Statistics and Probability

A. Answer the following questions: 1. If a population has a mean of 2.9, what is the mean of the sampling distribution of the means? 2. If a population has a variance of 3.2, what is the variance of the sampling distribution of the means if has a sample size of 2 and all possible samples are drawn with replacement? 3. If a population has a standard deviation of 5. What will be its population variance? 4. If a population has a variance of 12.25, what is the variance of the sampling distribution of the means if has a sample size of 2 and all possible samples are drawn with replacement? 5. In item number 4, what will be the standard deviation of the sampling distribution of the means? B. Sample size of n were randomly selected from populations with means and variances given below. In each case, find the mean and standard deviation of the sampling distribution of the means. 1. n = 4 H = 4.6 0' =4 2. n = 9 4 = 7 02 =4 3. n = 16 4 = 8.5 02 =9 4. n = 25 4 = 25 02 = 6.25 5. n = 36 4 = 40 02 = 5.76 C. Solve what are asked. Consider a population consisting of the values (1, 3, 4, 5). 1. Compute the population mean 2. Compute the population variance 3. List all possible samples of size 2 can be drawn from the population with replacement 4. Compute the mean of the sampling distribution of the means 5. Compute the variance of the sampling distribution of the means 6. Compute the standard deviation of the sampling distribution of the means 7. Construct the probability histogram of x with replacements when n = 2