Deck 13: F Tests and Analysis of Variance

Question 1

You are testing the equality of two population means using samples of size 10.The F_stat value for your ANOVA is 4.0.If, instead of an F test, you had conducted a t test to test the "no difference in population means" null hypothesis, the t_stat value would be 16.0.

Answer 1

False

Question 2

The computed F value (F_stat) in a one-way analysis of variance is the ratio of the between groups sum of squares (SSB) to the within groups sum of squares (SSW).

Answer 2

False

Question 3

You are testing the equality of two population means using ANOVA.The critical value F_c for your test is 3.634.If, instead of an F test, you had conducted a t test to test the "no difference in population means" null hypothesis, the t_c value would be 1.906.

Answer 3

True

Question 4

In an experimental study, the investigator has the ability to directly influence or manipulate one or more of the elements involved in the investigation.

Question 5

The computed F value (F_stat) in a one-way analysis of variance is the ratio of the within groups mean square (MSW) to the between groups mean square (MSB).

Question 6

The computed F value (F_stat) in a one-way analysis of variance is the ratio of the between groups mean square (MSB) to the within groups mean square (MSW).

Question 7

One of the assumptions for the one-way analysis of variance is that the standard deviations - and so the variances - are not the same for all the populations.

Question 8

The F distribution can be used to describe how the ratio of two sample variances behaves when the two samples have been independently selected from normal populations with the same variance.

Question 9

In a completely randomized design, experimental units are arranged into similar groups based on extraneous factors in an effort to reduce error variation in experimental results.

Question 10

You are testing the equality of population means using ANOVA.The partial ANOVA table appears below.If the samples used in the ANOVA are all the same size, that sample size must be 15.

Question 11

You are testing the equality of population means using ANOVA.The partial ANOVA table appears below.The between-groups mean square value is 1540.

Question 12

You are testing the equality of population means using ANOVA and a 5% significance level.If the p-value for the F_stat that you produce is .0212, you should conclude that the population means are not equal.

Question 13

You are testing the equality of population means using one-way ANOVA and a 5% significance level.If the p-value for the F_stat that you produce is .0711, you should conclude that the population means are not equal.

Question 14

The within groups mean square in a one-way analysis of variance is the within groups sum of squares divided by (n-1) degrees of freedom.

Question 15

You are testing the equality of three population means using samples of size 5.The F_stat value for your ANOVA is 3.256.At a 5% significance level, you should reject the null hypothesis that the population means are equal.

Question 16

You are testing the equality of population means using ANOVA.The partial ANOVA table appears below.According to the table, four population means are involved in the test.

Question 17

In a randomized block design, experimental units are arranged into similar groups based on extraneous factors in an effort to reduce error variation in experimental results.

Question 18

The within groups mean square in a one-way analysis of variance is the within groups sum of squares (SSW) divided by the between groups sum of squares (SSB).

Question 19

The within groups mean square in a one-way analysis of variance is the within groups sum of squares divided by its corresponding degrees of freedom.

Question 20

You are testing the equality of four population means with four samples of size six.To compute the within-groups mean square, you should divide the total sum of squares by 3.

Question 21

Use a statistical calculator or statistical software to determine the proportion of values in an F distribution that are greater than 10.3, with numerator degrees of freedom of 2 and denominator degrees of freedom of 12.

A)0.002
B)0.092
C)0.908
D)0.998

Question 22

You are testing the equality of population means using ANOVA.The partial ANOVA table appears below.What is the value of the between-groups mean square?

A)464.062
B)587.5
C)2350
D)783.33

Question 23

You are testing the equality of two population means using samples of size 10.The F_stat value for your ANOVA is 3.60.If, instead of an F test, you had conducted a t test to test the "no difference in two population means" null hypothesis, the t_stat value would be

A)3.60
B)12.96
C)1.897
D)2.965
E)The t_stat value cannot be determined from the information given.

