Parameters Use the same population of {4, 5, 9} from Example 1 in Section 6-4. Assume that samples of? size n? = 2 are randomly selected ?without replacement. ? a. Fin?? and ?? for the population. b. After finding all sam? ples of siz? = 2 that can be obtained ?without replacement, find the population of all values of by finding the mean of each?sample of size ?n = 2. c. Find the mean and standard deviation for the population of sample means found in part (b). d. Verify that

Answer: Step 1 The population given here is 4, 5, 9 then the population mean is denoted as is given by x i Population Mean () = n = 4 + 5 = 6 3 The value of population mean is 6. Step 2 The population standard deviation is given by (X ) = N (4 6) + (5 6) + (9 6) = 3 = 2.1587 The value of population standard deviation is 2.1587. Step 3 b) After finding all samples of size n = 2 that can be obtained without replacement, the population of all values of x by finding the mean of each sample of size n = 2 is given in the table below. The table of Simple Random Sampling for without replacement for sample mean and standard deviation is Sample Sample mean 4,5 4.5 -1.5 2.25 4,9 6.5 0.5 0.25 5,4 4.5 -1.5 2.25 5,9 7 1 1 9,4 6.5 0.5 0.25 9,5 7 1 1 Sum 36 7