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

Question 1

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

Answer 1

can be approximated by a normal distribution

Question 2

The process of using the same or similar experimental units for all treatments in order to remove a source of variation from the error term is called

A)replicating
B)partitioning
C)randomizing
D)blocking

Answer 2

blocking

Question 3

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

A)null hypothesis should state $\mu$ ₁ - $\mu$ ₂ $\lt$ 0
B)null hypothesis should state $\mu$ ₁ - $\mu$ ₂ $\le$ 0
C)alternative hypothesis should state $\mu$ ₁ - $\mu$ ₂ $\lt$ 0
D)alternative hypothesis should state $\mu$ ₁ - $\mu$ ₂ $\gt$ 0

Answer 3

alternative hypothesis should state $\mu$ ₁ - $\mu$ ₂ $\lt$ 0

Question 4

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 5

If we reject the hypothesis H₀: $\mu$ ₁ = $\mu$ ₂ = $\mu$ ₃, we can conclude that

A)all three population means are similar
B)all three population means are equal
C)all three population means are different
D)at least two population means are different

Question 6

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

A)Poisson distribution
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 7

The within-treatments estimate of $\sigma$ ² is called the

A)sum of squares due to error
B)mean square due to error
C)sum of squares due to treatments
D)mean square due to treatments

Question 8

In analysis of variance, the dependent variable is called the

A)response variable
B)factor
C)experimental unit
D)design variable

Question 9

The standard error of is the

A)variance of
B)variance of the sampling distribution of 11ec9e04_b41a_8f38_91b3_f9a71a5294bb_TB2074_11
C)standard deviation of the sampling distribution of 11ec9e04_b41a_8f38_91b3_f9a71a5294bb_TB2074_11
D)difference between the two means

Question 10

In testing for the equality of k population means, the number of treatments is

A)k
B)k - 1
C)n_T
D)n_T - k

Question 11

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

A)null hypothesis should state $\mu$ ₁ - $\mu$ ₂ $\gt$ 0
B)null hypothesis should state $\mu$ ₁ - $\mu$ ₂ $\ge$ 0
C)alternative hypothesis should state $\mu$ ₁ - $\mu$ ₂ $\gt$ 0
D)alternative hypothesis should state $\mu$ ₁ - $\mu$ ₂ $\lt$ 0

Question 12

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

A)binomial distribution
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 13

The test statistic F is the ratio

A)MSE/MST
B)MSTR/MSE
C)SSTR/SSE
D)SSTR/SST

Question 14

The process of allocating the total sum of squares and degrees of freedom to the various components is referred to as

A)replicating
B)partitioning
C)randomizing
D)blocking

Question 15

In making three pairwise comparisons, what is the experiment-wise Type I error rate $\alpha$ _ew if the comparison-wise Type I error rate $\alpha$ is .10?

A).001
B).081
C).271
D).300

Question 16

In analysis of variance, the independent variable of interest is called the

A)response variable
B)factor
C)experimental unit
D)design variable

Question 17

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 18

To construct an interval estimate for the difference between the means of two populations when the standard deviations of the two populations are unknown, 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

Question 19

In analysis of variance, the levels of the factor are called the

A)dependent variables
B)experimental units
C)treatments
D)observations

Question 20

If we are testing for the equality of 3 population means, we should use the

A)test statistic t
B)test statistics z
C)test statistic $\chi$ ²
D)test statistic F

Question 21

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 22

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)5

Question 23

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 24

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 25

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 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

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 28

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 29

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 30

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 31

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 32

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

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

Question 33

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

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

Question 34

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 35

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 36

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 37

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 38

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 39

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 40

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 41

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 42

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 43

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 44

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 45

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 46

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 47

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 48

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 49

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 50

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).0014
B).0027
C).4986
D).9972

Question 51

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 52

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. At 95% confidence, the margin of error is

A)1.694
B)3.32
C)1.96
D)15

Question 53

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 54

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

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 55

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 56

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)21
C)20
D)19

Question 57

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 95% confidence interval estimate for the difference between the average purchases of the customers using the two different credit cards is

A)49 to 64
B)11.68 to 18.32
C)125 to 140
D)8 to 10

Question 58

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

Question 59

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 60

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 61

Exhibit 10-11
To test whether or not there is a difference between treatments A, B, and C, a sample of 12 observations has been randomly assigned to the 3 treatments. You are given the results below.

Refer to Exhibit 10-11. The test statistic to test the null hypothesis equals

A)0.944
B)1.059
C)3.13
D)19.231

Question 62

Exhibit 10-11
To test whether or not there is a difference between treatments A, B, and C, a sample of 12 observations has been randomly assigned to the 3 treatments. You are given the results below.


-Refer to Exhibit 10-11. The null hypothesis for this ANOVA problem is

A) $\mu$ ₁= $\mu$ ₂
B) $\mu$ ₁= $\mu$ ₂= $\mu$ ₃
C) $\mu$ ₁= $\mu$ ₂= $\mu$ ₃= $\mu$ ₄
D) $\mu$ ₁= $\mu$ ₂= ... = $\mu$ ₁₂

Question 63

Exhibit 10-9
Two major automobile manufacturers have produced compact cars with the same size engines. We are interested in determining whether or not there is a significant difference in the MPG (miles per gallon) of the two brands of automobiles. A random sample of eight cars from each manufacturer is selected, and eight drivers are selected to drive each automobile for a specified distance. The following data show the results of the test.

