Deck 10: Comparisons Involving Means, Experimental Design and Analysis of Variance

Question 1

An experimental design where the experimental units are randomly assigned to the treatments is known as

A)factor block design
B)random factor design
C)completely randomized design
D)None of these alternatives is correct.

Answer 1

C

Question 2

To construct an interval estimate for the difference between the means of two populations when the standard deviations of the two populations are unknown and it can be assumed the two populations have equal variances, we must use a t distribution with (let n₁ be the size of sample 1 and n₂ the size of sample 2)

A)(n₁ + n₂) degrees of freedom
B)(n₁ + n₂ - 1) degrees of freedom
C)(n₁ + n₂ - 2) degrees of freedom
D)n₁ - n₂ + 2

Answer 2

C

Question 3

The ANOVA procedure is a statistical approach for determining whether or not

A)the means of two samples are equal
B)the means of two or more samples are equal
C)the means of more than two samples are equal
D)the means of two or more populations are equal

Answer 3

D

Question 4

The number of times each experimental condition is observed in a factorial design is known as

A)partition
B)replication
C)experimental condition
D)factor

Question 5

In an analysis of variance problem involving 3 treatments and 10 observations per treatment, SSE = 399.6. The MSE for this situation is

A)133.2
B)13.32
C)14.8
D)30.0

Question 6

The variable of interest in an ANOVA procedure is called

A)a partition
B)a treatment
C)either a partition or a treatment
D)a factor

Question 7

To compute an interval estimate for the difference between the means of two populations, the t distribution

A)is restricted to small sample situations
B)is not restricted to small sample situations
C)can be applied when the populations have equal means
D)None of these alternatives is correct.

Question 8

When an analysis of variance is performed on samples drawn from K populations, the mean square between treatments (MSTR) is

A)SSTR/n_T
B)SSTR/(n_T - 1)
C)SSTR/K
D)SSTR/(K - 1)

Question 9

In the ANOVA, treatment refers to

A)experimental units
B)different levels of a factor
C)the dependent variable
D)applying antibiotic to a wound

Question 10

In factorial designs, the response produced when the treatments of one factor interact with the treatments of another in influencing the response variable is known as

A)main effect
B)replication
C)interaction
D)None of these alternatives is correct.

Question 11

In an analysis of variance where the total sample size for the experiment is nT and the number of populations is K, the mean square within treatments is

A)SSE/(n_T - K)
B)SSTR/(n_T - K)
C)SSE/(K - 1)
D)SSE/K

Question 12

Independent simple random samples are taken to test the difference between the means of two populations whose standard deviations are not known, but are assumed to be equal. The sample sizes are n₁ = 25 and n₂ = 35. The correct distribution to use is the

A)t distribution with 61 degrees of freedom
B)t distribution with 60 degrees of freedom
C)t distribution with 59 degrees of freedom
D)t distribution with 58 degrees of freedom

Question 13

When developing an interval estimate for the difference between two sample means, with sample sizes of n₁ and n₂,

A)n₁ must be equal to n₂
B)n₁ must be smaller than n₂
C)n₁ must be larger than n₂
D)n₁ and n₂ can be of different sizes,

Question 14

The standard error of is the

A)variance of
B)variance of the sampling distribution of
C)standard deviation of the sampling distribution of
D)difference between the two means

Question 15

If two independent large samples are taken from two populations, the sampling distribution of the difference between the two sample means

A)can be approximated by a Poisson distribution
B)will have a variance of one
C)can be approximated by a normal distribution
D)will have a mean of one

Question 16

If we are interested in testing whether the mean of items in population 1 is larger than the mean of items in population 2, the

A)null hypothesis should state $\mu$ ₁ - $\mu$ ₂ < 0
B)null hypothesis should state $\mu$ ₁ - $\mu$ ₂ > 0
C)alternative hypothesis should state $\mu$ ₁ - $\mu$ ₂ > 0
D)alternative hypothesis should state $\mu$ ₁ - $\mu$ ₂ < 0

Question 17

In the analysis of variance procedure (ANOVA), "factor" refers to

A)the dependent variable
B)the independent variable
C)different levels of a treatment
D)the critical value of F

Question 18

For testing the following hypothesis at 95% confidence, the null hypothesis will be rejected if $\mu$ ₁ - $\mu$ ₂ $\le$ 0
H _$\alpha$ : $\mu$ ₁ - $\mu$ ₂ > 0

