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Statistics: Type I and Type II Error Analysis

A large courier company sends invoices to customers requesting payment within 30 days. The bill lists an address and customers are expected to use their own envelopes to return their payments. Currently the mean and standard deviation of the amount of time taken to pay bills are 24 days and 6 days, respectively. The chief financial officer (CFO) believes that including a stamped self-addressed envelope would decrease the amount of time. She calculates that the improved cash flow from a 2-day decrease in the payment period would pay for the costs of the envelopes and stamps. Any further decrease in the payment period would generate a profit. You have an MBA from the University of Phoenix and work for this company as a Business Analyst. Your core responsibility is to run analytics whose results are used by senior management for critical decision-making. One of your favorite classes in the program was Business Research and Statistics (QNT-561) and you see an opportunity to utilize some of the skills you gained in this course. Because of your strong understanding and background in Inferential Statistics, you decide to take up this important assignment. You have learned that any analysis in inferential statistics starts with sampling. To test the CFO's belief, you decide to randomly select 220 customers and propose to include a stamped self-addressed envelope with their invoices. The CFO accepts your proposal and allows you to run a pilot study. You then record the numbers of days until payment is received. Using your statistical expertise and skills you gained in the class, can you convince the CFO to conclude that the plan will be profitable? Explain to the CFO your reasoning behind selecting a level of significance (by analyzing Type I and Type II errors). Clearly show your Type I and Type II error analysis to me and the CFO.
The dataset for this case is included in the Excel spreadsheet uploaded to OLS
Payment
27
24
14
39
13
31
26
33
13
23
17
24
18
34
13
23
16
32
30
29
21
19
22
14
27
20
11
20
30
24
18
21
24
18
27
27
27
21
22
23
18
17
23
26
20
20
22
21
13
36
18
25
26
19
16
28
16
20
16
14
25
14
35
17
16
19
19
17
18
22
23
22
27
23
23
21
20
18
29
32
27
15
21
26
32
20
29
25
15
21
30
24
23
14
18
22
37
24
35
29
24
17
27
15
19
12
19
21
19
21
15
17
20
21
31
19
27
19
26
26
26
23
12
20
34
21
24
20
21
16
23
13
19
18
31
29
23
28
19
19
22
24
21
23
14
25
17
22
21
18
22
15
27
14
23
25
24
24
17
16
30
24
17
27
24
17
10
25
15
13
29
21
22
11
25
30
23
18
19
18
14
21
22
17
19
23
31
26
25
15
16
28
27
22
12
25
12
21
19
26
16
21
30
16
25
13
11
13
22
28
14
21
30
19
14
31
9
14
21
28

Solution Preview

I have answered your posting in the attached MS Word doc. Good luck.

Stat question
A large courier company sends invoices to customers requesting payment within 30 days. The bill lists an address and customers are expected to use their own envelopes to return their payments. Currently the mean and standard deviation of the amount of time taken to pay bills are 24 days and 6 days, respectively. The chief financial officer (CFO) believes that including a stamped self-addressed envelope would decrease the amount of time. She calculates that the improved cash flow from a 2-day decrease in the payment period would pay for the costs of the envelopes and stamps. Any further decrease in the payment period would generate a profit. You have an MBA from the University of Phoenix and work for this company as a Business Analyst. Your core responsibility is to run analytics whose results are used by senior management for critical decision-making. One of your favorite classes in the program was Business Research and Statistics (QNT-561) and you see an opportunity to utilize some of the skills you gained in this course. Because of your strong understanding and background in Inferential Statistics, you decide to take up this important assignment. You have learned that any analysis in inferential statistics starts with sampling. To test the CFO's belief, you decide to randomly select 220 customers and propose to include a stamped self-addressed envelope with their invoices. The CFO accepts your proposal and allows you to run a pilot study. You then record the numbers of days until payment is received. Using your statistical expertise and skills you gained in the class, can you convince the CFO to conclude that the plan will be profitable? ...

Solution Summary

Type I and Type II error analysis is examined.

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