Exam 10: Comparing Two Means and Two Proportions

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

When testing a hypothesis about the mean of a population of paired differences in which two different observations are taken on the same units,the correct test statistic to use is _________.

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.

In testing for the equality of means from two independent populations,if the hypothesis of equal population means is rejected at α = .01,it will __________ be rejected at α = .05.

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

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

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.

In testing the difference between the means of two normally distributed populations using independent random samples,we can only use a two-sided test.

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 $n _ { 1 } \text { and } n _ { 2 } = 10$ 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.

Given the following information about a hypothesis test of the difference between two means based on independent random samples,which one of the following is the correct rejection region at a significance level of .05? H_A: ?_A > ?_B, $\bar { X } _ { 1 } = 12$ $\bar { X } _ { 2 } = 9$ S₁ = 4,s₂ = 2,n₁ = 13,n₂ = 10.

When comparing two independent population means by using samples selected from two independent normally distributed populations with equal variances,the correct test statistic to use is ______.

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 What is the sample value of the test statistic?

The registrar at a state college is interested in determining whether there is a difference of more than one credit hour between male and female students in the average number of credit hours taken during a term.She selected a random sample of 60 male and 60 female students and observed the following sample information. Male Female Sample Mean 13.24 14.68 Population Std Dev 1.2 1.56 Sample Size 60 60 What do you conclude at α = .01? Assume unequal variances.

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 95 percent confidence interval.

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:

When we test H₀: p₁ - p₂ ≤ .01,H_A: p₁ - p₂ > .01,at α = .05,where $\hat { p } _ { 1 }$ = .08, $\hat { p } _ { 2 }$ = .035,n₁ = 200,and n₂ = 400,what is the standard deviation used in the calculation of the test statistic?

A marketing research company surveyed grocery shoppers on the East Coast and West Coast to see the percentage of the customers who prefer chicken to other meat.The data are given below. Sample Size Number Who Prefer Chicken East Coast 492 156 West Coast 386 172 Is the proportion of customers who prefer chicken the same for the two regions? Test at α = .10.

Calculate the pooled variance 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.

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

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.