Exam 14: Analysis of Categorical Data

Ages of National College Students Narrative A national survey states that 67% of college students are under the age of 25, 21% are between the ages of 25 and 30, 8% are between 30 and 40, and 4% are over 40. A random sample of 250 students at Vanier College in Montreal yielded the following data: -Refer to Ages of National College Students Narrative. Set up the appropriate rejection region for = 0.05.

A firm has been accused of engaging in prejudicial hiring practices. According to the most recent census, the percentages of whites, blacks, and Asians in a certain community are 72%, 10%, and 18%, respectively. A random sample of 200 employees of the firm revealed that 165 were white, 14 were black, and 21 were Asian. Do the data provide sufficient evidence to conclude at the 5% level of significance that the firm has been engaged in prejudicial hiring practices? Justify your conclusion.

Suppose that a response can fall into one of k = 5 categories with probabilities , and that n = 250 responses produced these category counts: The categories represent five car salespersons, and the observed frequencies represent the number of cars sold in a six-month period. -Refer to Car Sales Narrative. Are the five categories equally likely to occur? Specify the hypotheses of interest.

Seat Belts On School Buses Narrative 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 were recorded: Local Use the following output generated using statistical software to answer the questions below. Chi-Square Test Expected counts are printed below observed counts Chi-Sq = 0.003 + 0.402 + 0.393 + 0.099 + 0.000 + 0.101 + 0.152 + 2.016 + 0.837 = 4.003 DF = 4, P-Value = 0.406 -Refer to Seat Belts On School Buses Narrative. What is the appropriate conclusion at the 0.05 level of significance? Explain.

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. Set up the appropriate rejection region for = 0.05.

A multinomial experiment, where the outcome of each trial can be classified into one of two categories, is identical to a binomial experiment.

The degrees of freedom associated with a chi-square test of independence where data are summarized in a contingency table with r rows and c columns equal the number of rows times the number of columns in the table; that is, rc.

The following table shows the results of a study in which random samples of 200 members of each of five large unions were asked whether they are for, undecided, or against a certain piece of legislation. Use the 0.025 level of significance to test whether the unions differ with respect to their views.

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. Compute the value of the test statistic.

A cafeteria proposes to serve four main entrees. For planning purposes, the manager expects that the proportions of each that will be selected by his customers will be Of the first 100 customers, 44 selected chicken, 24 selected roast beef, 13 selected steak, and 10 selected fish. Should the manager revise his estimates? Justify your conclusion. (Use = 0.01.)

The chi-square test of independence is based upon three or more quantitative variables.

A chi-square test for independence with 10 degrees of freedom results in a test statistic of 17.894. 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.

In a goodness-of-fit test, suppose that a sample showed that the observed frequency and the expected frequency were equal for each cell i. Using this information, what may one conclude about the null hypothesis?

The degrees of freedom associated with a contingency table test of independence equal the number of rows times the number of columns in the table.

A study of education levels of 500 voters and their political party affiliations in a western province 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.

A goodness-of-fit test determines the likelihood that sample data have been generated from a population that conforms to a specified type of probability distribution.

Which of the following is the appropriate test to use if we wish to determine whether there is evidence that the proportion of successes is higher in group 1 than in group 2?

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

The area to the right of a chi-square value is 0.05. Given this information, for 9 degrees of freedom, what would be the table value?

Chi-square tests of independence are always lower-tailed because a perfect fit between and makes equal to 0.