Exam 10: Comparing Two Means and Two Proportions

In an opinion survey,a random sample of 1000 adults from the United States and 1000 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 decision at α = .05?

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. City A City B Sample Mean 86,900 84,000 Sample Std Dev 2300 1750 Sample Size 9 7 Calculate the pooled estimate of σ² (rounded to nearest hundred).

Find a 99 percent confidence interval for the difference between means,given that n₁ = 49,n₂ = 49,

Find a 90 percent confidence interval for the difference between the proportions of group l and group 2.Let p₁ represent the population proportion of the people in group 1 who are in favor of new packaging,and let p₂ represent the population proportion of the people in group 2 who are in favor of new packaging. $\hat { p } _ { 1 }$ = .21, $\hat { p } _ { 2 }$ = .13,n₁ = 300,and n₂ = 400.

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. Before After Student Class Class Difference 1 100 136 -36 2 121 129 -8 3 93 125 -32 4 146 150 -4 5 101 110 -9 6 109 138 -29 7 149 136 13 8 130 130 0 9 127 125 2 10 120 129 -9 Test the hypothesis that there is no difference between the before class scores and the after-class scores at α = .05.

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: μ₁ ≤ μ₂,H_A: μ₁ > μ₂ at α = .10,where $\bar { X } _ { 1 }$ = 77.4, $\bar { X } _ { 2 }$ = 72.2,s₁ = 3.3,s₂ = 2.1,n₁ = 6,n₂ = 6,can we reject the null hypothesis?

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.

In testing the difference between two means from two independent populations,the sample sizes do not have to be equal.

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. Before After Student Class Class Difference 1 100 136 -36 2 121 129 -8 3 93 125 -32 4 146 150 -4 5 101 110 -9 6 109 138 -29 7 149 136 13 8 130 130 0 9 127 125 2 10 120 129 -9 Write the null and alternative hypotheses testing the claim that the test score is not affected by the course.

When testing H₀: μ₁ - μ₂ = 2,H_A: μ₁ - μ₂ > 2,where $\bar { X } _ { 1 }$ = 522, $\bar { X }_ { 2}$ = 516,s₁² = 28,s₂² = 24,n₁ = 40,n₂ = 30,at α = .01,what can we conclude?

In a market research study conducted by a local winery on white wine preference,the following results were found.Of a sample of 500 men,120 preferred white wine.Of a sample of 500 women,210 preferred white wine.Set up the alternative hypothesis that will test the claim that the percentage of women who prefer white wine is 25 percent higher than the percentage of men who prefer white wine.

Given two independent normal distributions with s₁² - s₂² = 100,?₁ = ?₂ = 50,n₁ = n₂ = 50,the sampling distribution of the mean difference $\bar { X } _ { 1 } - \bar { X } _ { 2 }$ Will have a mean of _________.

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 the first method,and the remaining 16 trainees are assigned to the second training method.After three months of training,the management trainees took a standardized test.The test was designed to evaluate their performance and learning from training.The sample mean score and sample standard deviation of the two methods are given below.The management wants to determine if the company should implement the new training method. Mean Standard Deviation Method 1 69 3.4 Method 2 72 3.8 Is there evidence at α = .01 to conclude that the new training method is more effective than the traditional training method?

In order to test the effectiveness of a drug called XZR designed to reduce cholesterol levels,9 heart patients' cholesterol levels are measured before they are given the drug.The same 9 patients use XZR for two continuous months.After two months of continuous use,the 9 patients' cholesterol levels are measured again.The comparison of cholesterol levels before versus after administering the drug is an example of testing the difference between:

At α = .10,testing the hypothesis that the proportion of consumer industry companies' (CON)winter-quarter profit growth is more than 2 percent greater than the proportion of banking companies' (BKG)winter-quarter profit growth,given that $\hat { p }_{ C O N }= .20$ $\hat { p } _{B K G} = .14$ n_CON = 300,and n_BKG = 400,can we reject the null hypothesis?

Given the following information about a hypothesis test of the difference between two means based on independent random samples,what is the calculated value of the test statistic? Assume that the samples are obtained from normally distributed populations having equal variances. H_A: ?_A > ?_B, $\bar { Y } _ { 1 } = 12$ $\bar { X } _ { 2 } = 9$ S₁ = 5,s₂ = 3,n₁ = 13,n₂ = 10.

Find a 95 percent confidence interval for the difference between the proportions of people who prefer cola versus root beer (RB),where

In an experiment involving matched pairs,a sample of 12 pairs of observations is collected.The degrees of freedom for the t statistic is 10.

In testing the difference between two independent population means,it is assumed that the level of measurement is at least ______________.