A)p-value $\le$ 0.05
B)p-value > 0.05
C)p-value > 0.95
D)p-value $\ge$ 0.475

Question 19

Independent simple random samples are taken to test the difference between the means of two populations whose variances are not known, but are assumed to be equal. The sample sizes are n₁ = 32 and n₂ = 40. The correct distribution to use is the

A)t distribution with 73 degrees of freedom
B)t distribution with 72 degrees of freedom
C)t distribution with 71 degrees of freedom
D)t distribution with 70 degrees of freedom

Question 20

When each data value in one sample is matched with a corresponding data value in another sample, the samples are known as

A)corresponding samples
B)matched samples
C)independent samples
D)None of these alternatives is correct.

Question 21

The mean square is the sum of squares divided by

A)the total number of observations
B)its corresponding degrees of freedom
C)its corresponding degrees of freedom minus one
D)None of these alternatives is correct.

Question 22

A term that means the same as the term "variable" in an ANOVA procedure is

A)factor
B)treatment
C)replication
D)variance within

Question 23

In a completely randomized design involving three treatments, the following information is provided: The overall mean for all the treatments is

A)7.00
B)6.67
C)7.25
D)4.89

Question 24

In an analysis of variance, one estimate of $\sigma$ ² is based upon the differences between the treatment means and the

A)means of each sample
B)overall sample mean
C)sum of observations
D)populations have equal means

Question 25

An ANOVA procedure is applied to data obtained from 6 samples where each sample contains 20 observations. The degrees of freedom for the critical value of F are

A)6 numerator and 20 denominator degrees of freedom
B)5 numerator and 20 denominator degrees of freedom
C)5 numerator and 114 denominator degrees of freedom
D)6 numerator and 20 denominator degrees of freedom

Question 26

An ANOVA procedure is used for data obtained from four populations. Four samples, each comprised of 30 observations, were taken from the four populations. The numerator and denominator (respectively) degrees of freedom for the critical value of F are

A)3 and 30
B)4 and 30
C)3 and 119
D)3 and 116

Question 27

The F ratio in a completely randomized ANOVA is the ratio of

A)MSTR/MSE
B)MST/MSE
C)MSE/MSTR
D)MSE/MST

Question 28

An ANOVA procedure is used for data that was obtained from four sample groups each comprised of five observations. The degrees of freedom for the critical value of F are

A)3 and 20
B)3 and 16
C)4 and 17
D)3 and 19

Question 29

In ANOVA, which of the following is not affected by whether or not the population means are equal?

A) $\overline{\mathrm{x}}$
B)between-samples estimate of $\sigma$ ²
C)within-samples estimate of $\sigma$ ²
D)None of these alternatives is correct.

Question 30

If we are interested in testing whether the mean of items in population 1 is significantly smaller than the mean of items in population 2, the

A)null hypothesis should state $\mu$ ₁- $\mu$ ₂ < 0
B)null hypothesis should state P₁ - P₂ $\ge$ 0
C)alternative hypothesis should state P₁ - P₂ > 0
D)alternative hypothesis should state $\mu$ ₁- $\mu$ ₂ < 0

Question 31

Which of the following is not a required assumption for the analysis of variance?

A)The random variable of interest for each population has a normal probability distribution.
B)The variance associated with the random variable must be the same for each population.
C)At least 2 populations are under consideration.
D)Populations have equal means.

Question 32

In order to determine whether or not the means of two populations are equal,

A)a t test must be performed
B)an analysis of variance must be performed
C)either a t test or an analysis of variance can be performed
D)a chi-square test must be performed

Question 33

If we are interested in testing whether the mean of population 1 is significantly larger than the mean of population 2, the correct null hypothesis is

A)H₀: $\mu$ ₁- $\mu$ ₂ $\ge$ 0
B)H₀: $\mu$ ₁- $\mu$ ₂ = 0
C)H₀: $\mu$ ₁- $\mu$ ₂ > 0
D)H₀: $\mu$ ₁- $\mu$ ₂ < 0

Question 34

An ANOVA procedure is used for data obtained from five populations. five samples, each comprised of 20 observations, were taken from the five populations. The numerator and denominator (respectively) degrees of freedom for the critical value of F are

A)5 and 20
B)4 and 20
C)4 and 99
D)4 and 95

Question 35

The required condition for using an ANOVA procedure on data from several populations is that the

A)the selected samples are dependent on each other
B)sampled populations are all uniform
C)sampled populations have equal variances
D)sampled populations have equal means

Question 36

The critical F value with 8 numerator and 29 denominator degrees of freedom at $\alpha$ = 0.01 is

A)2.28
B)3.20
C)3.33
D)3.64

Question 37

Which of the following is not a required assumption for the analysis of variance?

