Exam 14: Analysis of Categorical Data

Preferred Television Drama Narrative A pollster was interested in determining whether three television dramas are equally preferred by men and women. The following data were recorded: Preference -A marketing research professor at Simon Fraser 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 were recorded: Perform the appropriate test of hypothesis using = 0.10.

Peony Plants Narrative A peony plant with red petals was crossed with another plant having streaky petals. A geneticist states that 80% of the offspring from this cross will have red flowers. To test this claim, 100 seeds from this cross were collected and germinated, and 65 plants had red petals. -Refer to Peony Plants Narrative. Use the chi-square goodness-of-fit test to determine whether the sample data confirm the geneticist's prediction. Find the approximate p-value and use it to make your decision.

If we want to perform a two-tailed test for differences between two populations of nominal data with exactly two categories, we can employ either the z test of , or the chi-square test of homogeneity, since squaring the value of the z statistic yields the value of statistics.

A major insurance firm interviewed a random sample of 1200 university students to find out the type of life insurance preferred, if any. The results follow: Is there evidence that life insurance preference of male students is different than that of female students? Explain. Test using the 5% level of significance.

The chi-square test statistic for a contingency table with r rows and c columns can be negative if r is much smaller than c.

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, what may one conclude about the null hypothesis?

Ice Cream Flavours Narrative The four most popular flavours of a particular brand of ice cream are French vanilla, natural vanilla, chocolate chip, and caramel almond swirl. The question arose as to whether each of these flavours is equally preferred. To answer that question, a random sample of 160 sales was selected, yielding the following data: -Refer to Ice Cream Flavours Narrative. What is the appropriate conclusion?

Ink Pen Colours Narrative A national survey stated that 30% of the population prefer to use a pen with black ink, 30% prefer blue ink, 25% prefer red ink, and 15% prefer some other colour. A statistics professor took a random sample of 80 students and asked them to state their ink colour preference. The following data was recorded: -Refer to Ink Pen Colours Narrative. Set up the appropriate rejection region for $\alpha$ = 0.05.

Preferred Television Drama Narrative A pollster was interested in determining whether three television dramas are equally preferred by men and women. The following data were recorded: Preference -Refer to Preferred Television Drama Narrative. State the null and alternative hypotheses.

If the test statistic for a chi-square goodness-of-fit test is larger than the critical value, the null hypothesis should be rejected.

By combining cells that have expected frequencies smaller than five, we guard against having an inflated test statistic that could have led us to incorrectly accept the null hypothesis.

Preferred Television Drama Narrative A pollster was interested in determining whether three television dramas are equally preferred by men and women. The following data were recorded: Preference -Refer to Preferred Television Drama Narrative. What is the appropriate conclusion? Explain.

A chi-square test of a contingency table with 4 rows and 5 columns shows that the value of the test statistic is 22.18. Which of the following is the most accurate statement that can be made about the p-value for this test?

Which of the following best describes the sampling distribution of the test statistic for a goodness-of-fit test with k categories?

Consider a cell in a contingency table. Given the cell's row total of 80, the cell's column total of 60, and a sample size of 250, what is the cell's expected frequency?

What summary data does a contingency table contain?

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? Explain. Conduct the test at the 0.10 level of significance.

A chi-square test for independence with 6 degrees of freedom results in a test statistic of 13.25. Using the chi-square table, the most accurate statement that can be made about the p-value for this test is that p-value is greater than 0.025 but smaller than 0.05.

The chi-square test of a contingency table is used to determine if there is enough evidence to infer that two nominal variables are related, and to infer that differences exist among two or more populations of nominal variables.

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