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Question: #1748

13.2 The F Distribution and the F-Ratio

Suppose a group is interested in determining whether teenagers obtain their drivers licenses at approximately the same average age across the country. Suppose that the following data are randomly collected from five teenagers in each region of the country. The numbers represent the age at which teenagers obtained their drivers licenses. (For next two problems)

H0: μ1 = μ2 = μ3 = μ4 = μ5

Hα: At least any two of the group means μ1, μ2, …, μ5 are not equal.

Northeast South West Central East
16.3 16.9 16.4 16.2 17.1
16.1 16.5 16.5 16.6 17.2
16.4 16.4 16.6 16.5 16.6
16.5 16.2 16.1 16.4 16.8
X¯= ________ ________ ________ ________ ________
s2 = ________ ________ ________ ________ ________

Q1.) Solve for x̄ and s²Above

Q1a.) Degrees of freedom – numerator: df(num) = _________

Q2.) F statistic = ________

Q3.) A researcher wants to know if the mean times (in minutes) that people watch their favorite news station are the same. Suppose that shows the results of a study.

Assume that all distributions are normal, the four population standard deviations are approximately the same, and the data were collected independently and randomly. Use a level of significance of 0.05.

CNN FOX Local
45 15 72
12 43 37
18 68 56
38 50 60
23 31 51
35 22

Q4.) Are the mean number of times a month a person eats out the same for whites, blacks, Hispanics and Asians? Suppose that shows the results of a study.

White Black Hispanic Asian
6 4 7 8
8 1 3 3
2 5 5 5
4 2 4 1
6 6 7