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Exam 13: F Tests and Analysis of Variance

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Question 41

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One-way analysis of variance is being used to test the equality of three population means using a sample of size 8 from each of the three populations.How many degrees of freedom are associated with the within groups sum of squares (SSW) ?

A) 18
B) 21
C) 24
D) 27

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Question 42

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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.

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Question 43

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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.

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

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?

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.

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.

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?

An investor would like to compare the volatility (variance) of the returns on international bonds to the volatility of the return of domestic bonds.A random sample of 10 international bonds (population 1) have average returns of 5.2% with a standard deviation of 3.2%.A random sample of 10 domestic bonds (population 2) have average returns of 3.6% with a standard deviation of 1.2%.The investor assumes that bond returns follow a normal distribution in both populations. She uses the data to test the following hypotheses: H₀: σ₁² = σ₂² (the population variances are equal) H_A: σ₁² ≠ σ₂² (the population variances are not equal) At a 10% significance level, what is the conclusion of the hypothesis test?

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?

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).

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.

One-way analysis of variance is being used to test the equality of four population means using a sample of size 8 from each of the four populations.The test statistic (F_stat) for the test turns out to be 3.991.The significance level is set at 5%.Report your conclusion.

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.

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

One-way analysis of variance is being used to test the equality of four population means using a sample of size 7 from each of the four populations.The significance level is set at 1%.What is the critical value of (Fc) that should be used for the test?

One-way analysis of variance is being used to test the equality of two population means using a sample of size 10 from the first population and a sample of size 12 from the second population.The test statistic (F_stat) turns out to be 5.160.If an equivalent t test had been used to test the "no difference in population means" null hypothesis, what would be the test statistic (t_stat) for the t test?

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) .

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

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 _____.