Exam 14: Analysis of Categorical Data

A study was conducted to determine whether opinion concerning the addition of seat belts in school buses is independent of the population density in which a person resides. The following data was recorded: Use the following output generated using Minitab to answer the questions below. What is ? ______________ What is the p-value associated with the test? ______________ Conclude that opinion concerning the addition of seat belts to school buses is ______________ the population density where the person resides.

A total of 200 people in each of three grocery stores were asked if they favored, opposed, or were indifferent to the sale of lottery tickets in grocery stores. The results of the survey are summarized below. Use the MINITAB computer output shown here to conduct a chi-square test of independence at = 0.05. The data show that one should ______________ . Thus we ______________ conclude that the two variables are dependent; that is, the opinion of people is not the same at the three stores.

The president of a state university collected data from students concerning building a new library, and classified the responses into different categories (strongly agree, agree, undecided, disagree, strongly disagree) and according to whether the student was male or female. To determine whether the data provide sufficient evidence to indicate that the responses depend upon gender, the most appropriate test is:

The chi-square test of independence is based upon:

If each element in a population is classified into one and only one of several categories, the population is:

Suppose that a response can fall into one of k = 5 categories with probabilities , and that n = 250 responses produced these category counts: Are the five categories equally likely to occur? If you were to test this hypothesis using the chi-square statistic, how many degrees of freedom would the test have? ______________ Compute : ______________ Reject when > ______________. Conclude that the five salespersons ______________ equally like to sell cars.

A chi-square goodness-of-fit test is always conducted as a two-tail test.

A pollster was interested in determining whether three television dramas are equally preferable among men and women. The following data was recorded: Compute = ______________ Reject when > ______________. Conclude that the preference of television drama is ______________ the viewer's gender.

The chi-square technique is a statistical technique for testing the alleged independence of two qualitative variables, making inferences about the relative sizes of more than two population proportions, and conducting goodness-of-fit tests to assess the plausibility that sample data come from a population that conforms to a specified probability distribution.

A casino customer is concerned about whether the dice the casino are using are "fair" (i.e., each face is equally likely to appear). The customer obtains a die that is being used by the casino and rolls it 240 times. The customer records the following data: Compute the value of the test statistic. = ______________ Set up the appropriate rejection region for = 0.10. Reject when > ______________. What is the appropriate conclusion? We ______________ conclude that the die is fair.

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

Which of the following statements about the chi-square distribution is false?

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. The most accurate statement that can be made about the p-value for this test is that:

In a goodness-of-fit test, suppose that a sample showed that the observed frequency and expected frequency were equal for each cell i. Then, the null hypothesis is:

By combining cells that have expected frequencies smaller than 5, we guard against having an inflated test statistic that could have led us to incorrectly accept the null hypothesis.

Which of the following is not a characteristic of a multinomial experiment?

The four most popular flavors 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 flavors is equally preferred. To answer that question, a random sample of 160 sales was selected, yielding the following data: Compute the value of the test statistic. What is ? ______________ Set up the appropriate rejection region for = 0.05. Reject when > ______________. What is the appropriate conclusion? Conclude that the ice cream flavors ______________ equally preferred.

In 2003, Brand A microwaves had 45% of the market, Brand B had 35%, and Brand C had 20%. This year the makers of Brand C launched a heavy advertising campaign. A random sample of appliance stores shows that of 10,000 microwaves sold, 4350 were Brand A, 3450 were Brand B, and 2200 were Brand C. Has the market changed? Test at = 0.01. = ______________ Critical Value(s) = ______________ Conclusion: ______________ The market ______________ changed since 2003.

When either the row or column totals in a contingency table are fixed, the test of independence of classifications becomes a test of the homogeneity of cell probabilities for several multinomial experiments.

The goodness-of-fit test is a two-way classification will cell probabilities specified in .