Exam 8: Estimation: Additional Topics

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 = 13, = 4,n₂ = 15,and = 10.

The estimation procedure used to compare two population means when the sample values from the first population are influenced by the sample values from the second population is known as matched pairs.

For confidence intervals of two means that are dependent samples,the margin of error is equal to t_n-1,tα/s .

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. -Estimate with 95% confidence the difference between the two population mean scores.Do not assume equal population variances.

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: In a recent survey of 240 teachers in Richmond,Virginia,77.2% supported standardized national testing of elementary students.In a survey of 162 teachers in Raleigh,North Carolina,64.2% supported national testing. -What is the lower confidence limit of the 99% confidence interval for the difference between the two population proportions?

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 -The pooled variance is formed by combining information from two independent samples. If = 39, = 25,and n₁ = n₂ = 12 then Is equal to:

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 -A 95% confidence interval estimate for the difference between two population means,μ₁ - μ₂,is determined to be 62.75 < μ₁ - μ₂ < 68.52.Which of the following is true if the confidence level is reduced to 90%?

Determine the number of degrees of freedom.

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 95% confidence interval for the difference in the means of the two populations.

Calculate the pooled sample variance.

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. -What is the lower confidence limit of the 95% confidence interval for the difference between the population means?

Assuming equal population variances,determine the number of degrees of freedom for the following: n₁ = 10, = 36;n₂ = 12,and = 34

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 margin of error for a 95% confidence interval for the difference between 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 margin of error for a 90% confidence interval using the given data:

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: A confidence interval for the difference between the means of two normally distributed populations based on the following dependent samples is desired: -What is the lower confidence limit of the 95% confidence interval?

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

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 margin of error for a 98% confidence interval for the difference in the means of the two populations.

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. -Find the 95% confidence for the difference between the two population mean scores.

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: In calculating the 95% confidence interval for μ₁ - μ₂ the difference between the means of two normally distributed populations,the summary statistics from two independent samples are: n_x = 10, = 50, = 0.64,n_y = 10, = 40,and = 1.86. -What is the lower confidence limit of the 95% confidence interval if the Population variances are unknown and are assumed to be equal?

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. -A random sample of 100 men contained 63 in favor of a state constitutional amendment to retard the rate of growth of property taxes.An independent random sample of 100 women contained 55 in favor of this amendment.The confidence interval 0.023 < P_x - P_y < 0.295 was calculated for the difference between the population proportions.What is the confidence level of this interval?