Exam 11: Comparisons Involving Proportions and a Test of Independence

During the recent primary elections, the democratic presidential candidate showed the following pre-election voter support in Alabama and Mississippi. a.We want to determine whether or not the proportions of voters favoring the Democratic candidate were the same in both states. Provide the hypotheses. b.Compute the test statistic. c.Determine the p-value; and at 95% confidence, test the above hypotheses.

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 and let p_u represent the proportion under and po the proportion over the age of 18. The null hypothesis is

From production line A, a sample of 500 items is selected at random, and it is determined that 30 items are defective. In a sample of 300 items from production process B (which produces identical items to line A), there are 12 defective items. Determine a 95% confidence interval estimate for the difference between the proportion of defectives in the two lines.

Before the rush began for Christmas shopping, a department store had noted that the percentage of its customers who use the store's credit card, the percentage of those who use a major credit card, and the percentage of those who pay cash are the same. During the Christmas rush in a sample of 150 shoppers, 46 used the store's credit card; 43 used a major credit card; and 61 paid cash. With $\alpha$ = 0.05, test to see if the methods of payment have changed during the Christmas rush.

An important application of the chi-square distribution is

Dr. Sherri Brock's diet pills are supposed to cause significant weight loss. The following table shows the results of a recent study where some individuals took the diet pills and some did not. We want to see if losing weight is independent of taking the diet pills. a.Compute the test statistic. b.Using the p-value approach at 95% confidence, test to determine if weight loss is independent on taking the pill. c.Use the critical method approach and test for independence.

Of 150 Chattanooga residents surveyed, 60 indicated that they participated in a recycling program. In Knoxville, 120 residents were surveyed and 36 claimed to recycle. a.Determine a 95% confidence interval estimate for the difference between the proportion of residents recycling in the two cities. b.From your answer in Part a, is there sufficient evidence to conclude that there is a significant difference in the proportion of residents participating in a recycling program?

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 $\alpha$ = .05 using the p-value approach, test to determine if the votes cast were independent of the sex of the individuals.

The office of records at a university has stated that the proportion of incoming female students who major in business has increased. A sample of female students taken several years ago is compared with a sample of female students this year. Results are summarized below. Has the proportion increased significantly? Test at $\alpha$ = 0.10.

Exhibit 11-9 The results of a recent poll on the preference of teenagers regarding the types of music they listen to are shown below. -Refer to Exhibit 11-9. The standard error of 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 p-value is

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

In a sample of 700 Republicans, 644 were opposed to the President's foreign policies. While in a sample of 600 Democrats, 528 were opposed to his policies. Develop a 95% confidence interval estimate for the difference between the proportions of the opinions of the individuals in the two parties.

Exhibit 11-5 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 11-5. The test statistic for this test of independence is