Which of the following represents the correct conclusion?

A)There is not enough evidence that the mean amount of time families in Gotham have been living in their current homes is less than families in Metropolis.
B)There is enough evidence that the mean amount of time families in Gotham have been living in their current homes is less than families in Metropolis.
C)There is not enough evidence that the mean amount of time families in Gotham have been living in their current homes is not less than families in Metropolis.
D)There is enough evidence that the mean amount of time families in Gotham have been living in their current homes is not less than families in Metropolis.

Question 54

Instruction 10-5
To test the effectiveness of a business school preparation course,8 students took a general business test before and after the course.The results are given below.

Referring to Instruction 10-5,the p-value of the test statistic is ________.

Question 55

Instruction 10-6
A buyer for a manufacturing plant suspects that his primary supplier of raw materials is overcharging.In order to determine if his suspicion is correct,he contacts a second supplier and asks for the prices on similar various materials.He wants to compare these prices with those of his primary supplier.The data collected is presented in the table below,with some summary statistics presented (all of these might not be necessary to answer the questions which follow).The buyer believes that the differences are normally distributed and will use this sample to perform an appropriate test at a level of significance of 0.01.

Referring to Instruction 10-6,if the buyer had decided to perform a two-tailed test,the p-value would have been between ________ and ________.

Question 56

Instruction 10-6
A buyer for a manufacturing plant suspects that his primary supplier of raw materials is overcharging.In order to determine if his suspicion is correct,he contacts a second supplier and asks for the prices on similar various materials.He wants to compare these prices with those of his primary supplier.The data collected is presented in the table below,with some summary statistics presented (all of these might not be necessary to answer the questions which follow).The buyer believes that the differences are normally distributed and will use this sample to perform an appropriate test at a level of significance of 0.01.

Referring to Instruction 10-6,the p-value of the test is between ________ and ________.

Question 57

Instruction 10-5
To test the effectiveness of a business school preparation course,8 students took a general business test before and after the course.The results are given below.
$$\begin{array} { c c c } \text { Student } & \begin{array} { c } \text { Exam Score } \\\text { Before Course (1) }\end{array} & \begin{array} { c } \text { Exam Score } \\\text { After Course (2) }\end{array} \\\hline { 3 - 3 } 2 & 530 & 670 \\2 & 690 & 770 \\3 & 910 & 1,000 \\4 & 700 & 710 \\5 & 450 & 550 \\6 & 820 & 870 \\7 & 820 & 770 \\8 & 630 & 610\end{array}$$

-Referring to Instruction 10-5,the value of the sample mean difference is ________ if the difference scores reflect the results of the exam after the course minus the results of the exam before the course.

A)400
B)50
C)68
D)0

Question 58

Instruction 10-6
A buyer for a manufacturing plant suspects that his primary supplier of raw materials is overcharging.In order to determine if his suspicion is correct,he contacts a second supplier and asks for the prices on similar various materials.He wants to compare these prices with those of his primary supplier.The data collected is presented in the table below,with some summary statistics presented (all of these might not be necessary to answer the questions which follow).The buyer believes that the differences are normally distributed and will use this sample to perform an appropriate test at a level of significance of 0.01.

Referring to Instruction 10-6,the decision rule is to reject the null hypothesis if ________.

Question 59

Instruction 10-5
To test the effectiveness of a business school preparation course,8 students took a general business test before and after the course.The results are given below.
$$\begin{array} { c c c } \text { Student } & \begin{array} { c } \text { Exam Score } \\\text { Before Course (1) }\end{array} & \begin{array} { c } \text { Exam Score } \\\text { After Course (2) }\end{array} \\\hline { 3 - 3 } 2 & 530 & 670 \\2 & 690 & 770 \\3 & 910 & 1,000 \\4 & 700 & 710 \\5 & 450 & 550 \\6 & 820 & 870 \\7 & 820 & 770 \\8 & 630 & 610\end{array}$$

-Referring to Instruction 10-5,what is the critical value for testing at the 5% level of significance whether the business school preparation course is effective in improving exam scores?