Refer to Exhibit 10-9. The mean for the differences is

A)0.50
B)1.5
C)2.0
D)2.5

Question 64

Exhibit 10-7
In order to estimate the difference between the average hourly wages of employees of two branches of a department store, the following data have been gathered.
For this problem, the degrees of freedom are computed to be 36.
Refer to Exhibit 10-7. A 95% interval estimate for the difference between the two population means is

A)0.078 to 1.922
B)1.922 to 2.078
C)1.09 to 4.078
D)1.078 to 2.922

Question 65

Exhibit 10-11
To test whether or not there is a difference between treatments A, B, and C, a sample of 12 observations has been randomly assigned to the 3 treatments. You are given the results below.

Refer to Exhibit 10-11. The null hypothesis

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

Question 66

Exhibit 10-11
To test whether or not there is a difference between treatments A, B, and C, a sample of 12 observations has been randomly assigned to the 3 treatments. You are given the results below.

Refer to Exhibit 10-11. The mean square within treatments (MSE) equals

A)1.872
B)5.86
C)34
D)36

Question 67

Exhibit 10-7
In order to estimate the difference between the average hourly wages of employees of two branches of a department store, the following data have been gathered.
For this problem, the degrees of freedom are computed to be 36.
Refer to Exhibit 10-7. A point estimate for the difference between the two sample means is

A)1
B)2
C)3
D)4

Question 68

Exhibit 10-10
A local department store is studying the shopping habits of its customers. They think that the longer customers spend in the store the more they buy. Their study resulted in the following information regarding the amount of time women and men spent in a store.

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

A)1.96
B)27.96
C)21.00
D)26.00

Question 69

Exhibit 10-9
Two major automobile manufacturers have produced compact cars with the same size engines. We are interested in determining whether or not there is a significant difference in the MPG (miles per gallon) of the two brands of automobiles. A random sample of eight cars from each manufacturer is selected, and eight drivers are selected to drive each automobile for a specified distance. The following data show the results of the test.

Refer to Exhibit 10-9. The test statistic is

A)1.645
B)1.96
C)2.096
D)2.256

Question 70

Exhibit 10-10
A local department store is studying the shopping habits of its customers. They think that the longer customers spend in the store the more they buy. Their study resulted in the following information regarding the amount of time women and men spent in a store.

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

A)1 minute 26 seconds
B)34 seconds
C)26 seconds
D)13 seconds

Question 71

Exhibit 10-10
A local department store is studying the shopping habits of its customers. They think that the longer customers spend in the store the more they buy. Their study resulted in the following information regarding the amount of time women and men spent in a store.

Refer to Exhibit 10-10. At 95% confidence, what is the conclusion for this study?

A)There is a significant difference in the time spent in the store between men and women.
B)There is no significant difference in the time spent in the store between men and women.
C)It is impossible to make a decision on the basis of the information given.
D)The sample sizes must be equal in order to answer this question.

Question 72

Exhibit 10-8
In order to determine whether or not there is a significant difference between the hourly wages of two companies, the following data have been accumulated.

Refer to Exhibit 10-8. The null hypothesis

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

Question 73

Exhibit 10-8
In order to determine whether or not there is a significant difference between the hourly wages of two companies, the following data have been accumulated.

Refer to Exhibit 10-8. The p-value is

A)0.0013
B)0.0026
C)0.0042
D)0.0084

Question 74

Exhibit 10-9
Two major automobile manufacturers have produced compact cars with the same size engines. We are interested in determining whether or not there is a significant difference in the MPG (miles per gallon) of the two brands of automobiles. A random sample of eight cars from each manufacturer is selected, and eight drivers are selected to drive each automobile for a specified distance. The following data show the results of the test.

Refer to Exhibit 10-9. At 90% confidence the null hypothesis

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

Question 75

Exhibit 10-11
To test whether or not there is a difference between treatments A, B, and C, a sample of 12 observations has been randomly assigned to the 3 treatments. You are given the results below.

Refer to Exhibit 10-11. The null hypothesis is to be tested at the 1% level of significance. The p-value is

A)greater than 0.1
B)between 0.1 and 0.05
C)between 0.05 and 0.025
D)between 0.025 and 0.01

Question 76

Exhibit 10-10
A local department store is studying the shopping habits of its customers. They think that the longer customers spend in the store the more they buy. Their study resulted in the following information regarding the amount of time women and men spent in a store.

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

A)9
B)-1
C)-9
D)1

Question 77

Exhibit 10-8
In order to determine whether or not there is a significant difference between the hourly wages of two companies, the following data have been accumulated.

Refer to Exhibit 10-8. The test statistic is

A)0.098
B)1.645
C)2.75
D)3.01

Question 78

Exhibit 10-10
A local department store is studying the shopping habits of its customers. They think that the longer customers spend in the store the more they buy. Their study resulted in the following information regarding the amount of time women and men spent in a store.

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

A)24.04 to 27.96
B)1.96
C)-1.96 to 1.96
D)-24.04 to 27.96

Question 79

Exhibit 10-8
In order to determine whether or not there is a significant difference between the hourly wages of two companies, the following data have been accumulated.

Refer to Exhibit 10-8. A point estimate for the difference between the two sample means is

A)20
B)0.50
C)0.25
D)1.00

Question 80

Exhibit 10-11
To test whether or not there is a difference between treatments A, B, and C, a sample of 12 observations has been randomly assigned to the 3 treatments. You are given the results below.

Refer to Exhibit 10-11. The mean square between treatments (MSTR) equals

A)1.872
B)5.86
C)34
D)36