Exam 10: Statistical Inferences Based on Two Samples

We are testing the hypothesis that the proportion of winter-quarter profit growth is more than 2 percent greater for consumer industry companies (CON)than for banking companies (BKG).At α = .10,given that can we reject the null hypothesis?

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 a junk food tax.At α = .01,can we conclude that the proportion of Democrats who favor a junk food tax is more than 5 percent higher than the proportion of Republicans who favor the new tax?

In testing the difference between the means of two independent populations,the variances of the two samples can be pooled if the population variances are assumed to ____________.

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. Test the claim at α = .01.

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?

Find a 95 percent confidence interval for the difference between the proportions of older and younger drivers who have tickets,where

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 p-value for this test?

What is the value of the F statistic for H₀: σ₁² ≤ σ₁²,H_A: σ₁²> σ₁²,where s₁ = 3.3 and s₂ = 2.1?

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 ______.

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.

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. )

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?

If the limits of the confidence interval of the difference between the means of two normally distributed populations were from -2.6 to 1.4 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.

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 one hospital produce a mean of 18.3 minutes.The 50 randomly selected patients from the other hospital produce a mean of 25.31 minutes.Assume s_a = 2.1 minutes and s_b = 2.92 minutes.Calculate the test statistic for testing the hypothesis that there is a difference in the mean waiting time between the two hospitals.Assume unequal variances.

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 alternative hypothesis for this problem would be stated as:

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 = .05 to conclude that the new training method is more effective than the traditional training method?

Assume that we are constructing a confidence interval for the difference in the means of two populations based on independent random samples.If both sample sizes n₁ and n₂ = 10,and the distributions of both populations are highly skewed,then a confidence interval for the difference in the means can be constructed using the t test statistic.

The value of F_α in a particular situation depends on the size of the right-hand tail area and on the numerator degrees of freedom.

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.Calculate the test statistic to test the claim that scores were higher after 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 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. Write the null and alternative hypotheses.