Exam 11: Statistical Inferences Based on Two Samples

Two hospital emergency rooms use different procedures for triage of their patients. We want to test the claim that the mean waiting time of patients is the same for both hospitals. The 40 randomly selected subjects from hospital A produce a mean of 18.3 minutes. The 50 randomly selected patients from hospital B produce a mean of 25.31 minutes. Sample standard deviations are s_a = 2.1 minutes and s_b = 2.92 minutes. Set up the null hypothesis to determine whether there is a difference in the mean waiting time between the two hospitals.

The controller of a chain of toy stores is interested in determining whether there is any difference in the weekly sales of store 1 and store 2. The weekly sales are normally distributed. This problem should be analyzed using an independent means method.

A test of driving ability is given to a random sample of 10 student drivers before and after they complete a formal driver education course. Results follow. Calculate the mean difference between the before-class scores and the after-class scores.

A fast-food company uses two management-training methods. Method 1 is a traditional method of training, and Method 2 is a new and innovative method. The company has just hired 31 new management trainees. 15 of the trainees are randomly selected and assigned to Method 1, and the remaining 16 trainees are assigned to Method 2. After three months of training, the management trainees take a standardized test. The test is designed to evaluate their performance and learning from the training. The sample mean score and sample standard deviation of the two methods are given below. Company management wants to determine whether the company should implement the new training method. What is the absolute value of the rejection point (critical value of the test statistic) at α = .05?

Two hospital emergency rooms use different procedures for triage of their patients. We want to test the claim that the mean waiting time of patients is the same for both hospitals. The 40 randomly selected subjects from hospital A produce a mean of 18.3 minutes. The 50 randomly selected patients from hospital B produce a mean of 25.31 minutes. Assume s_a = 2.1 minutes and s_b =2.92 minutes. What do you conclude about the waiting time for patients in the two hospitals, testing at α = .001?

A coffee shop franchise owner is looking at two possible locations for a new shop. To help make a decision, he looks at the number of pedestrians that go by each of the two locations in one-hour segments. At location A, counts are taken for 35 one-hour units, with a mean number of pedestrians of 421 and a sample standard deviation of 122. At the second location (B), counts are taken for 50 one-hour units, with a mean number of pedestrians of 347 and a sample standard deviation of 85. Assume the two population variances are not known but are equal. Calculate the pooled estimate of σ².

When we test H₀: p₁ − p₂ ≤ .01, H_A: p₁ − p₂ > .01 at α = .05 where = .08, = .035, n₁ = 200, and n₂ = 400, can we reject the null hypothesis?

When testing H₀: μ₁ − μ₂ = 2, H_A: μ₁ − μ₂ > 2, where ₁ = 522, ₂ = 516, σ₁² = 28, σ₂² = 24, n₁ = 40, n₂ = 30, at α = .01, what is the test statistic? (Assume unequal variances.)

Let p₁ represent the population proportion of U.S. senatorial and congressional (House of Representatives) Democrats who are in favor of a new modest tax on junk food. Let p₂ represent the population proportion of U.S. senatorial and congressional Republicans who are in favor of a new modest tax on junk food. Out of the 265 Democratic senators and members of Congress, 106 of them are in favor of a junk food tax. Out of the 285 Republican senators and members of Congress, only 57 are in favor of a junk food tax. Find a 95 percent confidence interval for the difference between proportions l and 2.

Find a 95 percent confidence interval for μ₁ − μ₂, where n₁ = 50, n₂ = 75, ₁ = 82, ₂ = 76, s₁² = 8, and s₂² = 6. Assume unequal variances.

When we test H₀: μ₁ ≤ μ₂, H_A: μ₁ > μ₂ at α = .10, where ₁ = 77.4, ₂ = 72.2, s₁ = 3.3, s₂ = 2.1, n₁ = 6, and n₂ = 6, what is the estimated pooled variance?

When testing the difference between two population proportions using large independent random samples, the ________ test statistic is used.

Suppose that a realtor is interested in comparing the price of midrange homes in two cities in a midwestern state. She conducts a small survey in the two cities, looking at the price of midrange homes. Assume equal population variances. Calculate the 95 percent confidence interval.

In an opinion survey, a random sample of 1,000 adults from the United States and 1,000 adults from Germany were asked whether they supported the death penalty. 590 American adults and 560 German adults indicated that they supported the death penalty. The researcher wants to know whether there is sufficient evidence to conclude that the proportion of adults who support the death penalty is higher in the United States than in Germany. What is the rejection point (critical value of the test statistic) at α = .10?

If the limits of the confidence interval of the difference between the means of two normally distributed populations were 8.5 and 11.5 at the 95 percent confidence level, then we can conclude that we are 95 percent certain that there is a significant difference between the two population means.

A test of driving ability is given to a random sample of 10 student drivers before and after they complete a formal driver education course. Results follow. Test the hypothesis that there is no difference between the before-class scores and the after-class scores at α = .05.

A marketing research company surveyed grocery shoppers on the East Coast and West Coast to find the percentage of the customers who prefer chicken to other meat. The data are given below. What is the test statistic for the alternative hypothesis that the West Coast prefers chicken at a higher proportion than the East Coast?

An experiment in which two different measurements are taken on the same units and inferences are made using the differences between the pairs of measurements is a(n) ________ experiment.

When comparing two population means based on independent random samples, the pooled estimate of the variance is used when there is an assumption of equal population variances.

In an opinion survey, a random sample of 1,000 adults from the United States and 1,000 adults from Germany were asked whether they supported the death penalty. 590 American adults and 560 German adults indicated that they supported the death penalty. The researcher wants to know whether there is sufficient evidence to conclude that the proportion of adults who support the death penalty is higher in the United States than in Germany. What is the p-value for this test?