Question 24

A statistical procedure using two independent estimates of the same population variance to test for differences between or among the means of populations is called

A)simple regression
B)observational analysis
C)discriminant analysis
D)one-way analysis of variance

Question 25

You are testing the equality of population means using one-way ANOVA.The partial ANOVA table appears below.If the samples used in the ANOVA are all the same size, what is the sample size?

A)12
B)15
C)10
D)5

Question 26

The dependent variable in an experiment is called the

A)treatment variable
B)within-groups variable
C)response variable
D)correlation variable

Question 27

You are testing the equality of two population means using one-way ANOVA.The critical value F_c for your test is 4.665.If, instead of an F test, you had conducted a t test to test the "no difference in population means" null hypothesis, the critical t_c value would be

A)21.762
B)2.16
C)4.665
D)2.84

Question 28

A study in which information from the population of interest is gathered without any attempt by those conducting the study to influence the population or intervene in any way is called a(n)

A)completely randomized study
B)block study
C)observational study
D)experimental study

Question 29

1% of the values in an F distribution with numerator degrees of freedom = 3 and denominator degree of freedom = 18 are greater than or equal to ______.

A)3.160
B)6.013
C)5.092
D)2.965

Question 30

Which of the following is NOT a required assumption for a one-way analysis of variance?

A)each population of values has a normal distribution
B)the variance is the same for each population of values
C)at least two populations are under consideration
D)the populations have equal means
E)the observations must be independent

Question 31

You are testing the equality of population means using one-way ANOVA.The partial ANOVA table appears below.According to the table, how many group means (population means) are involved in the test?

A)4
B)3
C)2
D)5

Question 32

Which of the following is true regarding the F distribution?

A)it is the ratio of two sample variances
B)it is not symmetric
C)values can never be negative
D)it has numerator degrees of freedom from sample 1 and denominator degrees of freedom from sample 2
E)all of the above

Question 33

In an F distribution with numerator degrees of freedom of 3 and denominator degrees of freedom of 8, 95% of values are less than _____ .

A)4.066
B)7.591
C)8.845
D)27.489

Question 34

A completely randomized experimental design would be the appropriate method to answer which of the following research questions?

A)To determine whether average teacher salaries differ in Ohio, Pennsylvania, and Indiana.
B)To determine whether average teacher salaries differ in Ohio, Pennsylvania, and Indiana, while controlling for differences in salaries that exist across grade levels.
C)To determine the effect of an additional year of experience on a teacher's salary.
D)To determine the joint effects of a teacher's field (math, English, etc.) and whether the teacher works in a public school or a private school on a teacher's salary.

Question 35

In an F distribution with numerator degrees of freedom of 5 and denominator degrees of freedom of 8, 5% of values are greater than _____ .

A)3.688
B)4.818
C)6.632
D)10.289

Question 36

In experimental design, factors not of primary interest in a study that may serve to obscure experimental results due to their effect on the response variable are called

A)extraneous factors
B)rigid factors
C)experimental factors
D)guided factors

Question 37

An experiment in which we can assess the simultaneous effect of multiple factors on a response variable and in which all factor combinations are represented is called a

A)partitioning experiment
B)cross reference experiment
C)block experiment
D)factorial experiment

Question 38

You are testing the equality of three population means using one-way ANOVA and a 5% significance level.If the p-value that you produce for the test is .0112, you should

A)conclude that the population means are equal.
B)not reject the "all means are equal" null hypothesis.
C)reject the alternative hypothesis.
D)conclude that at least one of the population means differs from the others.

Question 39

In an experiment, one of the various values or states that an experimental factor can take on is called a

A)treatment
B)response
C)premonition
D)crosstab

Question 40

Use a statistical calculator or statistical software to determine the proportion of values in an F distribution that are greater than 8.5, with numerator degrees of freedom of 3 and denominator degrees of freedom of 15.

