# Quiz 12: Analysis of Variance

Statistics

Q 1Q 1

To use an F distribution,the random variable must be:
A)a discrete random variable
B)a continuous random variable
C)a qualitative random variable
D)either a discrete or a continuous random variable

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Multiple Choice

B

Q 2Q 2

The shape of the F distribution curve is:
A)skewed to the left
B)skewed to the right
C)symmetric
D)rectangular

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Multiple Choice

B

Q 3Q 3

Which of the following is not a characteristic of an F distribution?
A)The F distribution is continuous and skewed to the right.
B)The F distribution has two numbers of degrees of freedom: degrees of freedom for the numerator and for the denominator.
C)The F distribution has two parameters: the mean and the standard deviation.
D)The units of an F distribution are always nonnegative.

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Multiple Choice

C

Q 4Q 4

The units of an F distribution:
A)are always negative
B)are always positive
C)are always nonnegative
D)can be negative,zero,or positive

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Multiple Choice

Q 5Q 5

The parameters of the F distribution are:
A)the mean and the standard deviation
B)the sample size minus one and F
C)the degrees of freedom for the numerator and the degrees of freedom for the denominator
D)F and n,where n is the sample size

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Multiple Choice

Q 6Q 6

The F value for 9 degrees of freedom for the numerator,12 degrees of freedom for the denominator,and a .01 area in the right tail is:
A)2.80
B)5.11
C)4.74
D)4.39

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Multiple Choice

Q 7Q 7

The F value for 25 degrees of freedom for the numerator,14 degrees of freedom for the denominator,and a .05 area in the right tail is:
A)2.78
B)2.34
C)3.19
D)1.87

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Multiple Choice

Q 8Q 8

We can use the analysis of variance procedure to test hypotheses about:
A)the mean of one population
B)the proportion of one population
C)two or more population proportions
D)two or more population means

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Multiple Choice

Q 9Q 9

Which of the following assumptions is not required to use ANOVA?
A)The populations from which the samples are drawn are (approximately)normally distributed.
B)The populations from which the samples are drawn have the same variance.
C)All samples are of the same size.
D)The samples drawn from different populations are random and independent.

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Multiple Choice

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Multiple Choice

Q 11Q 11

A one-way ANOVA test:
A)is a left-tailed test
B)is a right-tailed test
C)is a two-tailed test
D)can be a two-tailed,a right-tailed,or a left-tailed test

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Multiple Choice

Q 12Q 12

To make tests of hypotheses about more than two population means,we use the:
A)t distribution
B)normal distribution
C)chi-square distribution
D)analysis of variance procedure

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Multiple Choice

Q 13Q 13

Use the following to answer questions 13-22:
The table shown below gives information on a variable for three samples selected from three normally distributed populations with equal variances.
By using ANOVA,we wish to test the null hypothesis that the means of the three corresponding populations are equal.The significance level is 1%.
-The value of is:

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Short Answer

Q 14Q 14

Use the following to answer questions 13-22:
The table shown below gives information on a variable for three samples selected from three normally distributed populations with equal variances.
By using ANOVA,we wish to test the null hypothesis that the means of the three corresponding populations are equal.The significance level is 1%.
-The value of is:

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Short Answer

Q 15Q 15

Use the following to answer questions 13-22:
The table shown below gives information on a variable for three samples selected from three normally distributed populations with equal variances.
By using ANOVA,we wish to test the null hypothesis that the means of the three corresponding populations are equal.The significance level is 1%.
-The value of SSB,rounded to two decimal places,is:

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Short Answer

Q 16Q 16

Use the following to answer questions 13-22:
The table shown below gives information on a variable for three samples selected from three normally distributed populations with equal variances.
By using ANOVA,we wish to test the null hypothesis that the means of the three corresponding populations are equal.The significance level is 1%.
-The value of SSW is:

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Short Answer

Q 17Q 17

Use the following to answer questions 13-22:
The table shown below gives information on a variable for three samples selected from three normally distributed populations with equal variances.
By using ANOVA,we wish to test the null hypothesis that the means of the three corresponding populations are equal.The significance level is 1%.
-The value of MSB is:

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Short Answer

Q 18Q 18

Use the following to answer questions 13-22:
The table shown below gives information on a variable for three samples selected from three normally distributed populations with equal variances.
By using ANOVA,we wish to test the null hypothesis that the means of the three corresponding populations are equal.The significance level is 1%.
-The value of MSW,rounded to three decimal places,is:

