wk 8
dsmwnewng
stat200wk8.docxUMUC STAT-200 Homework Week #8
Dr. Brian Killough
The assignment must be completed before the start of the Final Exam on Thursday at midnight.
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.
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Northeast |
South |
West |
Central |
East |
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16.3 |
16.9 |
16.4 |
16.2 |
17.1 |
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16.1 |
16.5 |
16.5 |
16.6 |
17.2 |
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16.4 |
16.4 |
16.6 |
16.5 |
16.6 |
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16.5 |
16.2 |
16.1 |
16.4 |
16.8 |
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Mean |
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Variance |
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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 =
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Source of Variation |
Sum of Squares (SS) |
Degrees of Freedom (df) |
Mean Square (MS) |
F-Statistic |
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Factor (Between) |
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Error (Within) |
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Total |
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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
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Source of Variation |
Sum of Squares (SS) |
Degrees of Freedom (df) |
Mean Square (MS) |
F-Statistic |
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Factor (Between) |
3034 |
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Error (Within) |
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Total |
6535 |
23 |
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Problem #3 (40 points)
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Saturday |
Sunday |
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10 |
58 |
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120 |
61 |
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94 |
19 |
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20 |
99 |
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73 |
60 |
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Mean |
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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