A)0.002
B)0.052
C)0.948
D)0.998

Question 41

Crawford Industries purchases step-down electrical converters from two suppliers.The converters from the two suppliers appear to have the same average life (measured in hours) but the variability in useful life appears be different for the two suppliers.In random samples of 8 converters from supplier A and 8 converters from supplier B, the variance in sample A was 1600; the variance in sample B was 3800.Assume that the life of the converters is normally distributed in each population.Test the null hypothesis that the variance of population B is no greater than the variance of population A, against the alternative hypothesis that the variance of population B is greater than the variance of population A..Use a significance level of 5% and report the F statistic (F_stat) for this one-tailed test.

A)3.160
B)6.013
C)2.375
D)2.965

Question 42

A random sample of size 8 is selected from normal population A.A second, independent, random sample of size 5 is selected from normal population B.You test a null hypothesis that the variances of the two populations are equal, using a 10% significance level.If the test statistic is calculated as the ratio of sample variance A to sample variance B, the critical F value, F_c , for your test should be

A)6.094
B)6.041
C)4.818
D)4.876

Question 43

Crawford Industries purchases step-down electrical converters from two suppliers.The converters from the two suppliers appear to have the same average life (measured in hours) but the variability in useful life appears be different for the two suppliers.In random samples of 8 converters from supplier A and 8 converters from supplier B, the variance in sample A was 1600; the variance in sample B was 3800.Assume that the life of the converters is normally distrusted in each population..Test the null hypothesis that the variance of population B is no greater than the variance of population A, against the alternative hypothesis that the variation of population B variance is greater than the variance of population A.Use a significance level of 5% for this one-tailed test and report your conclusion.

A)Since F_stat is greater than F_c, we cannot reject the "variance of B no greater than variance of A" null hypothesis.
B)Since F_stat is less than F_c, we cannot reject the "variance of B no greater than variance of A" null hypothesis.
C)Since F_stat is less than F_c, we can reject the "variance of B no greater than variance of A" null hypothesis.
D)Since F_stat is greater than F_c, we can reject the "variance of B no greater than variance of A" null hypothesis.

Question 44

The ANOVA table below shows partial results for a test of a "no difference in population means" null hypothesis.At a 5% significance level, what is the.critical value (F_c) for the test.?

A)4.902
B)3.718
C)5.568
D)2.758

Question 45

5% of the variance ratios in an F distribution with numerator degrees of freedom = 3 and denominator degrees of freedom = 9 are greater than or equal to _____.

A)3.179
B)6.013
C)3.863
D)6.992

Question 46

A random sample of size 15 selected from normal population A has a standard deviation of 80.A second, independent, random sample of size 8 from normal population B has a standard deviation of 100.You will test a null hypothesis that the standard deviations of the two populations are equal, using a 2% significance level.Report the F statistic (F_stat) for the test.

A)2.35
B)1.56
C).65
D)1.25

Question 47

Crawford Industries purchases step-down electrical converters from two suppliers.The converters from the two suppliers appear to have the same average life (measured in hours) but the variability in useful life appears be different for the units provided by the two suppliers.In random samples of 8 converters from supplier A and 8 converters from supplier B, the standard deviation in sample A was 40 hours; the standard deviation in sample B was 55 hours.Assume that converter life is normally distributed in each population.Test the null hypothesis that the population variance B is no greater than the population variancedeviation A, against the alternative hypothesis that the population variance B is greater than population variance A.Use a significance level of 5% for this one-tailed test and report the critical F (F_c) for the test.

A)3.160
B)6.013
C)3.787
D)2.965

Question 48

The ANOVA table below shows partial results for a test of a "no difference in population means" null hypothesis.The significance level for the test is 5%.Report the F statistic (F_stat) for the test.

A)12.68
B)11.62
C)8.66
D)14.35

Question 49

A random sample of size 18 from normal population A has a standard deviation of 25.A random sample of size 8 from normal population B has a standard deviation of 50.You will test the hypothesis that the variance of population A is equal to the variance of population B, using a 10% significance level.Report the critical value of F (F_c) for the test.

A)2.510
B)1.393
C)2.614
D)2.965

Question 50

A factorial design would be the appropriate method to answer which of the following research questions?

