F Test Statistic


a. If s2,1 represents the larger of two sample variances, can the F test statistic ever be less than 1?

Which statement about the $F$-distribution is always true?

Two machines produce metal rods. You take independent random samples of their lengths (shown below) as part of a hypothesis test. Calculate the F statistic for this test.

Sample A: $s^2=2.1,n=10$

Sample B: $s^2=4.2,n=12$

In a two-sample Hypothesis Test for Variance, what does an $F$-statistic near 1 indicate?

F Test Statistic

b. Can the F test statistic ever be a negative number?

F Test Statistic

c. If testing the claim that sigma2,1 is not equals to sigma2,2 what do we know about the two samples if the test statistic F is very close to 1?

Test for Normality For the hypothesis test described in Exercise 2, the sample sizes are n1 = 2208 and n2 = 1986 When using the F test with these data, is it correct to reason that there is no need to check for normality because both samples have sizes that are greater than 30?

Color and Creativity Researchers from the University of British Columbia conducted trials to investigate the effects of color on creativity. Subjects with a red background were asked to think of creative uses for a brick; other subjects with a blue background were given the same task. Responses were scored by a panel of judges and results from scores of creativity are given below. Use a 0.05 significance level to test the claim that creative task scores have the same variation with a red background and a blue background.

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