A)The random variable of interest for each population has a normal probability distribution.
B)The variance associated with the random variable must be the same for each population.
C)At least 2 populations are under consideration.
D)Populations have equal means.

Question 38

The critical F value with 6 numerator and 60 denominator degrees of freedom at $\alpha$ = .05 is

A)3.74
B)2.25
C)2.37
D)1.96

Question 39

In a completely randomized design involving four treatments, the following information is provided. The overall mean (the grand mean) for all treatments is

A)40.0
B)37.3
C)48.0
D)37.0

Question 40

In an analysis of variance problem if SST = 120 and SSTR = 80, then SSE is

A)200
B)40
C)80
D)120

Question 41

If a hypothesis is rejected at 95% confidence, it

A)will not be rejected at 90% confidence
B)will also be rejected at 90% confidence
C)will sometimes be rejected at 90% confidence
D)None of these alternatives is correct.

Question 42

Independent simple random samples are taken to test the difference between the means of two populations whose variances are known. The sample sizes are n₁ = 38 and n₂ = 42. The correct distribution to use is the

A)normal distribution
B)t distribution with 80 degrees of freedom
C)t distribution with 79 degrees of freedom
D)t distribution with 78 degrees of freedom

Question 43

The p-value

A)is the same as the Z statistic
B)measures the number of standard deviations from the mean
C)is a distance
D)is a probability

Question 44

Which of the following does not need to be known in order to compute the p-value?

A)knowledge of whether the test is one-tailed or two-tailed
B)the value of the test statistic
C)the level of significance
D)None of these alternatives is correct.

Question 45

Exhibit 10-1
Salary information regarding male and female employees of a large company is shown below.

Refer to Exhibit 10-1. The 95% confidence interval for the difference between the means of the two populations is

A)0 to 6.92
B)-2 to 2
C)-1.96 to 1.96
D)-0.92 to 6.92

Question 46

Exhibit 10-1
Salary information regarding male and female employees of a large company is shown below.

Refer to Exhibit 10-1. The point estimate of the difference between the means of the two populations is

A)-28
B)3
C)4
D)-4

Question 47

If we are interested in testing whether the mean of population 1 is significantly different from the mean of population 2, the correct null hypothesis is

A)H₀: $\mu$ ₁- $\mu$ ₂ $\ge$ 0
B).H₀: $\mu$ ₁- $\mu$ ₂ = 0
C).H₀: $\mu$ ₁- $\mu$ ₂ > 0
D)H₀: $\mu$ ₁- $\mu$ ₂ = 0

Question 48

In hypothesis testing if the null hypothesis is rejected,

A)no conclusions can be drawn from the test
B)the alternative hypothesis is true
C)the data must have been accumulated incorrectly
D)the sample size has been too small

Question 49

We are interested in testing the following hypotheses.
H₀: $\mu$ ₁- $\mu$ ₂ = 0
H_a: $\mu$ ₁- $\mu$ ₂ ? 0
The test statistic Z is computed to be 1.85. The p-value for this test is

A)0.4678
B)0.9678
C)0.0322
D)0.0644

Question 50

For a two-tailed test at 86.12% confidence, Z =

A)1.96
B)1.48
C)1.09
D)0.8612

Question 51

Exhibit 10-1
Salary information regarding male and female employees of a large company is shown below.

Refer to Exhibit 10-1. If you are interested in testing whether or not the average salary of males is significantly greater than that of females, the test statistic is

A)2.0
B)1.5
C)1.96
D)1.645

Question 52

When the following hypotheses are being tested at a level of significance of $\alpha$ H₀: $\mu$ ₁- $\mu$ ₂ $\ge$ 0
H_a: $\mu$ ₁- $\mu$ ₂ < 0
The null hypothesis will be rejected if the p-value is

A)1- $\alpha$
B)> $\alpha$
C)> $\alpha$ /2
D) $\le$$\alpha$

Question 53

The level of significance

A)can be any positive value
B)can be any value
C)is (1 - confidence level)
D)can be any value between -1.96 to 1.96

Question 54

Exhibit 10-1
Salary information regarding male and female employees of a large company is shown below.