A)To determine whether average teacher salaries differ in Ohio, Pennsylvania, and Indiana.
B)To determine whether average teacher salaries differ in Ohio, Pennsylvania, and Indiana, controlling for salary differences across grade level.
C)To determine the effect of an additional year of experience on a teacher's salary.
D)To determine the joint effects of a teacher's field (math, English, etc.) and whether the teacher works in a public school or a private school on a teacher's salary.

Question 51

Crawford Industries purchases step-down electrical converters from two suppliers.The converters from the two suppliers appear to have the same average life (measured in hours) but the variability in useful life appears be different for the the two suppliers.In random samples of 9 converters from supplier A and 9 converters from supplier B, the variance in thesample A was 600; the variance in the sample B was 2800.Assume that the life of the converters is normally distributed in each population.Test the hypothesis that the variances of the two populations are equal, using a significance level of 2%.Report the F statistic (F_stat) for the test.

A)3.160
B)6.178
C)4.667
D)2.965

Question 52

A randomized block design would be the appropriate method to answer which of the following research questions?

A)To determine whether average teacher salaries differ in Ohio, Pennsylvania, and Indiana.
B)To determine whether average teacher salaries differ in Ohio, Pennsylvania, and Indiana, controlling for salary differences across grade level.
C)To determine the effect of an additional year of experience on a teacher's salary.
D)To determine the joint effects of a teacher's field (math, English, etc.) and whether the teacher works in a public school or a private school on a teacher's salary.

Question 53

A random sample of size 15 from normal population A has variance of 800.A second, independent, random sample of size 7 from normal population B has a variance of 1200.You will test a null hypothesis that the variances of the two populations are equal, using a 2% significance level.Report the critical value of F (F_c) for the test, assuming that the large sample variance appears in the numerator of the test statistic.

A)1.50
B)6.013
C)4.456
D)4.142

Question 54

A random sample of size 25 from normal population A has a variance of 110.A random sample of size 5 from normal population B has a variance of 200.You will test the hypothesis that the variance of population A is equal to the variance of population B, using a 2% significance level.Report the F statistic (F_stat) for the test, assuming that the larger sample variance appears in the numerator of the test statistic.

A)4.218
B)3.865
C)2.092
D)1.818

Question 55

A random sample of size 25 from normal population A has a variance of 110.A random sample of size 5 from normal population B has a variance of 200.You will test the hypothesis that the variance of population A is equal to the variance of population B, using a 2% significance level.Report your conclusion.

A)Since F_stat is greater than F_c, we cannot reject the "equal variances" null hypothesis.
B)Since F_stat is less than F_c, we cannot reject the "equal variances" null hypothesis.
C)Since F_stat is less than F_c, we can reject the "equal variances" null hypothesis.
D)Since F_stat is greater than F_c, we can reject the "equal variances" null hypothesis.

Question 56

The ANOVA table below shows partial results for a test of a "no difference in population means" null hypothesis.How many populations are involved in the test?

A)2
B)3
C)4
D)5

Question 57

The ANOVA table below shows partial results for a test of a "no difference in population means" null hypothesis.The significance level for the test is 5%.Compute the F statistic (F_stat) for the test.

A)3.90
B)4.12
C)2.56
D)5.60

Question 58

Crawford Industries purchases step-down electrical converters from two suppliers.The converters from the two suppliers appear to have the same average life (measured in hours) but the variability in useful life appears be different for the units provided by the two suppliers.In random samples of 8 converters from supplier A and 8 converters from supplier B, the standard deviation in sample A was 40 hours; the standard deviation in sample Bwas 55 hours.Assume that transformer life is normally distributed in each population..Test the null hypothesis that population variance B is no greater than the population variance A, against the alternative hypothesis that the population variance B is greater than the population variance A.Use a significance level of 5% for this one-tailed test and report your conclusion.

