Exam 10: Statistical Inferences Based on Two Samples

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?

A new company is in the process of evaluating its customer service.The company offers two types of sales: (1)Internet sales and (2)store sales.The marketing research manager believes that the Internet sales are more than 10 percent higher than store sales.The null hypothesis would be:

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 take 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. Is there evidence at α = .01 to conclude that the new training method is more effective than the traditional training method?

In forming a confidence interval for μ₁ - μ₂,only two assumptions are required: independent samples and sample sizes of at least 30.

Calculate the t statistic for testing equality of means where (Assume equal population variances. )

When testing H₀: σ₁² ≤ σ₂² and H_A: σ₁²> σ₂²,where s₁² = .004,s₂² = .002,n₁ = 4,and n₂ = 7 at α = .05,what critical value do we use?

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

In comparing the difference between two independent population means,the sampling distributions of the population means are at least approximately ________________.

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 population variances are not known but are equal.Calculate a 95 percent confidence interval for the difference in pedestrian traffic at the two locations.

In testing the difference between the means of two normally distributed populations,if μ₁ = μ₂ = 50,n₁ = 9,n₂ = 13,the degrees of freedom for the t statistic equals ___________.

The exact shape of the curve of the F distribution depends on two parameters,df₁ and df₂.

When we test H₀:p₁ - p₂≤ .01,H_A:p₁ - p₂>.01,at α = .05,where what is the standard deviation used to calculate the test statistic?

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. Write the null and alternative hypotheses testing the claim that the test score is not affected by the course.

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 take 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. What is the absolute value of the rejection point (critical value of the test statistic)at α = .01?

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

Given the following information about a hypothesis test of the difference between two variances based on independent random samples,what is the critical value of the test statistic at a significance level of .05? Assume that the samples are obtained from normally distributed populations.

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.Testing the equality of means at α = .05,can we reject the null hypothesis? (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 decision 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. Determine the 95 percent confidence interval for the difference between the proportion of customers on the West Coast who prefer chicken and the proportion of customers on the East Coast who prefer chicken.

When testing the difference for the population of paired differences in which two different observations are taken on the same units,the correct test statistic to use is ____.