Deck 9: Inferences From Two Samples

Question 1

Find $S _d .$ Consider the set of differences between two dependent sets: 84,85,83,63,61,100,98 . Round to the nearest tenth.

A) 15.3
B) 16.2
C) 15.7
D) 13.1

Answer 1

15.3

Question 2

When performing a hypothesis test for the ratio of two population variances, the upper critical F value is denoted The lower critical F value, can be found as follows: interchange the degrees of freedom, and then take the reciprocal of the resulting F value found in Table A-5. can be denoted and can be denoted
Find the critical values and for a two-tailed hypothesis test based on the following values:

A) 0.7351,2.2378
B) 0.5327,2.2878
C) 0.4745,2.2878
D) 0.4745,2.4371

Answer 2

0.4745,2.2878

Question 3

Assume that you plan to use a significance level of
to test the claim that Use the given sample sizes and numbers of successes to find the pooled estimate Round your answer to the nearest thousandth.

A) 0.479
B) 0.435
C) 0.305
D) 0.392

Answer 3

0.435

Question 4

Determine whether the samples are independent or dependent. The effectiveness of a headache medicine is tested by measuring the intensity of a headache in patients before and after drug
Treatment. The data consist of before and after intensities for each patient.

A)Independent samples
B)Dependent samples

Question 5

Assume that two samples are independent simple random samples selected from normally distributed populations, and do not assume that the population standard deviations are equal.
Which distribution is used to test the claim that women have a higher mean resting heart rate
Than men?

A)Normal
B)t
C)chi-square
D)F

Question 6

Determine whether the following statement regarding the hypothesis test for two population
proportions is true or false:
However small the difference between two population proportions, for sufficiently large
sample sizes, the null hypothesis of equal population proportions is likely to be rejected.

Question 7

Construct the indicated confidence interval for the difference between the two population means. Assume that the two samples are independent simple random samples selected from normally distributed populations. Do not assume that the population standard deviations are equal. Independent samples from two different populations yield the following data.

The sample size is 478 for both samples. Find the 85 % confidence interval for

A)
B)
C)
D)

Question 8

Find sd. The differences between two sets of dependent data are 0.4, 0.24, 0.22, 0.26, 0.34._ Round to the nearest hundredth.

A)0.08
B)0.12
C)0.04
D)0.24

Question 9

A paint manufacturer made a modification to a paint to speed up its drying time. Independent_ simple random samples of 11 cans of type A (the original paint)and 9 cans of type B (the
Modified paint)were selected and applied to similar surfaces. The drying times, in hours, were
Recorded. The summary statistics are as follows.

Question 10

Construct the indicated confidence interval for the difference between the two population_ means. Assume that the two samples are independent simple random samples selected from
Normally distributed populations. Do not assume that the population standard deviations are
Equal. A paint manufacturer wished to compare the drying times of two different types of
Paint. Independent simple random samples of 11 cans of type A and 9 cans of type B were
Selected and applied to similar surfaces. The drying times, in hours, were recorded. The
Summary statistics are as follows. $\begin{array} { | l | l | } \hline { \text { Type A } } & { \text { Type B } } \\\hline \bar { x } _ { 1 } = 75.7 \mathrm { hrs } & \bar { x } _ { 2 } = 64.3 \mathrm { hrs } \\\hline s _ { 1 } = 4.5 \mathrm { hrs } & s _ { 2 } = 5.1 \mathrm { hrs } \\\hline n _ { 1 } = 11 & n _ { 2 } = 9 \\\hline\end{array}$
Construct a $98 \%$ confidence interval for $\mu _ { 1 } - \mu _ { 2 }$ , the difference between the mean drying time for paint of type $\mathrm { A }$ and the mean drying time for paint of type $\mathrm { B }$ .

