Exam 11: Comparisons Involving Proportions and a Test of Independence

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-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.

A sample of 150 individuals (males and females) was surveyed, and the individuals were asked to indicate their yearly incomes. Their incomes were categorized as follows. The results of the survey are shown below. We want to determine if yearly income is independent of gender. a.Compute the test statistic. b.Using the p-value approach, test to determine if yearly income is independent of gender.

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. The standard error of is

The following table shows the results of recent study regarding 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.

In a random sample of 200 Republicans, 160 opposed the new tax laws. While in a sample of 120 Democrats, 84 opposed the new tax laws. Determine a 95% confidence interval estimate for the difference between the proportions of Republicans and Democrats opposed to this new law.

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.

In order not to violate the requirements necessary to use the chi-square distribution, each expected frequency in a goodness of fit test must be

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 p-value 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.)

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 11-6 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 calculated value for the test statistic equals

A medical journal reported the following frequencies of deaths due to cardiac arrest for each day of the week: We want to determine whether the number of deaths is uniform over the week. a.Compute the test statistic. b.Using the p-value approach at 95% confidence, test for the uniformity of death over the week. c.Using the critical value approach, perform the test for uniformity.

A comparative study of organic and conventionally grown produce was checked for the presence of E. coli. Results are summarized below. Is there a significant difference in the proportion of E. Coli in organic vs. conventionally grown produce? Test at $\alpha$ = 0.10.

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 p-value 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. 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 conclusion of the test (at 95% confidence) is that the

During the primary elections of 1996, candidate A showed the following pre-election voter support in Tennessee and Mississippi. a.Develop a 95% confidence interval estimate for the difference between the proportion of voters favoring candidate A in the two states. b.Is there conclusive evidence that one of the two states had a larger proportion of voters' support? If yes, which state? Explain.

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. This problem is an example of a

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. 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

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 expected number of adults who prefer coffee is

The results of a recent poll on the preference of voters regarding the presidential candidates are shown below. a.Develop a 90% confidence interval estimate for the difference between the proportion of voters favoring each candidate. b.Does your confidence interval provide conclusive evidence that one of the candidates is favored more? Explain.