Refer to Exhibit 10-1. At 95% confidence, the margin of error is

A)1.96
B)1.645
C)3.920
D)2.000

Question 55

We are interested in testing the following hypotheses.
H₀: $\mu$ ₁- $\mu$ ₂ $\ge$ 0
H_a: $\mu$ ₁- $\mu$ ₂ < 0
Based on 40 degrees of freedom, the test statistic t is computed to be 2.423. The p-value for this test is

A)0.01
B)0.02
C)0.025
D)between 0.025 to 0.05

Question 56

In order to test the following hypotheses at an $\alpha$ level of significance,
H₀: $\mu$ ₁- $\mu$ ₂ $\le$ 0
H_a: $\mu$ ₁- $\mu$ ₂ > 0
The null hypothesis will be rejected if the test statistic Z is

A) $\le$ Z _$\alpha$
B) $\ge$ Z _$\alpha$
C)< -Z _$\alpha$
D)< 0

Question 57

When the p-value is used for hypothesis testing, the null hypothesis is rejected if

A)p-value $\le$ $\alpha$
B) $\alpha$ < p-value
C)p-value $\ge$ $\alpha$
D)p-value = 1 - $\alpha$

Question 58

We are interested in testing the following hypotheses.
H₀: $\mu$ ₁- $\mu$ ₂ $\ge$ 0
H_a: $\mu$ ₁- $\mu$ ₂ < 0
The test statistic Z is computed to be 2.83. The p-value for this test is

A)0.4977
B)0.0023
C)0.0046
D)0.9977

Question 59

For a one-tailed test (lower tail) at 93.7% confidence, Z =

A)-1.86
B)-1.53
C)-1.96
D)-1.645

Question 60

Exhibit 10-1
Salary information regarding male and female employees of a large company is shown below.

Refer to Exhibit 10-1. The standard error for the difference between the two means is

A)4
B)7.46
C)4.24
D)2.0

Question 61

Exhibit 10-6
The management of a department store is interested in estimating the difference between the mean credit purchases of customers using the store's credit card versus those customers using a national major credit card. You are given the following information.

Refer to Exhibit 10-6. A point estimate for the difference between the mean purchases of the users of the two credit cards is

A)2
B)18
C)265
D)15

Question 62

Exhibit 10-5
The following information was obtained from matched samples.

Refer to Exhibit 10-5. The point estimate for the difference between the means of the two populations (Method 1 - Method 2) is

A)-1
B)0
C)-4
D)2

Question 63

Exhibit 10-3
A statistics teacher wants to see if there is any difference in the abilities of students enrolled in statistics today and those enrolled five years ago. A sample of final examination scores from students enrolled today and from students enrolled five years ago was taken. You are given the following information.

Refer to Exhibit 10-3. The 95% confidence interval for the difference between the two population means is

A)-9.92 to -2.08
B)-3.92 to 3.92
C)-13.84 to 1.84
D)-24.228 to 12.23

Question 64

Exhibit 10-4
The following information was obtained from independent random samples.
Assume normally distributed populations with equal variances.

Refer to Exhibit 10-4. The 95% confidence interval for the difference between the two population means is

A)-5.372 to 11.372
B)-5 to 3
C)-4.86 to 10.86
D)-2.65 to 8.65

Question 65

Exhibit 10-5
The following information was obtained from matched samples.


-Refer to Exhibit 10-5. The null hypothesis tested is H₀: $\mu$ _d = 0. The test statistic for the difference between the two population means is

A)2
B)0
C)-1
D)-2

Question 66

Exhibit 10-2
The following information was obtained from matched samples.
The daily production rates for a sample of workers before and after a training program are shown below.

Refer to Exhibit 10-2. Based on the results of question 18, the

A)null hypothesis should be rejected
B)null hypothesis should not be rejected
C)alternative hypothesis should be accepted
D)None of these alternatives is correct.

Question 67

Exhibit 10-3
A statistics teacher wants to see if there is any difference in the abilities of students enrolled in statistics today and those enrolled five years ago. A sample of final examination scores from students enrolled today and from students enrolled five years ago was taken. You are given the following information.