A) $6.08 \mathrm { hrs } < \mu _ { 1 } - \mu _ { 2 } < 16.72 \mathrm { hrs }$
B) $5.92 \mathrm { hrs } < \mu _ { 1 } - \mu _ { 2 } < 16.88 \mathrm { hrs }$
C) $5.85 \mathrm { hrs } < \mu _ { 1 } - \mu _ { 2 } < 16.95 \mathrm { hrs }$
D) $5.78 \mathrm { hrs } < \mu _ { 1 } - \mu _ { 2 } < 17.02 \mathrm { hrs }$

Question 11

Assume that you plan to use a significance level of to test the claim that Use the given sample sizes and numbers of successes to find the P -value for the hypothesis test.

A) 0.7794
B) 0.3897
C) 0.6103
D) 0.2206

Question 12

The two data sets are dependent. Find to the nearest tenth.

A) 50.7
B) 23.4
C) 48.8
D) 39.0

Question 13

When testing the claim that , a test statistic of z=2.04 is obtained. Find the P -value obtained from this test statistic.

A) 0.9586
B) 0.0207
C) 0.9793
D) 0.0414

Question 14

Determine the decision criterion for rejecting the null hypothesis in the given hypothesis test; i.e., describe the values of the test statistic that would result in rejection of the null hypothesis. We wish to compare the means of two populations using paired observations. Suppose that and that you wish to test the following hypothesis at the
10 % level of significance:

What decision rule would you use?

A) Reject if the test statistic is less than 1.415 .
B) Reject if the test statistic is greater than -1.145 .
C) Reject if the test statistic is greater than -1.145 or less than 1.415 .
D) Reject if the test statistic is greater than 1.415 .

Question 15

Which distribution is used to test the claim that the standard deviation of the ages (in years)of when girls first learn to ride a bike is equal to the standard deviation of the ages (in years)
When boys first lean to ride a bike?

A)Normal
B)t
C)chi-square
D)F

Question 16

Determine the decision criterion for rejecting the null hypothesis in the given hypothesis test; i.e., describe the values of the test statistic that would result in rejection of the null hypothesis. Suppose you wish to test the claim that the mean value of the differences d for a population of paired data, is greater than 0 . Given a sample of n=15 and a significance level of what criterion would be used for rejecting the null hypothesis?

A) Reject null hypothesis if test statistic <2.624 .
B) Reject null hypothesis if test statistic >2.602 .
C) Reject null hypothesis if test statistic >2.624 .
D) Reject null hypothesis if test statistic >2.977 or <-2.977 .

Question 17

Assume that the following confidence interval for the difference in the mean length of male (sample 1) and female babies (sample 2) at birth was constructed using independent simple random samples. -0.2 in
What does the confidence interval suggest about the difference in length between male babies and female babies?

A) Male babies are longer.
B) Female babies are longer.
C) There is no difference in the length between male and female babies.

Question 18

If the heights of male college basketball players and female basketball players are used to construct a 95 % confidence interval for the difference between the two population means, the result is 15.35 cm
where heights of male players correspond to population 1 and heights of female players correspond to population 2. Express the confidence interval with heights of female basketball players being population 1 and heights of male basketball players being population 2 .

A)
B)
C)
D) This cannot be determined without having the original data values.

Question 19

Express the alternative hypothesis in symbolic form. of time (in hours)sophomores spent studying for the statistics final exam is more than that of
Freshmen. Assume that the two samples are independent. Let the freshmen be the first
Population and the sophomores be the second population.

Question 20

Assume that you plan to use a significance level of to test the claim that Use the given sample sizes and numbers of successes to find the pooled estimate Round your answer to the nearest thousandth.

A) 0.163
B) 0.452
C) 0.204
D) 0.408

Question 21

Assume that you plan to use a significance level of to test the claim that Use the given sample sizes and numbers of successes to find the P -value for the hypothesis test.

A) 0.1610
B) 0.2130
C) 0.0412
D) 0.7718

Question 22

In the context of a hypothesis test for two proportions, which of the following statements about the pooled sample proportion, is/are true?
I. It estimates the common value of under the assumption of equal proportions.
II. It is obtained by averaging the two sample proportions
III. It is equal to the proportion of successes in both samples combined.

