Exam 11: Comparisons Involving Proportions and a Test of Independence

Exhibit 11-3 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 11-3. The standard error of is

The number of degrees of freedom for the appropriate chi-square distribution in a test of independence is

The sampling distribution of is approximated by a

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 number of degrees of freedom associated with this problem is

During the primary elections of 2008, 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 11-7 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 expected frequency for the Business College is

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.

If we are interested in testing whether the proportion of items in population 1 is larger than the proportion of items in population 2, the

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 proportions of defectives in the two lines.

In a sample of 100 Republicans, 60 favored the President's anti-drug program. While in a sample of 150 Democrats, 84 favored his program. At 95% confidence, test to see if there is a significant difference in the proportions of the Democrats and the Republicans who favored the President's anti-drug program.

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 hypothesis is to be tested at the 5% level of significance. The critical value from the table equals

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.

From a poll of 800 television viewers, the following data have been accumulated as to their levels of education and their preference of television stations. Test at   .05 to determine if the selection of a TV station is dependent upon the level of education. Use the p-value approach.

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. At 95% confidence, the null hypothesis

Exhibit 11-6 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 11-6. The expected frequency of those who received medication and were cured is

When a category in a contingency table has an expected frequency of less than five,

The assumptions for the multinomial experiment parallel those for the binomial experiment with the exception that for the multinomial

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 p-value is

When conducting a good of fit test, the expected frequencies for the multinomial population are based on the

A school administrator believes that there is no difference between student dropout rate for schools located in rural areas and schools located in urban areas. A random sample of 100 schools in the rural areas was taken. The student dropout rate of the schools in the sample was 27%. A random sample of 80 schools in the urban areas had a dropout rate of 20%. a.Give a point estimate for the difference between the population proportions for the two districts. b.Give a point estimate of the standard deviation for the difference between the population proportions. c.Compute the test statistic for testing the administrator's belief. d.At 95% confidence using the p-value approach, test the administrator's belief.