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Short Answer

Q 19Q 19

Use the following to answer questions 13-22:
The table shown below gives information on a variable for three samples selected from three normally distributed populations with equal variances.
By using ANOVA,we wish to test the null hypothesis that the means of the three corresponding populations are equal.The significance level is 1%.
-The degrees of freedom for the numerator of the F distribution are:

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Short Answer

Q 20Q 20

Use the following to answer questions 13-22:
The table shown below gives information on a variable for three samples selected from three normally distributed populations with equal variances.
By using ANOVA,we wish to test the null hypothesis that the means of the three corresponding populations are equal.The significance level is 1%.
-The degrees of freedom for the denominator of the F distribution are:

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Short Answer

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Multiple Choice

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Short Answer

Q 23Q 23

Use the following to answer questions 23-32:
The table shown below gives information on a variable for four samples selected from four normally distributed populations with equal variances.
By using ANOVA,we wish to test the null hypothesis that the means of the four corresponding populations are equal.The significance level is 5%.
-The value of is:

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Short Answer

Q 24Q 24

Use the following to answer questions 23-32:
The table shown below gives information on a variable for four samples selected from four normally distributed populations with equal variances.
By using ANOVA,we wish to test the null hypothesis that the means of the four corresponding populations are equal.The significance level is 5%.
-The value of is:

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Short Answer

Q 25Q 25

Use the following to answer questions 23-32:
The table shown below gives information on a variable for four samples selected from four normally distributed populations with equal variances.
By using ANOVA,we wish to test the null hypothesis that the means of the four corresponding populations are equal.The significance level is 5%.
-The value of SSB,rounded to three decimal places,is:

Free

Short Answer

Q 26Q 26

Use the following to answer questions 23-32:
The table shown below gives information on a variable for four samples selected from four normally distributed populations with equal variances.
By using ANOVA,we wish to test the null hypothesis that the means of the four corresponding populations are equal.The significance level is 5%.
-The value of SSW is:

Free

Short Answer

Q 27Q 27

Use the following to answer questions 23-32:
The table shown below gives information on a variable for four samples selected from four normally distributed populations with equal variances.
By using ANOVA,we wish to test the null hypothesis that the means of the four corresponding populations are equal.The significance level is 5%.
-The value of MSB,rounded to three decimal places,is:

Free

Short Answer

Q 28Q 28

Use the following to answer questions 23-32:
The table shown below gives information on a variable for four samples selected from four normally distributed populations with equal variances.
By using ANOVA,we wish to test the null hypothesis that the means of the four corresponding populations are equal.The significance level is 5%.
-The value of MSW,rounded to three decimal places,is:

Free

Short Answer

Q 29Q 29

Use the following to answer questions 23-32:
The table shown below gives information on a variable for four samples selected from four normally distributed populations with equal variances.
By using ANOVA,we wish to test the null hypothesis that the means of the four corresponding populations are equal.The significance level is 5%.
-The degrees of freedom for the numerator of the F distribution are:

Free

Short Answer

Q 30Q 30

Use the following to answer questions 23-32:
The table shown below gives information on a variable for four samples selected from four normally distributed populations with equal variances.
By using ANOVA,we wish to test the null hypothesis that the means of the four corresponding populations are equal.The significance level is 5%.
-The degrees of freedom for the denominator of the F distribution are:

Free

Short Answer

Free

Multiple Choice

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Short Answer

Q 33Q 33

Use the following to answer questions 33-42:
A dietician wanted to test three different diets to find out whether or not the mean weight loss for each of these diets is the same.Fifteen overweight persons were selected at random,then randomly divided into three groups of five,and each group was assigned one of the diets.The table shown below contains the weight loss information for these people after being on their respective diets for six weeks.
By using ANOVA,we wish to test the null hypothesis that the mean weight loss is the same for the three diets.The significance level is 2.5%.
-The value of is:

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Short Answer

Q 34Q 34

Use the following to answer questions 33-42:
A dietician wanted to test three different diets to find out whether or not the mean weight loss for each of these diets is the same.Fifteen overweight persons were selected at random,then randomly divided into three groups of five,and each group was assigned one of the diets.The table shown below contains the weight loss information for these people after being on their respective diets for six weeks.
By using ANOVA,we wish to test the null hypothesis that the mean weight loss is the same for the three diets.The significance level is 2.5%.
-The value of is:

