Assignment:
Q1. A research firm wants to compare the miles per gallon of unleaded regular, mid-grade, and super premium gasoline. Because of differences in the performance of different automobiles, seven different automobiles were selected and treated as blocks. Therefore, each brand of gasoline was tested with each type of automobile. The results of the trials, in miles per gallon, are shown in the following table. At the .05 significance level, is there a difference in the gasoline and automobiles?
Automobile Regular Mid-grade Super Premium
1 21 23 26
2 23 22 25
3 24 25 27
4 24 24 26
5 26 26 30
6 26 24 27
7 28 27 32
Q2. A sample of employees at a large chemical plant was asked to indicate a preference for one of three pension plans. The results are given in the following table. Does it seem that there is a relationship between the pension plan selected and the job classification of the employees? Use the .01 significance level.
PENSION PLAN
JOB CLASSIFICATION PLAN A PLAN B PLAN C
SUPERVISOR 10 13 29
CLERICAL 19 80 19
LABOR 81 57 22
State the hypotheses, show how the degrees of freedom are calculated, find the critical value of chisquare or from Excel's function =CHIINV(alpha, deg_freedom), and interpret the p-value. Tell whether the conclusion is sensitive to the level of significance chosen, identify cells that contribute the most to the chi-square test statistic, and check for small expected frequencies. If necessary, you can calculate the p-value by using Excel's function =CHIDIST(test statistic,deg_freedom).
Q3 Sixty-four students in an introductory college economics class were asked how many credits they had earned in college, and how certain they were about their choice of major. Research question: At α = .01, is the degree of certainty independent of credits earned?
Credits Earned Very Uncertain Somewhat Certain Very Certain Row Total
0-9 12 8 3 23
10-59 8 4 10 22
60 or more 1 7 11 19
Col Total 21 19 24 64