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    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
    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

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    https://brainmass.com/statistics/statistical-inference/statistics-type-type-error-analysis-496444

    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.

    $2.19