STAT 200 Week 8 Homework Assignment Solution

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 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
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) Degrees of Freedom (df) Mean Square (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) Degrees of Freedom (df) Mean Square (MS) F-Statistic
Factor (Between) 3034  
Error (Within)
Total  6535  23

 

 

Problem #3 (40 points)

 

Saturday Sunday
10 58
120 61
94 19
20 99
73 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