Exam 14: Analysis of Categorical Data

A statistics professor posted the following grade distribution guidelines for his elementary statistics class: 8% A, 35% B, 40% C, 12% D, and 5% F. A sample of 100 elementary statistics grades at the end of last semester showed 12 As, 30 Bs, 35 Cs, 15 Ds, and 8 Fs. Test at the 5% significance level to determine whether the actual grades deviate significantly from the posted grade distribution guidelines. = ______________ Critical Value = ______________ Conclusion: ______________ The actual grades ______________ from the posted grade distribution guidelines.

A study of educational levels of 500 voters and their political party affiliations in a southern state in the USA showed the following results: Use the 1% level of significance and test to see if party affiliation is independent of the educational level of the voters. = ______________ Critical Value = ______________ Conclusion: ______________ Political party affiliation ______________ on the educational level of the voters.

In a goodness-of-fit test, suppose that the value of the test statistic is 11.89 and the degrees of freedom are 5. At the 5% significance level, the null hypothesis is:

A left-tailed area in the chi-square distribution equals 0.10. For 5 degrees of freedom the table value equals 9.23635.

A chi-square test for independence is applied to a contingency table with 3 rows and 4 columns for two qualitative variables. The degrees of freedom for this test must be 12.

A sport preference poll showed the following data for men and women: Use the 5% level of significance and test to determine whether sport preferences depend on gender. = ______________ Critical Value = ______________ Conclusion: ______________ Sport preferences ______________ on gender.

Contingency tables are used in:

In a goodness-of-fit test, suppose that the value of the test statistic is 13.08 and the number of degrees of freedom is 6. At the 5% significance level, the null hypothesis is:

A contingency table classifies data according to two or more categories associated with each of two qualitative variables that are statistically independent of one another.

Historically, a bank has employed 50% permanent full-time workers, 25% permanent part-time workers, 15% temporary full-time workers, and 10% temporary part-time workers. In a recent sample of 400 workers, 190 were permanent full-time, 125 were permanent part-time, 55 were temporary full-time, and 30 were temporary part-time. Use these data and = 0.05 to assess whether there has been a change from the historical percentages. Find : ______________ This shows that one should ______________ . Conclude that ______________ from the historical expectation.

Of the values for a chi-square test statistic listed below, which one is likely to lead to rejecting the null hypothesis in a goodness-of-fit test?

Numbers in a contingency table show the frequency of occurrence of all possible combinations of categories.

Tests of homogeneity are used to compare several binomial populations.

A chi-square goodness-of-fit test with 3 degrees of freedom results in a test statistic of 6.789. Using the chi-square table, the most accurate statement that can be made about the p-value for this test is that 0.05 < p-value < 0.10.

A marketing research professor at Ferris State University conducted a survey to determine whether mode of transportation to the university and the person's position at the university were independent. The following data was recorded: Perform the appropriate test of hypothesis using = 0.10. Compute = ______________ Reject when > ______________. Conclude that the mode of transportation to the university and person's position at the university are ______________.

Which statistical technique is appropriate when we describe a single population of qualitative data with two or more categories?

Whenever the expected frequency of a cell is less than 5, one remedy for this condition is to increase the size of the sample.

The data that result from two binomial experiment can be displayed as a two-way classification with 2 rows and 2 columns, so that the chi-square test of homogeneity can be used to compare the two binomial proportions and .

The large-sample z tests for one and two binomial proportions are special cases of the chi-square statistic.

The total degrees of freedom for an r x c (fixed-column) contingency table are rc + 1.