A)Since F_stat is greater than F_c, we cannot reject the "B no greater than A" null hypothesis.
B)Since F_stat is less than F_c, we can reject the "B no greater than A" null hypothesis.
C)Since F_stat is greater than F_c, we can reject the "B no greater than A" null hypothesis.
D)Since F_stat is less than F_c, we cannot reject the "B no greater than A" null hypothesis

Question 59

A random sample of size 15 selected from normal population A has standard deviation of 80.A second, independent, random sample of size 8 selected from normal population B has a standard deviation of 100.You will test a null hypothesis that the variances of the two populations are equal, using a 2% significance level.Report your conclusion.

A)Since F_stat is greater than F_c, we cannot reject the "equal variances" null hypothesis.
B)Since F_stat is less than F_c, we cannot reject the "equal variances" null hypothesis.
C)Since F_stat is less than F_c, we can reject the "equal variances" null hypothesis.
D)Since F_stat is greater than F_c, we can reject the "equal variances" null hypothesis.

Question 60

A random sample of size 9 is selected from normal population A.A second, independent, random sample of size 6 is selected from normal population B.You test a null hypothesis that the variances of the two populations are equal, using a 10% significance level.The F_stat for your test, calculated as the ratio of the variance of sample A to the variance to the variance of sample B, turns out to be 1.21.Report your conclusion.

A)Since F_stat is greater than F_c, we cannot reject the "equal variances" null hypothesis.
B)Since F_stat is less than F_c, we cannot reject the "equal variances" null hypothesis.
C)Since F_stat is less than F_c, we can reject the "equal variances" null hypothesis.
D)Since F_stat is greater than F_c, we can reject the "equal variances" null hypothesis.

Question 61

Greengrow, Inc.is evaluating three new fertilizer mixes.During a trial period, five similar young plants of equal size were randomly assigned to each fertilizer mix.Plant heights (in centimeters) were measured at the end of the trial period.The tables below summarize (partially) the test results.Use the sample results to test the null hypothesis that average heights for the three populations represented here are the same, using a significance level of 5%.Compute the F value (F_stat) for the test.

A)Since the computed F (F_stat) is greater than the critical F value, we cannot reject the "no difference in population means" null hypothesis.
B)Since the p-value is greater than .025, we can reject the "no difference in population means" null hypothesis.
C)Since the p-value is greater than .05, we cannot reject the "no difference in population means" null hypothesis.
D)Since the computed F (F_stat) is greater than the critical F value, we can reject the "no difference in population means" null hypothesis.

Question 62

Greengrow, Inc.is evaluating three new fertilizer mixes.During a trial period, four young plants of equal size were randomly assigned to each fertilizer mix.Plant heights (in centimeters) at the end of the trial period are shown below: You are to use the sample data to test the null hypothesis that the average heights for the three populations represented here are the same, using a significance level of 5%.Compute the F value (F_stat) for the test and report your conclusion.

A)F_stat = 3.248.Since F_stat is less than the critical F value, we cannot reject the "no difference in population means" null hypothesis.
B)F_stat = 5.655.Since F_stat is greater than the critical F value, we can reject the "no difference in population means" null hypothesis.
C)F_stat = 7.323.Since F_stat is greater than the critical F value, we can reject the "no difference in population means" null hypothesis.
D)F_stat = 0.542.Since F_stat is less than the critical F value, we cannot reject the "no difference in population means" null hypothesis.

Question 63

The golf scores for a sample of 8 rounds of golf for three players are given in the table below, along with sample standard deviations. 18-hole scores
At a 5% significance level, test the hypothesis that the average scores for the three populations are the same., The ANOVA table for the test is shown below.What is your conclusion?

A)Since F_stat is less than 5.800, we can reject the "no difference in population means" null hypothesis.
B)Since the p-value is less than .05, we can reject the "no difference in population means" null hypothesis.
C)Since F_stat is greater than F_c, we cannot reject the "no difference in population means" null hypothesis.
D)Since the p-value is less than .05, we cannot reject the "no difference in population means" null hypothesis.