A)1.895
B)2.145
C)2.365
D)1.761

Question 60

Instruction 10-5
To test the effectiveness of a business school preparation course,8 students took a general business test before and after the course.The results are given below.
$$\begin{array} { c c c } \text { Student } & \begin{array} { c } \text { Exam Score } \\\text { Before Course (1) }\end{array} & \begin{array} { c } \text { Exam Score } \\\text { After Course (2) }\end{array} \\\hline { 3 - 3 } 2 & 530 & 670 \\2 & 690 & 770 \\3 & 910 & 1,000 \\4 & 700 & 710 \\5 & 450 & 550 \\6 & 820 & 870 \\7 & 820 & 770 \\8 & 630 & 610\end{array}$$

-Referring to Instruction 10-5,the number of degrees of freedom is

A)7.
B)14.
C)8.
D)13.

Question 61

Instruction 10-6
A buyer for a manufacturing plant suspects that his primary supplier of raw materials is overcharging.In order to determine if his suspicion is correct,he contacts a second supplier and asks for the prices on similar various materials.He wants to compare these prices with those of his primary supplier.The data collected is presented in the table below,with some summary statistics presented (all of these might not be necessary to answer the questions which follow).The buyer believes that the differences are normally distributed and will use this sample to perform an appropriate test at a level of significance of 0.01.

Referring to Instruction 10-6,what is the 99% confidence interval estimate for the mean difference in prices?

Question 62

In testing for the differences between the means of two related populations,the ________ hypothesis is the hypothesis of "no differences".

Question 63

Instruction 10-12
Two samples each of size 25 are taken from independent populations assumed to be normally distributed with equal variances.The first sample has a mean of 35.5 and standard deviation of 3.0 while the second sample has a mean of 33.0 and standard deviation of 4.0.
Referring to Instruction 10-12,what is the 95% confidence interval estimate for the difference in the two means?

Question 64

Instruction 10-12
Two samples each of size 25 are taken from independent populations assumed to be normally distributed with equal variances.The first sample has a mean of 35.5 and standard deviation of 3.0 while the second sample has a mean of 33.0 and standard deviation of 4.0.
Referring to Instruction 10-12,the computed t statistic is ________.

Question 65

Instruction 10-12
Two samples each of size 25 are taken from independent populations assumed to be normally distributed with equal variances.The first sample has a mean of 35.5 and standard deviation of 3.0 while the second sample has a mean of 33.0 and standard deviation of 4.0.
Referring to Instruction 10-12,if you were interested in testing against the one-tailed alternative that μ₁ > μ₂ at the α = 0.01 level of significance,the null hypothesis would ________ .

Question 66

Instruction 10-12
Two samples each of size 25 are taken from independent populations assumed to be normally distributed with equal variances.The first sample has a mean of 35.5 and standard deviation of 3.0 while the second sample has a mean of 33.0 and standard deviation of 4.0.
Referring to Instruction 10-12,what is the 90% confidence interval estimate for the difference in the two means?

Question 67

In testing for the differences between the means of two related populations,you assume that the differences follow a ________ distribution.

Question 68

When testing H₀: π₁ - π₂ ≥ 0 versus H₁: π₁ - π₂ < 0,the observed value of the Z test statistic was found to be -2.13.The p-value for this test is

A)0.0166.
B)0.0332.
C)0.9668.
D)0.9834.

Question 69

Instruction 10-12
Two samples each of size 25 are taken from independent populations assumed to be normally distributed with equal variances.The first sample has a mean of 35.5 and standard deviation of 3.0 while the second sample has a mean of 33.0 and standard deviation of 4.0.
Referring to Instruction 10-12,the p-value for a two-tailed test whose computed t statistic is 2.50 is between ________ and ________.

