Exam 10: Comparing Two Means and Two Proportions

In which of the following tests is the variable of interest the difference between the values of the observations from the two samples,rather than the actual observations themselves?

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.

When testing H₀: μ₁ - μ₂ = 2,H_A: μ₁ - μ₂ > 2,where $\bar { X } _ { 1 }$ = 522, $\bar { X } _ { 2 }$ = 516,σ₁² = 28,σ₂² = 24,n₁ = 40,n₂ = 30,at α = .01,what is the test statistic?

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 = .10?

A coffee shop franchise owner is looking at two possible locations for a new shop.To help him decide,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 populations variances are not known but are equal.Testing the claim that both sites have the same mean number of pedestrians at α = .01,what do you conclude?

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 rejection point (critical value of the test statistic)at α = .10?

When testing the difference between two population proportions,the _______ test statistic is used.

In testing the difference between two independent population means,if the assumption is of unequal variances,the critical value of the t statistic is obtained by calculating the ___________________.

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 Calculate the t statistic to test that there is no difference between the before-class scores and the after-class scores.

A financial analyst working for a financial consulting company wishes to find evidence that the average price-to-earnings ratio in the consumer industry is higher than the average price-to-earnings ratio in the banking industry.The alternative hypothesis is:

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 the administration of the drug is an example of testing the difference between two ____________.

If we are testing the difference between the means of two normally distributed independent populations with samples of n₁ = 10,n₂ = 10,the degrees of freedom for the t statistic is ______.

Determine the 95 percent confidence interval for the difference between two population means,where sample 1 has data: 16,14,19,18,19,20,15,18,17,18;and sample 2 has data: 13,19,14,17,21,14,15,10,13,15.(Assume equal population variances. )

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 sample value of the test statistic?

Find a 95 percent confidence interval for the difference between the proportions of older and younger drivers who have tickets,where $\hat { p } _ { 1 }$ = .275, $\hat { p } _ { 2 }$ = .25,n₁ = 1000,n₂ = 1000.

When testing the difference between two proportions selected from populations with large independent samples,the z test statistic is used.

A test of spelling ability is given to a random sample of 10 students before and after they complete a spelling course.The mean score before the course was 119.60 and after the course the mean score was 130.80.The standard deviation of the difference is 16.061.Test the hypothesis at α =.05 using a t test.

When we are testing a hypothesis about the difference in two population proportions based on large independent samples,we compute a combined (pooled)proportion from the two samples if we assume that there is no difference between the two proportions in our null hypothesis.