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Short Answer

Q 35Q 35

Use the following to answer questions 33-42:
A dietician wanted to test three different diets to find out whether or not the mean weight loss for each of these diets is the same.Fifteen overweight persons were selected at random,then randomly divided into three groups of five,and each group was assigned one of the diets.The table shown below contains the weight loss information for these people after being on their respective diets for six weeks.
By using ANOVA,we wish to test the null hypothesis that the mean weight loss is the same for the three diets.The significance level is 2.5%.
-The value of SSB is:

Free

Short Answer

Q 36Q 36

Use the following to answer questions 33-42:
A dietician wanted to test three different diets to find out whether or not the mean weight loss for each of these diets is the same.Fifteen overweight persons were selected at random,then randomly divided into three groups of five,and each group was assigned one of the diets.The table shown below contains the weight loss information for these people after being on their respective diets for six weeks.
By using ANOVA,we wish to test the null hypothesis that the mean weight loss is the same for the three diets.The significance level is 2.5%.
-The value of SSW is:

Free

Short Answer

Q 37Q 37

Use the following to answer questions 33-42:
A dietician wanted to test three different diets to find out whether or not the mean weight loss for each of these diets is the same.Fifteen overweight persons were selected at random,then randomly divided into three groups of five,and each group was assigned one of the diets.The table shown below contains the weight loss information for these people after being on their respective diets for six weeks.
By using ANOVA,we wish to test the null hypothesis that the mean weight loss is the same for the three diets.The significance level is 2.5%.
-The value of MSB is:

Free

Short Answer

Q 38Q 38

Use the following to answer questions 33-42:
A dietician wanted to test three different diets to find out whether or not the mean weight loss for each of these diets is the same.Fifteen overweight persons were selected at random,then randomly divided into three groups of five,and each group was assigned one of the diets.The table shown below contains the weight loss information for these people after being on their respective diets for six weeks.
By using ANOVA,we wish to test the null hypothesis that the mean weight loss is the same for the three diets.The significance level is 2.5%.
-The value of MSW,rounded to three decimal places,is:

Free

Short Answer

Q 39Q 39

Use the following to answer questions 33-42:
A dietician wanted to test three different diets to find out whether or not the mean weight loss for each of these diets is the same.Fifteen overweight persons were selected at random,then randomly divided into three groups of five,and each group was assigned one of the diets.The table shown below contains the weight loss information for these people after being on their respective diets for six weeks.
By using ANOVA,we wish to test the null hypothesis that the mean weight loss is the same for the three diets.The significance level is 2.5%.
-The degrees of freedom for the numerator of the F distribution are:

Free

Short Answer

Q 40Q 40

Use the following to answer questions 33-42:
A dietician wanted to test three different diets to find out whether or not the mean weight loss for each of these diets is the same.Fifteen overweight persons were selected at random,then randomly divided into three groups of five,and each group was assigned one of the diets.The table shown below contains the weight loss information for these people after being on their respective diets for six weeks.
By using ANOVA,we wish to test the null hypothesis that the mean weight loss is the same for the three diets.The significance level is 2.5%.
-The degrees of freedom for the denominator of the F distribution are:

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Short Answer

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Multiple Choice

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Short Answer

Q 43Q 43

Which of the following is not a characteristic of the F distribution?
A)It has two numbers of degrees of freedom: df for the numerator,and df for the denominator,and these two numbers may or may not be equal to each other.
B)It is symmetric.
C)It is continuous.
D)All units are nonnegative.

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Multiple Choice

Q 44Q 44

Use the following to answer questions 44-48:
A market research company randomly divides 12 stores from a large grocery chain into three groups of four stores each in order to compare the effect on mean sales of three different types of displays.The company uses display type 1 in four of the stores,display type 2 in four others,and display type 3 in the remaining four stores.Then it records the amount of sales (in $1,000's)during a one month period at each of the twelve stores.The table shown below reports the sales information.
By using ANOVA,we wish to test the null hypothesis that the means of the three corresponding populations are equal.The significance level is 1%.
-The value of SSB is:

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Short Answer

Q 45Q 45

Use the following to answer questions 44-48:
A market research company randomly divides 12 stores from a large grocery chain into three groups of four stores each in order to compare the effect on mean sales of three different types of displays.The company uses display type 1 in four of the stores,display type 2 in four others,and display type 3 in the remaining four stores.Then it records the amount of sales (in $1,000's)during a one month period at each of the twelve stores.The table shown below reports the sales information.
By using ANOVA,we wish to test the null hypothesis that the means of the three corresponding populations are equal.The significance level is 1%.
-The value of SSW,rounded to two decimal places,is:

