The proportion of adults living in Tempe, Arizona who are college graduates is estimated to be p...

Question:

The proportion of adults living in Tempe, Arizona who are college graduates is estimated to be p = 0.4. To test this hypothesis, a random sample of 15 Tempe adults is selected. If the number of college graduates is between 4 and 8, the hypothesis will be accepted; otherwise, we will conclude that p is not equal to 0.4.

(a) Find the type I error probability for this procedure, assuming that p = 0.4.

(b) Find the probability of committing a type II error if the true proportion is really p = 0.2.

Type I and Type II Errors

A type I error in statistics occurs when a true null hypothesis is rejected. That means we reject the null hypothesis with the appropriate statistic, but the null hypothesis is in fact true. A type II error occurs when a false null hypothesis is not reject. That means the test statistic does not show sufficient evidence to reject the null hypothesis, but the null hypothesis is in fact false and should be rejected.

Answer and Explanation:

(a) Find the type I error probability for this procedure, assuming that p = 0.4.

To determine this probability we need to find the probability of...

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Type I & Type II Errors in Hypothesis Testing: Differences & Examples

from Statistics 101: Principles of Statistics

Chapter 10 / Lesson 4
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