Exam 8: Estimation: Additional Topics

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: From a random sample of seven students in a marketing research class that uses group-learning techniques,the mean examination score was found to be 78.25 and the sample standard deviation was 2.87.For an independent random sample of ten students in another marketing research class that does not use group-learning techniques,the sample mean and standard deviation of exam scores were 74.94 and 9.15,respectively. -Based on the 95% confidence interval for the difference between the two population mean scores,is there evidence that the population means are different? Do not assume equal population variances.

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 = 200 _x = 0.56 n_y = 230 _y = 0.46

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: From a random sample of ten students in an operations management class that uses group-learning techniques,the mean examination score was found to be 82.75 and the sample standard deviation was 3.24.For an independent random sample of eight students in another marketing research class that does not use group-learning techniques,the sample mean and standard deviation of exam scores were 75.62 and 7.27,respectively.It is assumed that the and unknown population variances are not assumed to be equal. -Determine the number of degrees of freedom.

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: Two dependent random samples from two normally distributed populations gives the following results: n = 10; = 20.5;s_d = 3.2 -Find the width of the 95% confidence interval.

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. -What is the lower confidence limit of the 95% confidence interval for the difference between the population mean salary for men and women?

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 margin of error for a 90% confidence interval for the difference in the means of the two populations.

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: = 32.5 s_d = 8.1 and n = 15 -Calculate the width of the interval for a 90% confidence interval.

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: A dependent random sample from two normally distributed populations gives the following results: n = 20, = 27.5,and s_d = 3.2 -Find the margin of error for a 90% 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 sample variance of the Group 2?

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: Consider the data in the table below. -What is the mean of the Group 1?

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: The means and variances are obtained from two independent samples.Assume that the populations from which the samples were drawn have unequal variances. -Determine the number of degrees of freedom for n₁ = 7, = 24,n₂ = 8,and = 30.

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: = 19.56 s_d = 2.5 and n = 20 -Calculate the margin of error for a 95% confidence interval using the given data:

You are interested in examining the salaries earned by graduate business school students at the end of the first year after graduation.In particular,you are interested in seeing whether there is a difference between men and women graduates' salaries.From a random sample of 55 women,you find the mean salary to be $47,520 with a standard deviation of $5,633.From a sample of 64 men,you find the mean salary to be $44,304 with a standard deviation of $4,793.Assume the random sample observations are from normally distributed populations,and that the population variances are assumed to be equal.Develop a 95% confidence interval for the difference between the population mean salary for men and women.

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: The residents of Austin,Texas,complain that parking fines given in their city are higher than the parking fines that are given in Houston.Independent random samples of the amounts paid by residents for parking tickets in each of two cities over the last four months were obtained.Assume the population variances are equal.These amounts were as follows: -What is the sample variance of the parking fines issued in Austin?

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: A dependent random sample from two normally distributed populations gives the following results: n = 15, = 20.5,and s_d = 2.4 -Find the 95% confidence interval for the difference in the means of the two populations.

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: The residents of Austin,Texas,complain that parking fines given in their city are higher than the parking fines that are given in Houston.Independent random samples of the amounts paid by residents for parking tickets in each of two cities over the last four months were obtained.Assume the population variances are equal.These amounts were as follows: -Calculate the pooled sample variance.

To develop a confidence interval for the difference between the means of two populations which are normally distributed and have equal variances,two independent samples of sizes n₁ and n₂ are randomly selected from the two populations.What is the formula used to determine the number of degrees of freedom for the t distribution?

While constructing a confidence interval for the mean difference in paired data,as the sample size increases,the width of the interval also increases.

A 100(1- α)% confidence interval for the difference between two means,independent samples,and known population variances is given by - ± z_α/2 .

Certain situations that involve dependent samples are known as repeated measurements.