Question 64

You are conducting a study to compare the characteristics of women and men in senior executive positions at major US corporations.Samples of four senior executive men and four senior executive women are selected.The table below shows the number of years of management experience before promotion to a senior executive position for each of the two samples. At a 5% significance level, you use one-way analysis of variance to test the hypothesis that the average time before promotion is the same in the populations of men and women represented here.Compute the test statistic (F_stat).

A)2.667
B)2.149
C)3.115
D)1.633

Question 65

A test involving three brands of cell phone was conducted to compare the brands with respect to the average number of battery recharges before the battery no longer functioned properly.Ten phones of each brand were tested, with the following results: Number of recharges before battery no longer functions
At a 5% significance level, test the hypothesis that the average maximum number of recharges is equal for the three brands.What is the F statistic (F_stat) for the test?

A)3.391
B)4.962
C)3.520
D)7.250

Question 66

Loomis, Inc.is evaluating three possible bonus incentive programs for its sales staff.During a trial period, a sample of four sales staff was randomly assigned to each bonus program.Individual sales figures (in $1000s) are shown below: Use the sample data to test the null hypothesis that average sales for the three populations represented here are the same, at a significance level of 5%.Report the within group mean square (MSW).

A)8300
B)834.11
C)922.22
D)688.44

Question 67

You are conducting a study to compare the characteristics of women and men in senior executive positions at major US corporations.Samples of four senior executive men and four senior executive women are selected.At a 5% significance level, you use one-way analysis of variance to test the null hypothesis that the average time before promotion is the same for men and women.Report the critical value for F (F_c) that should be used in the test.

A)5.318
B)2.306
C)5.987
D)13.745

Question 68

Greengrow, Inc.is evaluating three new fertilizer mixes.During a trial period, five young plants of equal size were randomly assigned to each fertilizer mix.Plant heights (in centimeters) were measured at the end of the trial period.The tables below summarize (partially) the test results.You are to use the sample results to test the null hypothesis that average heights for the three populations represented here are the same, using a significance level of 5%.Compute the F value (F_stat) for the test.

A)2.411
B)1.957
C)3.725
D)2.571

Question 69

Morton Products is testing three procedures for processing and shipping online orders.In the test, 12 orders were randomly selected.Four of the orders were randomly assigned Procedure 1, four others were assigned Procedure 2, and the remaining four were assigned Procedure 3.Processing/shipping times for each of the three samples are given below: At a 5% significance level, test the null hypothesis that the average processing/shipping times for the three populations are equal..Report the between group sum of squares (SSB).

A)108
B)92
C)64
D)56

Question 70

The golf scores for a sample of 10 rounds of golf for three players are given in the table below, along with sample standard deviations. 18-hole scores
At a 5% significance level, test the hypothesis that the average scores for the three populations are the same.What is the F statistic (F_stat) for the test?

A)4.900
B)8.960
C)10.568
D)7.750

Question 71

Morton Products is testing three procedures for processing and shipping online orders.In the test, 12 orders were randomly selected.Four of the orders were randomly assigned Procedure 1, four others were assigned Procedure 2, and the remaining four were assigned Procedure 3.Processing/shipping times for each of the three samples are given below: At a 5% significance level, test the null hypothesis that the average processing/shipping times for the three populations are the same.Report the between group sum of squares (SSB) for this test.

A)108.00
B)34.67
C)22.89
D)15.33

Question 72

A study is being conducted to compare characteristics of women in senior executive positions and men in senior executive positions at major US corporations.A sample of four senior executive men and four senior executive women is selected.The table below shows the number of years of management experience before promotion to a senior executive position for each of the two samples. You will use a t-test assuming equal population variances (standard deviations) to test the null hypothesis that the average time before promotion in the populations represented here is the same for men and women.The significance level is .05.Report the t-score (t_stat) for the test.

A)2.407
B).920
C)3.115
D)1.633

Question 73

A test involving three brands of cell phone was conducted to compare the brands with respect to the average number of battery recharges before the battery no longer functioned properly.Six phones of each brand were tested, with the following results: Number of recharges before battery no longer functions
At a 5% significance level, test the hypothesis that the average maximum number of possible recharges prior to failure is the same for all three brands.The ANOVA table for the test is shown below.Complete the table and report your conclusion.

