Exam 11: Estimation: Comparing Two Populations

If two random samples of sizes $n _ { 1 }$ and $n _ { 2 }$ are selected independently from two populations with means $\mu _ { 1 }$ and $\mu _ { 2 }$ , then the mean of the sampling distribution of the sample mean difference, $\bar { X } _ { 1 } - \bar { X } _ { 2 }$ , equals:

If two populations are not known to be normally distributed, the sampling distribution of the sample mean difference, $\bar { X } _ { 1 } - \bar { X } _ { 2 }$ , will be:

Ten functionally illiterate adults were given an experimental one-week crash course in reading. Each of the 10 was given a reading test prior to the course and another test after the course. The results are shown below. Adult 1 2 3 4 5 6 7 8 9 10 Score after course 48 42 43 34 50 30 43 38 41 30 Score before course 31 34 18 30 44 28 34 33 27 32 a. Estimate the mean improvement with 95% confidence. b. Briefly describe what the interval estimate in part a. tells you.

A quality control inspector keeps a tally sheet of the numbers of acceptable and unacceptable products that come off two different production lines. The completed sheet is shown below. Production line Acceptable products Unacceptable products 1 152 48 2 136 54 Estimate with 95% confidence the difference in population proportions.

In an experiment comparing two populations, we find the following statistics: n1 = 150, x1 = 72. n2 = 175, x2 = 70. Estimate with 95% confidence the difference between the two population proportions.

If two random samples of sizes $n _ { 1 }$ and $n _ { 2 }$ are selected independently from two non-normally distributed populations, then the sampling distribution of the sample mean difference, $\bar { X } _ { 1 } - \bar { X } _ { 2 }$ , is:

Estimate p1 − p2 with 99% confidence, given that n1 = 50 and n2 = 50 and the first sample has a proportion of 0.50 and the second sample has a proportion of 0.20

If two random samples of sizes 30 and 45 are selected independently from two non-normal populations with means of 53 and 57, then the mean of the sampling distribution of the sample mean difference, $\bar { X } _ { 1 } - \bar { X } _ { 2 }$ , equals -4.

If two random samples of sizes $n _ { 1 }$ and $n _ { 2 }$ are selected independently from two populations with variances $\sigma _ { 1 } ^ { 2 }$ and $\sigma _ { 2 } ^ { 2 }$ , then the standard error of the sampling distribution of the sample mean difference, $\bar { X } _ { 1 } - \bar { X } _ { 2 }$ , equals:

In an experiment comparing two populations, we find the following statistics: n1 = 200, x1 = 80. n2 = 400, x2 = 140. Estimate with 95% confidence the difference between the two population proportions.

Suppose that the starting salaries of male workers are normally distributed with a mean of $56 000 and a standard deviation of $12 000. The starting salaries of female workers are normally distributed with a mean of $50 000 and a standard deviation of $10 000. A random sample of 50 male workers and a random sample of 40 female workers are selected. a. What is the sampling distribution of the sample mean difference $\bar { X } _ { 1 } - \bar { X } _ { 2 }$ ? Explain. b. Find the expected value and the standard error of the sample mean difference. c. What is the probability that the sample mean salary of female workers will not exceed that of the male workers?

Given the following statistics: n1 = 10, $\bar { X } _ { 1 }$ = 58.6, s1 = 13.45. n2 = 10, $\bar { X } _ { 2 }$ = 64.6, s2 = 11.15. Estimate with 95% confidence the difference between the two population means.

Thirty-five employees who completed two years of tertiary education were asked to take a basic mathematics test. The mean and standard deviation of their marks were 75.1 and 12.8, respectively. In a random sample of 50 employees who only completed high school, the mean and standard deviation of the test marks were 72.1 and 14.6, respectively. Estimate with 90% confidence the difference in mean scores between the two groups of employees.

Two independent random samples are drawn from two normal populations. The sample sizes are 20 and 25, respectively. The parameters of these populations are: Population 1: \mu=505,\sigma=10 Population 2: \mu=475,\sigma=7 Find the probability that the difference between the two sample means $\bar { X } _ { 1 } - \bar { X } _ { 2 }$ is between 25 and 35.

The expected value of the difference of two sample means equals the difference of the corresponding population means:

Which of the following statements is correct when estimating the difference between two population proportions p₁ − p₂?