STAT 200 Week 8 Homework Assignment Solution
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STAT 200 Week 8 Homework Assignment Solution Lane – Chapter 15 Illowsky – Chapter 13 Problem #1 (40 points) 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. The null hypothesis is all group means are equal. The alternate hypothesis is that any two group means are not equal. Northeast 16.3 16.1 16.4 16.5
South 16.9 16.5 16.4 16.2
West 16.4 16.5 16.6 16.1
Central 16.2 16.6 16.5 16.4
East 17.1 17.2 16.6 16.8
Mean Variance Find the F-statistic using an ANOVA table. In order to receive full credit, you need to show your values of group mean and group variance (table above), grand mean (below), and all of the values in the ANOVA table (below). Grand Mean =
Source of Variation
Sum of Squares (SS)
Mean Degrees of Square Freedom (df) (MS)
F-Statistic
Factor (Between) Error (Within) Total HINT: In order to create an ANOVA table, you will need to follow examples 13.1 and 13.2 in your Illowsky book. At the end of this homework assignment, there is also another detailed example. DO NOT calculate the SSwithin by hand. Use EXCEL (or calculate by hand) the value for SStotal and then calculate the value for SSbetween. The value of SSwithin = SStotal – SSbetween.
Problem #2 (20 points) A study of 3 different groups of 8 employees (24 people total) were surveyed to determine their daily commuting mileage. The boss wants to test the claim that the commuting mileage is the same for each group. Complete the ANOVA table with the missing information
Source of Variation
Sum of Squares (SS)
Factor 3034 (Between) Error (Within) Total 6535
Mean Degrees of Square Freedom (df) (MS)
F-Statistic
23
Problem #3 (40 points) Saturday 10 120 94 20 73
Sunday 58 61 19 99 60
Mean Variance We would like to test if there is any variation in spending at a mall between Saturday and Sunday. The table shows the results of a study. Assume a 10% significance level. HINT: See Section 13.4 (Test of Two Variances) in the Illowsky book to find the F-statistic. Assume the null hypothesis is the variances are the same and assume the alternate hypothesis is the variances are not the same. So, you will use a two-tail probability. Should we accept or reject the null hypothesis?
Example: Calculations in the Analysis of Variance (ANOVA)
Example Solution Table
P-value using F-distribution (use EXCEL formula) FDIST (F, df1, df2) = FDIST(9.085,4,45) = 0.00001815