Exam 8: Estimation: Additional Topics

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: A dependent random sample from two normally distributed populations gives the following results: n = 20; = 14.8;s_d = 4.0 -Find the lower confidence limit of the 99% confidence interval for the difference between the means of the two populations.

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: Independent random sampling from two normally distributed populations gives the following results: n_x = 55, = 520,σ_x = 30,n_y = 45, = 482,and σ_y = 24 -Find the 98% confidence interval for the difference in the means of the two populations.

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: Consider the data in the table below. -What is the mean of the Group 2?

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: A career counselor is interested in examining the salaries earned by graduate business school students at the end of the first year after graduation.In particular,the counselor is interested in seeing whether there is a difference between men and women graduates' salaries.From a random sample of 20 men,the mean salary is found to be $42,780 with a standard deviation of $5,426.From a sample of 12 women,the mean salary is found to be $40,136 with a standard deviation of $4,383.Assume that the random sample observations are from normally distributed populations,and that the population variances are assumed to be equal. -In order to construct a confidence interval estimate for the difference between two population means,independent samples are obtained from two normal populations with unknown but assumed to be equal variances.If the first sample contains 18 items and the second sample contains 14 items,which of the following distributions will be used?

The margin of error of confidence intervals for the difference between two means,independent samples,and known population variances is given by - ± z_α/2 .

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: In a random sample of 125 large retailers,90 used regression as a method of forecasting.In an independent random sample of 160 small retailers,80 used regression as a method of forecasting. -Find a 95% confidence interval for the difference between the two population proportions.

The Student's t-distribution is required to determine the confidence interval for the difference between two normal population means with unknown population variances.

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: = 32.5 s_d = 8.1 and n = 15 -What is the benefit of matching observations for two dependent samples from two populations as opposed to treating the two samples as independent?

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: A dependent random sample from two normally distributed populations gives the following results: n = 20, = 26.5,s₂ = 3.2 -Find the width of the 98% confidence interval.

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: A computer information systems manager was in charge of purchasing new battery packs for laptop computers.The choices were narrowed to two available models.Since the two models cost about the same,the manager was interested in determining whether there was a difference in the average time the battery packs would function before needing to be recharged.Based on two independent random samples,the following summary information was computed: -Find a 90% confidence interval for the difference in average functioning time before recharging the two models.

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: A dependent random sample from two normally distributed populations gives the following results: n = 20, = 26.5,s₂ = 3.2 -Calculate the margin of error for the given data assuming 95% confidence level: n_x = 250 _x = 0.65 n_y = 360 _y = 0.78

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: Independent random sampling from two normally distributed populations gives the following results: n_x = 64, = 441,σ_x = 20,n_y = 36, = 361,and σ_y = 25 -Find the 90% confidence interval for the difference in the means of the two populations.

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: A dependent random sample from two normally distributed populations gives the following results: n = 20; = 14.8;s_d = 4.0 -Find the upper confidence limit of the 99% confidence interval for the difference between the means of the two populations.

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: Independent samples of math scores from students in the U.S.and Europe were collected from normal populations.A sample of 50 students from the U.S.had an average score of 570 while a sample of 50 European students had an average score of 540.The population standard deviations for the average scores of the US and European students are 102 and 115 respectively. -The confidence interval for the difference between two population means that are normally distributed where the population variances are unknown and are not assumed to be equal rely on the use of:

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: n₁ = 35, ₁ = 140 = 60.84;n₂ = 48, ₂ = 130,and = 156.25 -What is the upper confidence limit of the 95% confidence interval?

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: For constructing a 95% confidence interval estimate for the difference between the means of two normally distributed populations,where the unknown population variances are assumed not to be equal,the summary statistics computed from two independent samples are as follows: n₁ = 50, ₁ = 175,s₁ = 18.5,n₂ = 42, ₂ = 158,and s₂ = 32.4 -What is the lower confidence limit of the 95% confidence interval for the difference between the means?

Assuming unknown but equal population variances,determine the number of degrees of freedom for the following: n₁ = 30, = 16.5;n₂ = 45,and = 17.2.

Find the 95% confidence interval for the difference in the mean costs of parking tickets in these two cities.

In a random sample of 500 California residents,350 indicated that they were home owners.In another random sample of 700 Florida residents,455 indicated that they were home owners.What is the 99% confidence interval for the difference between the proportions?

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: A restaurant manager was in charge of purchasing new microwaves for his restaurant.The choices were narrowed to two available models.Since the two models cost about the same,the manager was interested in determining whether there was a difference in the amount of power consumed when operated at high voltages.Based on two independent random samples,the following summary information was computed: -Find a 90% confidence interval for the difference in the amount of power consumed at high voltages by the two models.