A) I and II
B) III only
C) I, II, and III
D) I and III

Question 23

Assume that you want to test the claim that the paired sample data come from a population for which the mean difference is
Compute the value of the t test statistics. Round intermediate calculations to four decimal places as needed and final answers to three decimal places as needed.

A) t=0.578
B) t=2.890
C) t=1.292
D) t=0.415

Question 24

Find the number of successes x suggested by the given statement. A computer manufacturer_ randomly selects 2680 of its computers for quality assurance and finds that 1.98% of these
Computers are found to be defective.

A)56
B)51
C)58
D)53

Question 25

A test of abstract reasoning is given to a random sample of students before and after they_ completed a formal logic course. The results are given below. Construct a 95% confidence
Interval for the mean difference between the before and after scores. $\begin{array} { l l l l l l l l l l l l } \text { Before } & 74 & 83 & 75 & 88 & 84 & 63 & 93 & 84 & 91 & 77 \\\hline \text { After } & 73 & 77 & 70 & 77 & 74 & 67 & 95 & 83 & 84 & 75\end{array}$

A) $1.0 < \mu _ { d } < 6.4$
B) $0.2 < \mu _ { d } < 7.2$
C) $0.8 < \mu _ { d } < 6.6$
D) $1.2 < \mu _ { d } < 8.7$

Question 26

Determine whether the samples are dependent or independent. The effectiveness of a_ headache medicine is tested by measuring the intensity of a headache in patients before and
After drug treatment. The data consist of before and after intensities for each patient.

A)Dependent samples
B)Independent samples

Question 27

When performing a hypothesis test for the ratio of two population variances, the upper critical F value is denoted The lower critical F value, can be found as follows: interchange the degrees of freedom, and then take the reciprocal of the resulting F value found in Table A-5. can be denoted
can be denoted
Find the critical values
for a two-tailed hypothesis test based on the following values: n₁=9, n₂ -7 ,

A) 0.2150,5.5996
B) 0.2150,4.8232
C) 0.3931,4.1468
D) 0.2411,4.1468

Question 28

Assume that you want to test the claim that the paired sample data come from a population for which the mean difference is Compute the value of the t test statistic. Round intermediate calculations to four decimal places as needed and final answers to three decimal places as needed.

A) 9.468
B) 3.156
C) 0.351
D) 1.052

Question 29

Assume that the following confidence interval for the difference in the mean time (in minutes) for male students to complete a statistics test (sample 1) and the mean time for female students to complete a statistics test (sample 2) was constructed using independent simple random samples. -0.2 minutes
What does the confidence interval suggest about the difference in length between male and female test completion times?

A) Male students take longer to complete a statistics test.
B) Female students take longer to complete a statistics test.
C) There is no difference in the length of time for statistics test completion between male and female students.

Question 30

Construct a confidence interval for the mean of the differences d for the population of paired data. Assume that the population of paired differences is normally distributed. Using the sample paired data below, construct a 90 % confidence interval for the population mean of all differences.

A)
B)
C)
D)

Question 31

Assume that two samples are independent simple random samples selected from normally distributed populations, and do not assume that the population standard deviations are equal.
Which distribution is used to test the claim that mothers spend more time (in minutes)
Driving their kids to activities than fathers do?

A)Normal
B)t
C)chi-square
D)F

Question 32

Construct the indicated confidence interval for the difference between the two population means. Assume that the two samples are independent simple random samples selected from
Normally distributed populations. Also assume that the population standard deviations are
Equal $$\left( \sigma _ { 1 } = \sigma _ { 2 } \right)$$ , so that the standard error of the difference between means is obtained by
Pooling the sample variances. A paint manufacturer wanted to compare the drying times of
Two different types of paint. Independent simple random samples of 11 cans of type A and 9
Cans of type B were selected and applied to similar surfaces. The drying times, in hours,
Were recorded. The summary statistics are as follows. $\begin{array} { | l | l | } \hline{ \text { Type A } } & { \text { Type B } } \\\hline \bar { x } _ { 1 } = 71.5 \mathrm { hrs } & \bar { x } _ { 2 } = 68.5 \mathrm { hrs } \\\hline s _ { 1 } = 3.4 \mathrm { hrs } & s _ { 2 } = 3.6 \mathrm { hrs } \\\hline n _ { 1 } = 11 & n _ { 2 } = 9 \\\hline\end{array}$

