Exam 11: Comparisons Involving Proportions and a Test of Independence

The degrees of freedom for a chi-square test involving 5 proportions are

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 p-value is

The makers of Compute-All know that in the past, 40% of their sales were from people under 30 years old, 45% of their sales were from people who are between 30 and 50 years old, and 15% of their sales were from people who are over 50 years old. A sample of 300 customers was taken to see if the market shares had changed. In the sample, 100 of the people were under 30 years old, 150 people were between 30 and 50 years old, and 50 people were over 50 years old. 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 1% level of significance. Determine the critical value from the table. d.What do you conclude?

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.

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  .10.

The following table shows the results of a recent study regarding the gender of individuals and their selected field of study. We want to determine if the selected field of study is independent of gender. a.Compute the test statistic. b.Using the p-value approach at 90% confidence, test to see if the field of study is independent of gender. c.Using the critical method approach at 90% confidence, test for the independence of major and gender.

Exhibit 11-2 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. -Refer to Exhibit 11-2 and let p_U represent the proportion under and p_O the proportion over the age of 18. The null hypothesis 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   .05. c.Using the critical value approach, test the hypotheses. Let   .05.

In the last presidential election before the candidates began their major campaigns, the percentages of registered voters who favored the various candidates were as follows. After the major campaigns began, a random sample of 400 voters showed that 172 favored the Republican candidate; 164 were in favor of the Democratic candidate; and 64 favored the Independent candidate. Test with   .01 to see if the proportion of voters who favored the various candidates changed.

The purpose of the hypothesis test for proportions of a multinomial population is to determine whether the actual proportions

Which of the following does not need to be known in order to compute the p-value?

During "sweeps week" last year, the viewing audience was distributed as follows: 36% NBC, 22% ABC, 24% CBS, and 18% FOX. This year during "sweeps week" a sample of 50 homes yielded the following data. Use Excel to test at   .05 to determine if the audience proportions have changed.

In a two-tailed hypothesis test the test statistic is determined to be z  -2.5. The p-value for this test

Babies weighing less than 5.5 pounds at birth are considered "low-birth-weight babies." In the United States, 7.6% of newborns are low-birth-weight babies. The following information was accumulated from samples of new births taken from two counties. a.Develop a 95% confidence interval estimate for the difference between the proportions of low-weight babies in the two counties. a. Do not perform any test. b.Is there conclusive evidence that one of the proportions is significantly more than the other? If yes, which county? Explain, using the results of Part

If the chi-square test indicates that there is no difference between two proportions, this indicates that

Of 200 UTC seniors surveyed, 60 were planning on attending Graduate School. At UTK, 400 seniors were surveyed; and 100 indicated that they were planning to attend Graduate School. a.Determine a 95% confidence interval estimate for the difference between the proportions of seniors at the two universities that were planning to attend Graduate School. b.Is there conclusive evidence to prove that the proportion of students from UTC who plan to go to Graduate School is significantly more than those from UTK? Explain.

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 11-2 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. -Refer to Exhibit 11-2. The pooled proportion is

Of 300 female registered voters surveyed, 120 indicated they were planning to vote for the incumbent president; while of 400 male registered voters, 140 indicated they were planning to vote for the incumbent president. a.Compute the test statistic. b.At alpha  .05, test to see if there is a significant difference between the proportions of females and males who plan to vote for the incumbent president. (Use the p-value approach.)

All of the following tests follow a chi-square distribution except