Question 70

When testing H₀: π₁ - π₂ ≤ 0 versus H₁: π₁ - π₂ > 0,the observed value of the Z test statistic was found to be -2.13.The p-value for this test is

A)0.0166.
B)0.0332.
C)0.9668.
D)0.9834.

Question 71

Instruction 10-6
A buyer for a manufacturing plant suspects that his primary supplier of raw materials is overcharging.In order to determine if his suspicion is correct,he contacts a second supplier and asks for the prices on similar various materials.He wants to compare these prices with those of his primary supplier.The data collected is presented in the table below,with some summary statistics presented (all of these might not be necessary to answer the questions which follow).The buyer believes that the differences are normally distributed and will use this sample to perform an appropriate test at a level of significance of 0.01.

Referring to Instruction 10-6,what is the 90% confidence interval estimate for the mean difference in prices?

Question 72

Instruction 10-12
Two samples each of size 25 are taken from independent populations assumed to be normally distributed with equal variances.The first sample has a mean of 35.5 and standard deviation of 3.0 while the second sample has a mean of 33.0 and standard deviation of 4.0.
Referring to Instruction 10-12,a two-tailed test of the null hypothesis of no difference would ________ (be rejected/not be rejected)at the α= 0.05 level of significance.

Question 73

In testing for the differences between the means of two independent populations,you assume that the two populations each follow a ________ distribution.

Question 74

Instruction 10-6
A buyer for a manufacturing plant suspects that his primary supplier of raw materials is overcharging.In order to determine if his suspicion is correct,he contacts a second supplier and asks for the prices on similar various materials.He wants to compare these prices with those of his primary supplier.The data collected is presented in the table below,with some summary statistics presented (all of these might not be necessary to answer the questions which follow).The buyer believes that the differences are normally distributed and will use this sample to perform an appropriate test at a level of significance of 0.01.

Referring to Instruction 10-6,what is the 95% confidence interval estimate for the mean difference in prices?

Question 75

When testing H₀: π₁ - π₂ = 0 versus H₁: π₁ - π₂ ≠ 0,the observed value of the Z test statistic was found to be -2.13.The p-value for this test is

A)0.0166.
B)0.0332.
C)0.9668.
D)0.9834.

Question 76

Instruction 10-12
Two samples each of size 25 are taken from independent populations assumed to be normally distributed with equal variances.The first sample has a mean of 35.5 and standard deviation of 3.0 while the second sample has a mean of 33.0 and standard deviation of 4.0.
Referring to Instruction 10-12,there are ________ degrees of freedom for this test.

Question 77

Instruction 10-12
Two samples each of size 25 are taken from independent populations assumed to be normally distributed with equal variances.The first sample has a mean of 35.5 and standard deviation of 3.0 while the second sample has a mean of 33.0 and standard deviation of 4.0.
Referring to Instruction 10-12,the pooled (i.e. ,combined)variance is ________.

Question 78

Instruction 10-12
Two samples each of size 25 are taken from independent populations assumed to be normally distributed with equal variances.The first sample has a mean of 35.5 and standard deviation of 3.0 while the second sample has a mean of 33.0 and standard deviation of 4.0.
Referring to Instruction 10-12,the critical values for a two-tailed test of the null hypothesis of no difference in the population means at the α = 0.05 level of significance are ________.

Question 79

Instruction 10-12
Two samples each of size 25 are taken from independent populations assumed to be normally distributed with equal variances.The first sample has a mean of 35.5 and standard deviation of 3.0 while the second sample has a mean of 33.0 and standard deviation of 4.0.
Referring to Instruction 10-12,what is the 99% confidence interval estimate for the difference in the two means?

Question 80

Instruction 10-12
Two samples each of size 25 are taken from independent populations assumed to be normally distributed with equal variances.The first sample has a mean of 35.5 and standard deviation of 3.0 while the second sample has a mean of 33.0 and standard deviation of 4.0.
Referring to Instruction 10-12,the p-value for a one-tailed test whose computed statistic is 2.50 (in the hypothesised direction)is between ________ and ________.