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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?

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.

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