A)Since F_stat is greater than 3.682, we cannot reject the "equal population means" null hypothesis.
B)Since the p-value is greater than .05, we can reject the "equal population means" null hypothesis.
C)Since F_stat is greater than F_c, we can reject the "equal population means" null hypothesis.
D)Since the p-value is less than .05, we cannot reject the "equal population means" null hypothesis.

Question 74

You are conducting a study to compare the characteristics of women and men in senior executive positions at major US corporations.Samples of four senior executive men and four senior executive women are selected.The table below shows the number of years of management experience before promotion to a senior executive position for each of the two samples. At a 5% significance level, you conduct a t-test (assuming equal population variances) to test the null hypothesis that the average time before promotion is the same for men and women.The test statistic (t_stat) turns out to be 2.121.Report your conclusion.

A)Since the test statistic is greater in absolute value than the critical t-score for the test, we reject the "no difference" null hypothesis.
B)Since the test statistic is less in absolute value than the critical t-score for the test, we cannot reject the "no difference" null hypothesis
C)Since the test statistic is greater in absolute value than the critical t-score for the test, we cannot reject the "no difference" null hypothesis.
D)Since the test statistic is less in absolute value than the critical t-score for the test, we reject the "no difference" null hypothesis.

Question 75

Kensington, Inc.is evaluating three possible bonus incentive programs for its sales staff.During a trial period, a sample of four sales staff was randomly assigned to each bonus program.Individual sales figures (in $1000s) are shown below: Use the sample data to test the null hypothesis that average sales for the three populations represented here are the same, at a significance level of 5%.Report the between group mean square (MSB).

A)1160
B)1300
C)1020
D)1800

Question 76

You are conducting a study to compare the characteristics of women and men in senior executive positions at major US corporations.Samples of four senior executive men and four senior executive women are selected.At a 5% significance level, you use a t-test assuming equal population variances to test the null hypothesis that the average time before promotion is the same for men and women.Report the critical value for t (t_c) that should be used in the test.

A)2.447
B)2.306
C)3.707
D)3.355

Question 77

You are conducting a study to compare the characteristics of women and men in senior executive positions at major US corporations.Samples of four senior executive men and four senior executive women are selected.At a 5% significance level, At a 5% significance leve, you use one-way analysis of variance to test the null hypothesis that the average time before promotion is the same for men and women.The tables below show partial results.Report the test statistic (F_stat).

A)6.320
B)2.496
C)5.467
D)8.000

Question 78

Morton Products is testing three procedures for processing and shipping online orders.In the test, 12 orders were randomly selected.Four of the orders were randomly assigned Procedure 1, four others were assigned Procedure 2, and the remaining four were assigned Procedure 3.Processing/shipping times for each of the three samples are given below: At a 5% significance level, test the null hypothesis that the average processing/shipping times for the three populations are equal.Report the between group sum of squares (SSB) for this test.

A)144
B)56
C)24
D)68

Question 79

Loomis, Inc.is evaluating three possible bonus incentive programs for its sales staff.During a trial period, a sample of four sales staff was randomly assigned to each bonus program.Sales figures (in $1000) are shown below: Use the sample data to test the null hypothesis that the average sales for the three populations represented here are the same, using a significance level of 5%.Report the F value (F_stat) for the test.

A)4.151
B)3.236
C)5.197
D)2.305

Question 80

Morton Products is testing three procedures for processing and shipping online orders.In the test, 12 orders were randomly selected.Four of the orders were randomly assigned Procedure 1, four others were assigned Procedure 2, and the remaining four were assigned Procedure 3.Processing/shipping times for each of the three samples are given below: At a 5% significance level, test the null hypothesis that the average processing/shipping times for the three are equal.Report the within group sum of squares (SSW) for this test.

A)104
B)56
C)82
D)94