Exam 10: Comparing Two Means and Two Proportions

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 ____________.

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.What do you conclude at α = .01? Use confidence intervals to draw your conclusion.

The mid-distance running coach,Zdravko Popovich,for the Olympic team of an eastern European country claims that his six-month training program significantly reduces the average time to complete a 1500-meter run.Five mid-distance runners were randomly selected before they were trained with coach Popovich's six-month training program,and their completion times (in minutes)of the 1500-meter run were recorded.After six months of training under coach Popovich,the same five runners' 1500-meter run times were recorded again.The results are given below.

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 Set up the alternative hypothesis to test the claim.

Find a 90 percent confidence interval for the difference between the proportions of failures in factory 1 and factory 2,where $\hat { p } _ { 1 }$ = .05, $\hat { p } _ { 2 }$ = .04,n₁ = 500,n₂ = 2000.

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:

Find a 95 percent confidence interval for μ₁ - μ₂,where n₁ = 9,n₂ = 6, $\bar { X } _ { 1 } = 64$ $\bar { X } _ { 2 } = 59$ s₁² = 6,and s₂² = 3.(Assume equal population variances. )

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

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 higher at the West Coast? Test at α = .05.

Construct a 95 percent confidence interval for μ₁ - μ₂,where $\bar { X } _ { 1 }$ = 34.36, $\bar { X } _ { 2 }$ = 26.45,s₁ = 9,s₂ = 6,n₁ = 10,n₂ = 16.(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 rejection point (critical value of the test statistic)at α = .05?

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?

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.Set up the null hypothesis to test the claim that both sites have the same number of pedestrians.

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. Mean Standard Deviation Method 1 69 3.4 Method 2 72 3.8 Write the null and alternative hypotheses.

In testing the difference between the means of two independent populations,if neither population is normally distributed,then the sampling distribution of the difference in means will be approximately normal,provided that the sum of the sample sizes obtained from the two populations is at least 30.

The test of means for two related populations matches the observations (matched pairs)in order to reduce the ________________ attributable to the difference between individual observations and other factors.

An independent samples experiment is an experiment in which there is no relationship between the measurements in the different samples.

The mid-distance running coach,Zdravko Popovich,for the Olympic team of an eastern European country claims that his six-month training program significantly reduces the average time to complete a 1500-meter run.Five mid-distance runners were randomly selected before they were trained with coach Popovich's six-month training program,and their completion times (in minutes)of the 1500-meter run were recorded.After six months of training under coach Popovich,the same five runners' 1500-meter run times were recorded again.The results are given below.

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 What is the test statistic for this hypothesis test?

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 1 .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. 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 = .05?