# Statistics: Type I and Type II Error Analysis

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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

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18

17

23

26

20

20

22

21

13

36

18

25

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19

16

28

16

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14

25

14

35

17

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22

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27

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18

29

32

27

15

21

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32

20

29

25

15

21

30

24

23

14

18

22

37

24

35

29

24

17

27

15

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12

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19

21

15

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21

31

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34

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24

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31

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14

25

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24

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24

17

10

25

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13

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12

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30

16

25

13

11

13

22

28

14

21

30

19

14

31

9

14

21

28

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Type I and Type II error analysis is examined.

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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? ...

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