Free

Short Answer

Q 46Q 46

Use the following to answer questions 44-48:
A market research company randomly divides 12 stores from a large grocery chain into three groups of four stores each in order to compare the effect on mean sales of three different types of displays.The company uses display type 1 in four of the stores,display type 2 in four others,and display type 3 in the remaining four stores.Then it records the amount of sales (in $1,000's)during a one month period at each of the twelve stores.The table shown below reports the sales information.
By using ANOVA,we wish to test the null hypothesis that the means of the three corresponding populations are equal.The significance level is 1%.
-The degrees of freedom for the numerator of the F distribution are:

Free

Short Answer

Q 47Q 47

Use the following to answer questions 44-48:
A market research company randomly divides 12 stores from a large grocery chain into three groups of four stores each in order to compare the effect on mean sales of three different types of displays.The company uses display type 1 in four of the stores,display type 2 in four others,and display type 3 in the remaining four stores.Then it records the amount of sales (in $1,000's)during a one month period at each of the twelve stores.The table shown below reports the sales information.
By using ANOVA,we wish to test the null hypothesis that the means of the three corresponding populations are equal.The significance level is 1%.
-The degrees of freedom for the denominator of the F distribution are:

Free

Short Answer

Q 48Q 48

Use the following to answer questions 44-48:
A market research company randomly divides 12 stores from a large grocery chain into three groups of four stores each in order to compare the effect on mean sales of three different types of displays.The company uses display type 1 in four of the stores,display type 2 in four others,and display type 3 in the remaining four stores.Then it records the amount of sales (in $1,000's)during a one month period at each of the twelve stores.The table shown below reports the sales information.
By using ANOVA,we wish to test the null hypothesis that the means of the three corresponding populations are equal.The significance level is 1%.
-The value of the test statistic F,rounded to three decimal places,is:

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Short Answer

Q 49Q 49

Use the following to answer questions 49-53:
The marketing manager for a software company is trying to decide whether to market her company's newest product by mail,on television,or through the Internet.She selects 20 communities in which to test-market the product,advertising through one of the three media in each community.The following table shows the amount of sales,in hundreds of dollars,for each community:
Sales are normally distributed and the standard deviations are equal for all three methods of advertising.You are to test the hypothesis that the means are the same for all three treatments using the ANOVA method.
-The value of SSB,rounded to four decimal places,is:

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Short Answer

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Short Answer

Q 54Q 54

Using ANOVA,you test the hypothesis that the means of 3 treatments are the same.You calculate the MSW as 16.6.The value of the test statistic F is 2.1.What is the between samples sum of squares,rounded to two decimal places?

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Short Answer

Q 55Q 55

Use the following to answer questions 55-61:
Your associate just took a lunch break and gave you the following incomplete ANOVA table she was trying to finish before noon.The null hypothesis for this test is .
-How many data points were used in this analysis?

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Short Answer

Q 56Q 56

Use the following to answer questions 55-61:
Your associate just took a lunch break and gave you the following incomplete ANOVA table she was trying to finish before noon.The null hypothesis for this test is .
-How many degrees of freedom are there for the between groups variation?

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Short Answer

Q 57Q 57

Use the following to answer questions 55-61:
Your associate just took a lunch break and gave you the following incomplete ANOVA table she was trying to finish before noon.The null hypothesis for this test is .
-How many degrees of freedom are there for the within groups variation?

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Short Answer

Q 58Q 58

Use the following to answer questions 55-61:
Your associate just took a lunch break and gave you the following incomplete ANOVA table she was trying to finish before noon.The null hypothesis for this test is .
-What is the value of the total sum of squares? Round your answer to one decimal place.

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Short Answer

Q 59Q 59

Use the following to answer questions 55-61:
Your associate just took a lunch break and gave you the following incomplete ANOVA table she was trying to finish before noon.The null hypothesis for this test is .
-What is the value of the mean square between groups? Round your answer to three decimal places.

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Short Answer

Q 60Q 60

Use the following to answer questions 55-61:
Your associate just took a lunch break and gave you the following incomplete ANOVA table she was trying to finish before noon.The null hypothesis for this test is .
-What is the value of the mean square within groups? Round your answer to three decimal places.

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Short Answer

Q 61Q 61

Use the following to answer questions 55-61:
Your associate just took a lunch break and gave you the following incomplete ANOVA table she was trying to finish before noon.The null hypothesis for this test is .
-What is the value of the test statistic F? Round your answer to three decimal places.

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Short Answer

Q 62Q 62

Find the critical value of F for d.f = (7,2)and the area in the right tail = 0.025.
A)39.36
B)99.36
C)19.35
D)1.96

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Short Answer