Sampling Distribution of the Mean. See attached file for full problem description.

The Golden Calendar Company has population of 16 customers. These customers are brokers who sell the calendars to stores and catalogs. The following datareflect the number of calendars sold to each of the 16 customers last year. Information attached

41,591 48,600 48,348 60,977

26,226 51,269 21,519 20,124

36,526 51,836 40,444 43,572

47,091 31,444 39,580 67,452

a. Compute the population mean and standard deviation.

b. Suppose that Golden managers selected four customers to take part in a special promotional test. The test is designed to increase the number of calendars that each customer will purchase next year. The simple random sampleof four was obtained from this population. The data were:

40,444 21,519 67,452 47,091

________________________________________________________________________

1. Calculate the sample mean number of calendars sold.

2. How much samplingerror is present in this sample?

c. A second simple random sample of 4 was obtained from the population of 16 customers. The data obtained were

36,526 51,836 20,124 43,572

1. Determine the sampling error for this sample

2. Explain why sampling error occurs and why the sampling error in part c is different than the sampling error in part b

3. Discuss the ramifications of sampling error. What problems might it cause in this case, in which the promotion is intended to increase calendar sales next year?

d. Take a sample of size n=8 from the original population.

1. Compute the sampling error

2. Compare the sampling error for this sample with those for the two samples of size n=4.

3. Without regard to the results you obtained here, explain why it is possible for a smaller sample to explain why it is possible for a smaller sample to have a smaller sampling error than a larger sample from the same population.

Please see the attached file. The symbols and tables may not print here correctly.

Customer Calendars

1 41,591

2 26,226

3 36,526

4 47,091

5 48,600

6 51,269

7 51,836

8 31,444

9 48,348

10 21,519

11 40,444

12 39,580

13 60,977

14 20,124

15 43,572

16 67,452

Part a)

Mean 42,287.44

Standard Deviation 12,743.15

Part b 40,444 21,519 67,452 47,091

Sample Mean 44,126.50

Sample Standard Deviation 18951.93

Sampling error (Standard Error) 9475.97

Standard Error=Population standard deviation / square root of sample size

Since we do not know the population standard deviation we will use the sample standard as estimation for …

This problem presents a short case problem to understand the concepts of sampling distribution. After solving this problem the students will understand how the sampling distributing of the mean and sampling error will change as we increase the sample size.