# Interpretation of Type I and Type II Errors in Hypothesis Testing

Dr. Jeffrey M. Barrett of Lakeland, Florida, reported data on eight cases of

umbilical cord prolapse. The maternal ages were 25, 28, 17, 26, 27, 22, 25, and 30.

He was interested in determining if he could conclude that the mean age of the

population of his sample was greater than 20 years. Let x = .01.

The null and alternative hypotheses for this problem are defined as:

H0 : μ=20 and Ha : μ>20

a. explain the meaning of a type I error in the context of this problem

b. explain th meaning of a Type II error in the context of this problem.

c. suppose dr barrett expanded his study to include a total of 50 subjects and then calculated a test statistic or z=2.33 for his hypothesis test. what is the associated p-value? what is the conclusion for this test?

https://brainmass.com/statistics/frequentist-inference/571540

#### Solution Preview

Inferential Statistics

Dr. Jeffrey M. Barrett of Lakeland, Florida, reported data on eight cases of

umbilical cord prolapse. The maternal ages were 25, 28, 17, 26, 27, 22, 25, and 30.

He was interested in determining if he could conclude that the mean age of the

population of his sample was greater than 20 years. Let x = .01. (I'm assuming that this means that alpha = 0.01?)

The null and alternative hypotheses for this problem are defined as:

H0 : μ=20 and Ha : μ>20

a. explain the meaning of a type I error in the context of this problem

A Type I Error is said to occur in a hypothesis test whenever the null hypothesis is actually true (which means that the alternative hypothesis must be false), but the data collected leads you to reject the null hypothesis, which leads you to believe what the alternative hypothesis says.

In the context of his problem, if a type I error were to occur, then that would mean that in reality the ...

#### Solution Summary

Type I and Type II errors are defined, and the meaning of making a type I error or a type II error in a hypothesis test is interpreted within the context of the specific hypothesis test being conducted. Also, the p-value approach to deciding whether to reject or fail to reject the null hypothesis is explored and explained with an example.

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

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