Exam 13: F Tests and Analysis of Variance

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.

One-way analysis of variance is being used to test the equality of three population means using samples of size 8 from the first population, 11 from the second population and 7 from the third population.The test statistic (F_stat) is 2.712.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 equal..Report the between group sum of squares (SSB).

Eva would like to determine whether her running pace is more consistent in the afternoon than in the morning.A sample of 10 morning runs (from population 1) has an average pace of 7 minutes, 32 seconds per mile, with a standard deviation of 45 seconds per mile.A sample of 12 afternoon runs (from population 2) has an average pace of 7 minutes, 20 seconds per mile, with a standard deviation of 32 seconds per mile.She assumes that her running times follow a normal distribution in both populations. She uses the data to test the following hypotheses: H₀: σ₁² ≤ σ₂² (the morning variance is less than or equal to the afternoon variance) H_A: σ₁² > σ₂² (the morning variance is greater than the afternoon variance) At a 5% significance level, what is the conclusion of the hypothesis test?

One-way analysis of variance is being used to test the equality of four population means using a sample of size 6 from each of the four populations.The test statistic (F_stat) for the test turns out to be 3.237.The significance level is set at 5%.Report your conclusion.

An investor would like to compare the volatility (variance) of the returns on international bonds to that of domestic bonds.A random sample of 10 international bonds (from population 1) has average returns of 5.2 percent with a standard deviation of 3.2 percent.A random sample of 10 domestic bonds (from population 2) has average returns of 3.6 percent with a standard deviation of 1.2 percent.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) What is the value of the test statistic, F_stat?

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.

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

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.

The dependent variable in an experiment is called the

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.

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 ______.

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).

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 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.

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

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.

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 major hardware store chain has three large stores in the city.Random samples of the daily sales of the three stores (in $1,000s) are shown below: At a significance level of 5%, you use the sample data to test the null hypothesis that average sales for the three populations represented here are the same, What is the between group sum of squares for the 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.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.