The High School and Beyond study is from a large-scale longitudinal study conducted by the National Opinion Research Center under contract with the National Center for Education Statistics. Below is a table (note: this is called summarized data!) representing a sample of 100 students from this data that includes the student's gender and whether the high school they attended was public or private. Perform a Chi-square analysis of independence for this data. For Minitab and SPSS users you will first need to enter this data into your worksheet. [Special Note: Recall from the probability lesson this would be a test of independence: that is, can we say that the probability of being Female is independent of the probability that school type is public?]
Minitab users: you can just enter the counts as displayed below with 38 and 46 being in the first two cells of C1 and 7 and 9 being in the first two cells of C2. For Minitab users (Stat > Tables > Table in Worksheet)
SPSS users: after opening SPSS you need to enter the counts in first column (e.g. 38, 46, 7, 9), then in second column type in Female or Male depending on which gender the number relates to (e.g. Female, Male, Female, Male) and make sure you spell each correctly and using consistent casing, i.e. capitalization. Finally in third column type in school type for that count (note SPSS defaults to 6 letters) (e.g. Pu, Pu, Pr, Pr). Then go to Data > Weight cases > click radio button for Weight cases and enter the column containing the counts. Now do chi-square test by Analyze > Descriptives > Crosstabs.
Public Private Total
Female 38 7 45
Male 46 9 55
Total 84 16 100
(i) Complete following table using conditional percents (this would be the row percents),
Public Private Total
Female
Male
Total
(ii) based on the percents, discuss the nature of any relationship, and
(iii) from the chi-square test, state a clear conclusion for this test of significance.