Exam 11: Comparisons Involving Proportions and a Test of Independence

Among 1,000 managers with degrees in business administration, the following data have been accumulated as to their fields of concentration. We want to determine if the position in management is independent of field (major) of concentration. a.Compute the test statistic. b.Using the p-value approach at 90% confidence, test to determine if management position is independent of major. c.Using the critical value approach, test the hypotheses. Let $\alpha$ = 0.10.

Exhibit 11-7 The results of a recent poll on the preference of shoppers regarding two products are shown below. -Refer to Exhibit 11-7. At 95% confidence, the margin of error is

Exhibit 11-6 The following shows the number of individuals in a sample of 300 who indicated they support the new tax proposal. We are interested in determining whether or not the opinions of the individuals of the three groups are uniformly distributed. -Refer to Exhibit 11-6. The expected frequency for each group is

Before the presidential debates, it was expected that the percentages of registered voters in favor of various candidates would be as follows. After the presidential debates, a random sample of 1200 voters showed that 540 favored the Democratic candidate; 480 were in favor of the Republican candidate; 40 were in favor of the Independent candidate, and 140 were undecided. We want to see if the proportion of voters has changed. a.Compute the test statistic. b.Use the p-value approach to test the hypotheses. Let $\alpha$ = .05. c.Using the critical value approach, test the hypotheses. Let $\alpha$ = .05.

Exhibit 11-1 When individuals in a sample of 150 were asked whether or not they supported capital punishment, the following information was obtained. We are interested in determining whether or not the opinions of the individuals (as to Yes, No, and No Opinion) are uniformly distributed. -Refer to Exhibit 11-1. The number of degrees of freedom associated with this problem is

A lottery is conducted that involves the random selection of numbers from 0 to 4. To make sure that the lottery is fair, a sample of 250 was taken. The following results were obtained: a.State the null and alternative hypotheses to be tested. b.Compute the test statistic. c.The null hypothesis is to be tested at the 5% level of significance. Determine the critical value from the table. d.What do you conclude about the fairness of this lottery?

A major automobile manufacturer claimed that the frequencies of repairs on all five models of its cars are the same. A sample of 200 repair services showed the following frequencies on the various makes of cars. At $\alpha$ = 0.05, test the manufacturer's claim.

Shown below is 2 x 3 contingency table with observed values from a sample of 500. At 95% confidence using the critical value approach, test for independence of the row and column factors.

Exhibit 11-4 In the past, 35% of the students at ABC University were in the Business College, 35% of the students were in the Liberal Arts College, and 30% of the students were in the Education College. To see whether or not the proportions have changed, a sample of 300 students was taken. Ninety of the sample students are in the Business College, 120 are in the Liberal Arts College, and 90 are in the Education College. -Refer to Exhibit 11-4. The expected frequency for the Business College is

Exhibit 11-8 An insurance company selected samples of clients under 18 years of age and over 18 and recorded the number of accidents they had in the previous year. The results are shown below. We are interested in determining if the accident proportions differ between the two age groups. -Refer to Exhibit 11-8. The test statistic is

During the first few weeks of the new television season, the evening news audience proportions were recorded as ABC- 31%, CBS- 34%, and NBC- 35%. A sample of 600 homes yielded the following viewing audience data. We want to determine whether or not there has been a significant change in the number of viewing audience of the three networks. a.State the null and alternative hypotheses to be tested. b.Compute the expected frequencies. c.Compute the test statistic. d.The null hypothesis is to be tested at 95% confidence. Determine the critical value for this test. What do you conclude? e. Determine the p-value and perform the test.

From a poll of 800 television viewers, the following data have been accumulated as to their levels of education and their preference of television stations. Test at $\alpha$ = .05 to determine if the selection of a TV station is dependent upon the level of education. Use the p-value approach.

The results of a recent study regarding smoking and three types of illness are shown in the following table. We are interested in determining whether or not illness is independent of smoking. a.State the null and alternative hypotheses to be tested. b.Show the contingency table of the expected frequencies. c.Compute the test statistic. d.The null hypothesis is to be tested at 95% confidence. Determine the critical value for this test. What do you conclude? e. Determine the p-value and perform the test.

Exhibit 11-4 In the past, 35% of the students at ABC University were in the Business College, 35% of the students were in the Liberal Arts College, and 30% of the students were in the Education College. To see whether or not the proportions have changed, a sample of 300 students was taken. Ninety of the sample students are in the Business College, 120 are in the Liberal Arts College, and 90 are in the Education College. -Refer to Exhibit 11-4. The conclusion of the test is that the

The personnel department of a large corporation reported sixty resignations during the last year. The following table groups these resignations according to the season in which they occurred: Test to see if the number of resignations is uniform over the four seasons. Let $\alpha$ = 0.05.

Exhibit 11-1 When individuals in a sample of 150 were asked whether or not they supported capital punishment, the following information was obtained. We are interested in determining whether or not the opinions of the individuals (as to Yes, No, and No Opinion) are uniformly distributed. -Refer to Exhibit 11-1. The expected frequency for each group is

The degrees of freedom for a contingency table with 10 rows and 11 columns is

Exhibit 11-2 Last school year, the student body of a local university consisted of 30% freshmen, 24% sophomores, 26% juniors, and 20% seniors. A sample of 300 students taken from this year's student body showed the following number of students in each classification. We are interested in determining whether or not there has been a significant change in the classifications between the last school year and this school year. -Refer to Exhibit 11-2. The expected number of freshmen is

Exhibit 11-2 Last school year, the student body of a local university consisted of 30% freshmen, 24% sophomores, 26% juniors, and 20% seniors. A sample of 300 students taken from this year's student body showed the following number of students in each classification. We are interested in determining whether or not there has been a significant change in the classifications between the last school year and this school year. -Refer to Exhibit 11-2. The calculated value for the test statistic equals

If we are interested in testing whether the proportion of items in population 1 is larger than the proportion of items in population 2, the