Refer to Exhibit 10-3. What is the conclusion that can be reached about the difference in the average final examination scores between the two classes? (Use a .05 level of significance.)

A)There is a statistically significant difference in the average final examination scores between the two classes.
B)There is no statistically significant difference in the average final examination scores between the two classes.
C)It is impossible to make a decision on the basis of the information given.
D)There is a difference, but it is not significant.

Question 68

Exhibit 10-1
Salary information regarding male and female employees of a large company is shown below.

Refer to Exhibit 10-1. The p-value is

A)0.0668
B)0.0334
C)1.336
D)1.96

Question 69

Exhibit 10-2
The following information was obtained from matched samples.
The daily production rates for a sample of workers before and after a training program are shown below.


-Refer to Exhibit 10-2. The null hypothesis to be tested is H₀: $\mu$ _d = 0. The test statistic is

A)-1.96
B)1.96
C)0
D)1.645

Question 70

Exhibit 10-4
The following information was obtained from independent random samples.
Assume normally distributed populations with equal variances.

Refer to Exhibit 10-4. The standard error of is

A)3.0
B)4.0
C)8.372
D)19.48

Question 71

Exhibit 10-3
A statistics teacher wants to see if there is any difference in the abilities of students enrolled in statistics today and those enrolled five years ago. A sample of final examination scores from students enrolled today and from students enrolled five years ago was taken. You are given the following information.

Refer to Exhibit 10-3. The test statistic for the difference between the two population means is

A)-.47
B)-.65
C)-1.5
D)-3

Question 72

Exhibit 10-4
The following information was obtained from independent random samples.
Assume normally distributed populations with equal variances.

Refer to Exhibit 10-4. The point estimate for the difference between the means of the two populations is

A)0
B)2
C)3
D)15

Question 73

Exhibit 10-3
A statistics teacher wants to see if there is any difference in the abilities of students enrolled in statistics today and those enrolled five years ago. A sample of final examination scores from students enrolled today and from students enrolled five years ago was taken. You are given the following information.

Refer to Exhibit 10-3. The point estimate for the difference between the means of the two populations is

A)58.5
B)9
C)-9
D)-6

Question 74

Exhibit 10-4
The following information was obtained from independent random samples.
Assume normally distributed populations with equal variances.

Refer to Exhibit 10-4. The degrees of freedom for the t-distribution are

A)22
B)23
C)24
D)19

Question 75

Exhibit 10-5
The following information was obtained from matched samples.

Refer to Exhibit 10-5. If the null hypothesis is tested at the 5% level, the null hypothesis

A)should be rejected
B)should not be rejected
C)should be revised
D)None of these alternatives is correct.

Question 76

Exhibit 10-3
A statistics teacher wants to see if there is any difference in the abilities of students enrolled in statistics today and those enrolled five years ago. A sample of final examination scores from students enrolled today and from students enrolled five years ago was taken. You are given the following information.

Refer to Exhibit 10-3. The p-value for the difference between the two population means is

A).0013
B).0026
C).4987
D).9987

Question 77

Exhibit 10-2
The following information was obtained from matched samples.
The daily production rates for a sample of workers before and after a training program are shown below.

Refer to Exhibit 10-2. The point estimate for the difference between the means of the two populations is

A)-1
B)-2
C)0
D)1

Question 78

Exhibit 10-3
A statistics teacher wants to see if there is any difference in the abilities of students enrolled in statistics today and those enrolled five years ago. A sample of final examination scores from students enrolled today and from students enrolled five years ago was taken. You are given the following information.

Refer to Exhibit 10-3. The standard error of is

A)12.9
B)9.3
C)4
D)2

Question 79

Exhibit 10-1
Salary information regarding male and female employees of a large company is shown below.

Refer to Exhibit 10-1. At 95% confidence, the conclusion is the

A)average salary of males is significantly greater than females
B)average salary of males is significantly lower than females
C)salaries of males and females are equal
D)None of these alternatives is correct.

Question 80

Exhibit 10-5
The following information was obtained from matched samples.

Refer to Exhibit 10-5. The 95% confidence interval for the difference between the two population means is

A)-3.776 to 1.776
B)-2.776 to 2.776
C)-1.776 to 2.776
D)0 to 3.776