Construct a $99 \%$ confidence interval for $\mu _ { 1 } - \mu _ { 2 }$ , the difference between the mean drying time for paint type $\mathrm { A }$ and the mean drying time for paint type $\mathrm { B }$ .

A) $- 1.51 \mathrm { hrs } < \mu _ { 1 } - \mu _ { 2 } < 7.51 \mathrm { hrs }$
B) $- 2.24 \mathrm { hrs } < \mu _ { 1 } - \mu _ { 2 } < 8.24 \mathrm { hrs }$
C) $- 1.00 \mathrm { hrs } < \mu _ { 1 } - \mu _ { 2 } < 7.00 \mathrm { hrs }$
D) $- 0.14 \mathrm { hrs } < \mu _ { 1 } - \mu _ { 2 } < 6.14 \mathrm { hrs }$

Question 33

Construct a confidence interval for the mean of the differences d for the population of paired data. Assume that the population of paired differences is normally distributed. A test of writing ability is given to a random sample of students before and after they completed a formal writing course. The results are given below. Construct a 99 % confidence interval for the mean difference between the before and after scores.

A)
B)
C)
D)

Question 34

Determine whether the samples are dependent or independent. The effectiveness of a new_ headache medicine is tested by measuring the amount of time before the headache is cured
For patients who use the medicine and another group of patients who use a placebo drug.

A)Dependent samples
B)Independent samples

Question 35

If the lengths of male skis and female skis are used to construct a 95 % confidence interval for the difference between the two population means, the result is
14.32 cm
where lengths of male skis correspond to population 1 and lengths of female skis correspond to population 2. Express the confidence interval with the lengths of female skis being population 1 and lengths of male skis being population

A)
B)
C)
D) This cannot be determined without having the original data values.

Question 36

Which distribution is used to test the claim that the standard deviation of the lengths (in cm)18)___________ of male babies at birth is equal to the standard deviation of the lengths (in cm)of female
Babies at birth?

A)Normal
B)t
C)chi-square
D)F

Question 37

Assume that you plan to use a significance level of to test the claim that Use the given sample sizes and numbers of successes to find the P -value for the hypothesis test.

A) 0.1201
B) 0.0032
C) 0.0001
D) 0.0146

Question 38

A researcher wishes to compare how students at two different schools perform on a math test._
He randomly selects 40 students from each school and obtains their test scores. He pairs the
first score from school A with the first school from school B, the second score from school A
with the second school from school B and so on. He then performs a hypothesis test for
matched pairs. Is this approach valid? Why or why not? If it is not valid, how should the
researcher have proceeded?

Question 39

Construct the indicated confidence interval for the difference between the two population means. Assume that the two samples are independent simple random samples selected from
Normally distributed populations. Do not assume that the population standard deviations are
Equal. A paint manufacturer wished to compare the drying times of two different types of
Paint .Independent simple random samples of 11 cans of type A and 9 cans of type B were
Selected and applied to similar surfaces. The drying times, in hours, were recorded. The
Summary statistics are as follows. $\begin{array} { | l | l | } \hline { \text { Type A } } & { \text { Type B } } \\\hline \bar { x } _ { 1 } = 75.7 \mathrm { hrs } & \bar { x } _ { 2 } = 64.3 \mathrm { hrs } \\\hline s _ { 1 } = 4.5 \mathrm { hrs } & s _ { 2 } = 5.1 \mathrm { hrs } \\\hline n _ { 1 } = 11 & n _ { 2 } = 9 \\\hline\end{array}$

Construct a $99 \%$ confidence interval for $\mu _ { 1 } - \mu _ { 2 }$ , the difference between the mean drying time for paint type A and the mean drying time for paint type $\mathrm { B }$ .

