Exam 14: Analysis of Categorical Data

A contingency table test with 4 rows and 15 degrees of freedom implies:

If there are more than two row categories in a contingency table with fixed c column totals, then the test of independence is equivalent to a test of the equality of c sets of multinomial proportions.

To determine the critical values in the chi-square distribution table, the process requires the following:

When there are only 2 categories in a multinomial experiment, the experiment reduces to a binomial experiment.

In 2003, the student body of a state university in Michigan consists of 30% freshmen, 25% sophomores, 27% juniors, and 18% seniors. A sample of 400 students taken from the 2004 student body showed that there are 138 freshmen, 88 sophomores, 94 juniors, and 80 seniors. Test with 5% significance level to determine whether the student body proportions have changed. = ______________ Critical Value = ______________ Conclusion: ______________ The student body proportions ______________ changed since 2003.

The number of degrees of freedom for a contingency table with 6 rows and 6 columns is:

A contingency table:

In a chi-square test of independence, the value of the test statistic was 15.652, and the critical value at was 11.1433. Thus, we must reject the null hypothesis at .

A sports enthusiast believes that among sports television viewers 60% prefer to watch football, 25% prefer basketball and 15% prefer hockey. A random sample of 120 viewers was selected and the following data recorded: Perform the appropriate test of hypothesis to determine whether the percentages are correct. Use = 0.05. Compute : ______________ Reject when > ______________. Conclude that the data support the stated percentages; that is, the sports enthusiast's belief ______________ correct.

In a typical chi-square test of independence, we calculate each expected cell frequency ( ) as the product of row total ( ) times column total ( ) times sample size (n).

A chi-square goodness-of-fit test is always conducted as:

Chi-square tests of independence are always lower-tailed because a perfect fit between and makes the test statistic equal to zero.

Which statistical technique is appropriate when we wish to analyze the relationship between two qualitative variables with two or more categories?

A contingency table classifies data with respect to two qualitative variables that are each divided into two or more categories.

In a chi-square goodness-of- fit test with 5 degrees of freedom and a significance level of 0.05, the chi-square value from the table is 11.0705. Which of the following computed values of the chi-square test statistic will lead to rejection of the null hypothesis?

To be valid, a chi-square test of independence requires that each expected frequency equal 30 or more.

In applying the chi-square goodness-of-fit test, the rule of thumb for all expected frequencies is that each expected frequency is 5 or more.

If the expected frequency for any cell i is less than 5, we:

If we wish to determine whether there is evidence that the proportion of successes is higher in group 1 than in group 2, the appropriate test to use is the:

The personnel manager of a consumer product company asked a random sample of employees how they felt about the work they were doing. The following table gives a breakdown of their responses by gender. Do the data provide sufficient evidence to conclude that the level of job satisfaction is related to gender? Conduct the test at the 0.10 level of significance. Test statistic = ______________ Critical Value(s) = ______________ Conclusion: ______________ The data provide ______________ evidence to conclude that the level of job satisfaction is related to gender.