Exam 10: Comparing Two Means and Two Proportions

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 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.

There are two types of machines called type A and type B.Both type A and type B can be used to produce a certain product.The production manager wants to compare efficiency of the two machines.He assigns each of the 15 workers to both types of machines to compare their hourly production rate.In other words,each worker operates machine A and machine B for one hour each.These two samples are independent.

Find a 95 percent confidence interval for μ₁ - μ₂,where n₁ = 50,n₂ = 75, $\bar { X } _ { 1 }$ = 82, $\bar { X } _ { 2 }$ = 76,s₁² = 8,and s₂² = 6.Assume unequal variances.

In testing the difference between the means of two normally distributed populations using large independent random samples,the sample sizes from the two populations must be equal.

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 mean difference between the before-class scores and the after-class scores.

Using 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 of [-.0076,.0276],can we reject the null hypothesis at α = .10?

When we test H₀: μ₁ - μ₂ ≤ 0,H_A: μ₁ - μ₂ > 0, $\bar { X }_ { 1 }$ = 15.4, $\bar { X }_ { 1 }$ = 14.5,s₁ = 2,s₂ = 2.28,n₁ = 35,and n₂ = 18 at α = .01,can we reject the null hypothesis? (Assume unequal variances. )

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

Two different firms design their own tests for business graduates,and an employer administers both versions to a random selection of prospective employees.Results are below.At α = .02,test the claim that both versions produce the same score. Mean difference = -4.25 Standard error of the difference = 1.411 Variable 1 Variable 2 Mean 99.75 104 Variance 65.92857 48.28571 Observations 8 8 Pearson Correlation 0.870992 Hypothesized Mean Difference 0 df 7 t Stat -3.01193 (<=) one-tail 0.009804 Critical one-tail 2.516752 (<=) two-tail 0.019608 Critical two-tail 2.997952

Testing the equality of means at α = .05,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,can we reject the null hypothesis? (Assume equal population variances. )

An experiment in which there is no relationship between the measurements on the different samples is a(n)______ experiment.

When we test H₀: μ₁ - μ₂ ≤ 0,H_A: μ₁ - μ₂ > 0, $\bar { X } _ { 1 }$ = 15.4, $\bar { X} _ { 2 }$ = 14.5,σ₁ = 2,σ₂ = 2.28,n₁ = 35,and n₂ = 18 at α = .01,what is the value of the test statistic?

When comparing two independent population means,if n₁ = 13 and n₂ = 10,degrees of freedom for the t statistic is 22.

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.What do you conclude about the waiting time for patients in the two hospitals,testing at α = .001?

In testing the difference between the means of two normally distributed populations using independent random samples,the correct test statistic to use is:

Find a 98 percent confidence interval for the paired difference. $d_{1}-d_{2} \text { where } \overline{\mathrm{D}}=1.6, s_{d}^{2}=40.96, n=30$

If we are testing the hypothesis about the mean of a population of paired differences with samples of n₁ = 8,n₂ = 8,the degrees of freedom for the t statistic is ____.

If we are testing the hypothesis about the mean of a population of paired differences 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 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?

When we test H₀: μ₁ ≤ μ₂,H_A: μ₁ > μ₂ at α = .10,where $\bar { X } _ { 1 }$ = 77.4, $\bar { X } _ { 2 }$ = 72.2,s₁ = 3.3,s₂ = 2.1,n₁ = 6,n₂ = 6,what is the estimated pooled variance?