A researcher would like to know which factors are most important to people who are buying a new car. A sample of n = 200 customers between the ages of 20 and 29 are asked to identify the most important factor in the decision process: Performance, Reliability, or Style. The researcher would like to know whether there is a difference between the factors identified by women compared to those identified by men. The data are as follows: Observed Frequencies of Most Important factor According to Gender   Performance Reliability Style Totals Male 21 33 26 80 Female 19 67 34 120 Totals 40 100 60 n=200 a) State the null and alternative hypothesis. b) Determine the degrees of freedom and Chi square statistic when alpha = 0.05

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.6: Summarizing Categorical Data
Problem 10CYU
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A researcher would like to know which factors are most important to people who are buying a new car. A sample of n = 200 customers between the ages of 20 and 29 are asked to identify the most important factor in the decision process:

Performance, Reliability, or Style.

The researcher would like to know whether there is a difference between the factors identified by women compared to those identified by men. The data are as follows:

Observed Frequencies of Most Important factor According to Gender

  Performance Reliability Style Totals
Male 21 33 26 80
Female 19 67 34 120
Totals 40 100 60 n=200

a) State the null and alternative hypothesis.

b) Determine the degrees of freedom and Chi square statistic when alpha = 0.05

What are the expected frequencies?  For Performance, the total is 40, so we divide the total in performance by the total in the sample - 40/200 = .2, or 20%. Then we apply that percentage to the Males to get the first cell for Performance and Males. 80 X .2 = 16. 16 is the expected frequency for Performance and Males. 

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