Exam 11: Comparisons Involving Proportions and a Test of Independence

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

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?

The sampling distribution of is approximated by a $\bar { p } _ { 1 } - \bar { p } _ { 2 }$

The reliability of two types of machines used in the same manufacturing process is to be tested. The first machine failed to operate correctly in 90 out of 300 trials while the second type failed to operate correctly in 50 out of 250 trials. a. Give a point estimate for the difference between the population proportions of these machines. b. Calculate the pooled estimate of the population proportion. c. Carry out a hypothesis test to check whether there is a statistically significant difference in the reliability for the two types of machines using a .10 level of significance.

Exhibit 11-1 When individuals in a sample of 150 were asked whether or not they supported capital punishment, the following information was obtained. Do you support capital punishment? Do you support capital punishment? Number of individuals Yes 40 No 60 No Opinion 50 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 calculated value for the test statistic equals

Babies weighing less than 5.5 pounds at birth are considered "low­birth­weight 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. Hamilton Shelby Sample size 150 200 Number of "low-birth-weight babies 18 22 a. Develop a 95% confidence interval estimate for the difference between the proportions of low-birth-weight babies in the two counties. 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 a). Do not perform any test.

During the recent primary elections, the democratic presidential candidate showed the following pre-election voter support in Alabama and Mississippi. State Voters Surveyed Voters Favoring the Democratic Candidate Alabama 800 440 Mississippi 600 360 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 11-2 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. Freshmen 83 Sophomores 68 Juniors 85 Seniors 64 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. At 95% confidence, the null hypothesis

Exhibit 11-5 The table below gives beverage preferences for random samples of teens and adults. Teens Adults Total Coffee 50 200 250 Tea 100 150 250 Soft Drink 200 200 400 Other 50 50 100 400 400 600 1,000 We are asked to test for independence between age i.e., adult and teen) and drink preferences. -Refer to Exhibit 11-5. With a .05 level of significance, the critical value for the test 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. Diet Pill No Diet Pills Total No Weight Lo55 80 20 100 Weight Loss 100 100 200 Total 180 120 300 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.

Exhibit 11-7 The results of a recent poll on the preference of shoppers regarding two products are shown below. Shoppers Favoring Product Shoppers Surveyed This Product A 800 560 B 900 612 -Refer to Exhibit 11-7. At 95% confidence, the margin of error is

Exhibit 11-1 When individuals in a sample of 150 were asked whether or not they supported capital punishment, the following information was obtained. Do you support capital punishment? Do you support capital punishment? Number of individuals Yes 40 No 60 No Opinion 50 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

Exhibit 11-7 The results of a recent poll on the preference of shoppers regarding two products are shown below. Shoppers Favoring Product Shoppers Surveyed This Product A 800 560 B 900 612 -Refer to Exhibit 11-7. The point estimate for the difference between the two population proportions in favor of this product is

The results of a recent poll on the preference of voters regarding presidential candidates are shown below. Candidate Voters Surveyed Voters Favoring This Candidate A 400 192 B 450 225 At 95% confidence, test to determine whether or not there is a significant difference between the preferences for the two candidates.

Before the presidential debates, it was expected that the percentages of registered voters in favor of various candidates would be as follows. Percentages Democrats 48\% Republicans 38\% Independent 4\% Underiderl 10\% 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 α = .05. c. Using the critical value approach, test the hypotheses. Let α = .05.

Exhibit 11-3 In order to determine whether or not a particular medication was effective in curing the common cold, one group of patients was given the medication, while another group received sugar pills. The results of the study are shown below. Patients Cured Patients Not Cured Received medication 70 10 Received sugar pills 20 50 We are interested in determining whether or not the medication was effective in curing the common cold. -Refer to Exhibit 11-3. The expected frequency of those who received medication and were cured is

Exhibit 11-3 In order to determine whether or not a particular medication was effective in curing the common cold, one group of patients was given the medication, while another group received sugar pills. The results of the study are shown below. Patients Cured Patients Not Cured Received medication 70 10 Received sugar pills 20 50 We are interested in determining whether or not the medication was effective in curing the common cold. -Refer to Exhibit 11-3. The test statistic is

A statistical test conducted to determine whether to reject or not reject a hypothesized probability distribution for a population is known as a

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. Under Age of 18 Over Age of 18 =500 =600 Number of accidents =180 Number of accidents =150 We are interested in determining if the accident proportions differ between the two age groups. -Refer to Exhibit 11-8 and let pu represent the proportion under and po the proportion over the age of 18. The null hypothesis is

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. Column Factor Row Factor 40 50 110 60 100 140 Row Factor 40 50 110 60 100 140