Bluman A.G. Elementary Statistics- A Step By Step Approach

Important Terms 621Example XL11–3Using a significance level a 0.05, determine whether the number of years of college aperson has completed is related to residence.1. Enter the location variable labels in column A, beginning at cell A2.2. Enter the categories for the number of years of college in cells B1, C1, and D1, respectively.3. Enter the observed values in the appropriate block (cell).4. From the toolbar, select Add-Ins, MegaStat>Chi-Square/Crosstab>ContingencyTable. Note: You may need to open MegaStat from the MegaStat.xls file on yourcomputer’s hard drive.5. In the dialog box, type A1:D4 for the Input range.6. Check chi-square from the Output Options.7. Click [OK].Chi-Square Contingency Table Test for IndependenceNone 4-year Advanced TotalUrban 15 12 8 35Suburban 8 15 9 32Rural 6 8 7 21Total 29 35 24 883.01 chi-square4df.5569 P-valueThe results of the test indicate that at the 5% level of significance, there is not enough evidenceto conclude that a person’s location is dependent on number of years of college.Summary• Three uses of the chi-square distribution were explained in this chapter. It can beused as a goodness-of-fit test to determine whether the frequencies of a distributionare the same as the hypothesized frequencies. For example, is the number ofdefective parts produced by a factory the same each day? This test is always a righttailedtest. (11–1)• The test of independence is used to determine whether two variables are related orare independent. This test uses a contingency table and is always a right-tailed test.An example of its use is a test to determine whether the attitudes of urban residentsabout the recycling of trash differ from the attitudes of rural residents. (11–2)• Finally, the homogeneity of proportions test is used to determine if several proportionsare all equal when samples are selected from different populations. (11–2)The chi-square distribution is also used for other types of statistical hypothesistests, such as the Kruskal-Wallis test, which is explained in Chapter 13.Important Termscontingency table 606expected frequency 593goodness-of-fit test 593homogeneity ofproportions test 611independence test 606 observed frequency 59311–31