Chi-Square Analysis Worksheet MTH 160: Statistics

Suppose the local state university wants to determine whetherthere is a relationship between a student’s gender and a student’smajor in college. The registrar was asked to randomly select 55students and record their gender and major. The majors were groupedinto categories of Natural Science (NS), Social Sciences (SS), andHumanities (H). Answer the following questions based on the resultsin the table below.

NS SS H Total

Men 11 9 3 23

Wom 9 13 10 32

Total 20 22 13 55

Part I: 1. Determine the expected frequency for each of thecells within the table.

2. Compute the sample chi-square statistic from the contingencytable. 3. Conduct a chi-square test of independence to determinewhether there is a relationship between gender and college majors.Show all of your work to support your chi-square test. 4. Whatconclusion can be determined from the results of the chi-squaretest? Part II:

Suppose we are only interested in the college majors of thewomen in our study. We would like to compare our sample to thenational percentage of women majoring in each of the categories(NS, SS, and H) and determine whether the sample distribution fitsthe national distribution. Suppose the national percentage of womenmajoring in Natural Sciences is 22%, majoring in Social Sciences is28%, and majoring in the Humanities is 30%.

NS SS H Total

Women 9 13 10 32

1.Conduct a chi-square goodness-of-fit test to determine whetherour sample data fits the national distribution. Show all of yourwork to support your chi-square test.

2. What conclusion can be determined from the results of thechi-square test?