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Golden Calendar Company - Sampling Distribution of the Mean

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 data reflect 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 sample of 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 sampling error 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.

Attachments

Solution Preview

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 ...

Solution Summary

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.

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