Exam 11: Comparisons Involving Proportions and a Test of Independence

Exhibit 11-5 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 11-5. The p-value is

Exhibit 11-1 The results of a recent poll on the preference of shoppers regarding two products are shown below. -Refer to Exhibit 11-1. The point estimate for the difference between the two population proportions in favor of this product is

Employee panel preferences for three proposed company logo designs follow. Use a = .05 and test to determine any difference in preference among the three logo designs.

A company gives a test to prospective employees before granting an interview. A researcher hypothesizes that men tend to answer one particular test question correctly more often than women. Independent samples of both groups are given the test. The results for the question of interest follow. Does the data provide sufficient evidence to conclude that the proportion of correct answers given by men is greater than that of women? Use Excel to conduct the appropriate test at   .05.

Exhibit 11-4 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 11-4. The calculated value for the test statistic equals

Exhibit 11-5 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 11-5. The expected frequency of seniors is

The test for goodness of fit

Exhibit 11-8 The table below gives beverage preferences for random samples of teens and adults. We are asked to test for independence between age (i.e., adult and teen) and drink preferences. -Refer to Exhibit 11-8. The test statistic for this test of independence is

The results of recent polls on presidential approval ratings are shown below. Does the data provide sufficient evidence to conclude that the presidential approval ratings differ between the two months? Use Excel to conduct the appropriate test at   .05.

A group of 500 individuals were asked to cast their votes regarding a particular issue of the Equal Rights Amendment. The following contingency table shows the results of the votes: At   .05 using the p-value approach, test to determine if the votes cast were independent of the sex of the individuals.

A study of wage discrimination at a local store compared employees' race and their status. Partial results of the study follow. Use Excel and test at   .05 to determine if gender is independent of status.

Five hundred randomly selected automobile owners were questioned on the main reason they had purchased their current automobile. The results are given below. a.State the null and alternative hypotheses for a contingency table test. b.State the decision rule for the critical value approach. Let   0.10. c.Calculate the x² test statistic. d.Give your conclusion for this test.

Exhibit 11-7 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 11-7. The conclusion of the test is that the

Exhibit 11-7 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 11-7. This problem is an example of a

A poll was taken this year asking college students if they considered themselves overweight. A similar poll was taken five ago. Results are summarized below. Has the proportion increased significantly? Let   0.05.

A manufacturing company wants to estimate the difference in the proportion of defective parts between two machines. Independent random samples of parts are taken from both machines. The results follow. Use Excel to estimate the difference in the proportion of defective parts between two machines with a 99% level of confidence.

Shown below is 3 x 2 contingency table with observed values from a sample of 1,500. At 95% confidence, test for independence of the row and column factors.

A population where each element of the population is assigned to one and only one of several classes or categories is a

The degrees of freedom for a contingency table with 12 rows and 12 columns is

Among a sample of 50 MDs (medical doctors) in the city of Memphis, Tennessee, 10 indicated they make house calls; while among a sample of 100 MDs in Atlanta, Georgia, 18 said they make house calls. Determine a 95% interval estimate for the difference between the proportions of doctors who make house calls in the two cities.