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# Chi-Square test for independence and ANOVA

1. Use the given contingency table to
(a) find the expected frequencies of each cell in the table,
(b) perform a chi-square test for independence, and
(c) comment on the relationship between the two variables.
Assume the variables are independent.

The contingency table shows the results of a random sample of 500 individuals classified by gender and type of vehicle owned. Use ? = 0.01.

Type of vehicle owned
Gender Car Truck SUV Van
Male 90 100 50 7
Female 110 75 65 3

2. A researcher wanted to investigate whether there is a significant difference in the average age of instructors, assistant professors, associate professors, and full professors at a university. The faculty was selected at random and their ages were recorded. Use the collected data to complete the ANOVA chart given below.

Raw Data
Instructors Assistant Professors Associate Professors Professors
26 28 45 58
32 32 48 56
29 36 52 62
36 45 54 65
40 50 62 52
45 46 65 49

ANOVA Summary
Source of Variation/ Sum of Squares/ Degrees of freedom Variation/ F Value/Fcr Between-Groups / / 3 / 12.88 /3.10
Within-Groups / 1120.17 / /

Total / 3283.63 / 23 /

#### Solution Summary

This solution is comprised of a detailed explanation of Chi-Square test for independence and ANOVA with the help of excel. In this solution, step-by-step explanation of this complicated topic provides students with a clear perspective of Chi-Square test for independence and ANOVA with the interpretation of results.

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