A) $5.85 \mathrm { hrs } < \mu _ { 1 } - \mu _ { 2 } < 16.95 \mathrm { hrs }$
B) $5.78 \mathrm { hrs } < \mu _ { 1 } - \mu _ { 2 } < 17.02 \mathrm { hrs }$
C) $5.92 \mathrm { hrs } < \mu _ { 1 } - \mu _ { 2 } < 16.88 \mathrm { hrs }$
D) $6.08 \mathrm { hrs } < \mu _ { 1 } - \mu _ { 2 } < 16.72 \mathrm { hrs }$

Question 40

Express the alternative hypothesis in symbolic form. An automobile technician claims that the mean amount of time (in hours)per domestic car repair is more than that of foreign cars.
Assume that two samples are independent. Let the domestic car repair times be the first
Population and the foreign car repair times be the second population.

Question 41

Assume that the two samples are independent simple random samples selected from normally
distributed populations. Do not assume that the population standard deviations are equal. A
researcher wishes to determine whether people can reduce their resting heart rate by following
a particular diet. Construct a 95% confidence interval estimate for the following data. Does
the confidence interval support that the mean resting heart rate for those on the diet is lower
than that of those not on the diet? Explain your reasoning.

Question 42

Assume
marketing survey involves product recognition in New York and California. Of 558 New
Yorkers surveyed, 193 knew the product while 196 out of 614 Californians knew the product.
At the 0.05 significance level, test the claim that the recognition rates are the same in both
states. Include your null and alternative hypotheses, the test statistic, P-value or critical value(s),
conclusion about the null hypothesis, and conclusion about the claim in your answer.

Question 43

To test the null hypothesis that the difference between two population proportions is
equal to a nonzero constant c, use the test statistic

Question 44

A Dean of Students conducted a survey to test the claim that women spend more time visiting
the STEM lab than men do. A survey was administered to a simple random sample of 15
female student volunteers and 12 male volunteers that asked, "How many minutes have you
spent in the STEM lab this semester?" The results are shown below. Test the claim at the 1% level of significance. Assume that the number of minutes that
women and men spent in the STEM lab is normally distributed. Do not assume that the
population standard deviations are equal. Include your null and alternative hypotheses, the
test statistic, P-value or critical value(s), conclusion about the null hypothesis, and conclusion
about the claim in your answer.

Question 45

Test the given claim about the means of two populations. Assume that two dependent samples
have been randomly selected from normally distributed populations. Using a 0.01 level of significance, test the claim that the tutoring has an effect on the math
scores. Include your null and alternative hypotheses, the test statistic, P-value or critical
value(s), conclusion about the null hypothesis, and conclusion about the claim in your answer.

Question 46

A researcher wishes to determine whether the blood pressure of vegetarians is, on average,_
lower than the blood pressure of nonvegetarians. Independent simple random samples of 85
vegetarians and 75 nonvegetarians yielded the following sample statistics for systolic blood
pressure: Use a significance level of 0.01 to test the claim that the mean systolic blood pressure of
vegetarians is lower than the mean systolic blood pressure of nonvegetarians. Include your null
and alternative hypotheses, the test statistic, P-value or critical value(s), conclusion about the
null hypothesis, and conclusion about the claim in your answer.

Question 47

Test the indicated claim about the variances or standard deviations of two populations.
Assume that both samples are independent simple random samples from populations having
normal distributions. A random sample of 16 women resulted in blood pressure levels with a
standard deviation of 23 mm Hg. A random sample of 17 men resulted in blood pressure
levels with a standard deviation of 19.2 mm Hg. Use a 0.05 significance level to test the claim
that blood pressure levels for women vary more than blood pressure levels for men. Include
your null and alternative hypotheses, the test statistic, P-value or critical value(s), conclusion
about the null hypothesis, and conclusion about the claim in your answer.

Question 48

Brian wants to obtain a confidence interval estimate of where represents the proportion of American women who smoke and represents the proportion of American men who smoke. He randomly selects 100 married couples. Among the 100 women in the sample are 21 smokers. Among the 100 men are 29 smokers. Are the requirements for obtaining a confidence interval estimate of satisfied? If not, which requirement is not satisfied?

Question 49

Test the indicated claim about the means of two populations. Assume that the two samples are
independent simple random samples selected from normally distributed populations. Do not
assume that the population standard deviations are equal. A researcher wishes to determine
whether people with high blood pressure can reduce their blood pressure, measured in mm Hg,
by following a particular diet. Use a significance level of 0.01 to test the claim that the treatment
group is from a population with a smaller mean than the control group. Include your null and
alternative hypotheses, the test statistic, P-value or critical value(s), conclusion about the null
hypothesis, and conclusion about the claim in your answer.

Question 50

Test the given claim about the means of two populations. Assume that two dependent samples_
have been randomly selected from normally distributed populations. A test of abstract reasoning
is given to a random sample of students before and after they completed a formal logic course.
The results are given below. At the 0.05 significance level, test the claim that the mean score is
not affected by the course. Include your null and alternative hypotheses, the test statistic, P-value
or critical value(s), conclusion about the null hypothesis, and conclusion about the claim in your
answer.

Question 51

Test the indicated claim about the means of two populations. Assume that the two samples are
independent simple random samples selected from normally distributed populations. Do not
assume that the population standard deviations are equal.

Question 52

When testing for a difference between the means of a treatment group and a placebo group, the
computer display below is obtained. Using a 0.05 significance level, is there sufficient evidence
to support the claim that the treatment group (variable 1)comes from a population with a mean
that is less than the mean for the placebo population? Explain.

Question 53

Identify the test statistic that should be used for testing the following given claims.
a. The mean of the differences between IQ scores of brothers and IQ scores of their sisters is
equal to 0.
b. The proportion of offices with windows is equal to the proportion of offices without
windows.
c. The variation among temperature inside buildings in winter is equal to the variation in the
temperature inside building in summer.
d. The mean age of female math professors is equal to the mean age of male math professors.

Question 54

Test the given claim about the means of two populations. Assume that two dependent samples_
have been randomly selected from normally distributed populations. A coach uses a new
technique to train gymnasts. 7 gymnasts were randomly selected and their competition scores
were recorded before and after the training. The results are shown below. Using a 0.01 level of significance, test the claim that the training technique is effective in raising
the gymnasts' scores. Include your null and alternative hypotheses, the test statistic, P-value or
critical value(s), conclusion about the null hypothesis, and conclusion about the claim in your
answer.

Question 55

Suppose you wish to test a claim about the mean of the differences from dependent samples or_
to construct a confidence interval estimate of the mean of the differences from dependent
samples. What are the requirements?

Question 56

Test the indicated claim about the means of two populations. Assume that the two samples are
independent simple random samples selected from normally distributed populations. Do not
assume that the population standard deviations are equal. Use a 0.05 significance level to test the claim that the mean amount of time spent watching
television by women is smaller than the mean amount of time spent watching television by
men. Include your null and alternative hypotheses, the test statistic, P-value or critical value(s),
conclusion about the null hypothesis, and conclusion about the claim in your answer.

Question 57

In a random sample of 300 women, 45% favored stricter DUI legislation. In a random
sample of 200 men, 25% favored stricter DUI legislation. Construct a 95% confidence
interval for the difference between the population proportions . Assume that the
samples are independent and that they have been randomly selected.

Question 58

A random sample of 10 employees of an engineering company was selected. Each employee
was asked to report the number of sick days he/she claimed on Wednesdays and Fridays of
the previous calendar year. Use this information to test the employer's claim that more
employees call in sick on Fridays than on Wednesdays. Assume that the
differences between Wednesday's and Friday's sick day counts is normally distributed. Include your null and alternative hypotheses, the test statistic, P-value or critical value(s),
conclusion about the null hypothesis, and conclusion about the claim in your answer.