Question

3. According to the Center for Disease Control, 15.2% of adult Americans experience migraine headaches. Stress is a major contributor to the frequency and intensity of headaches. A massage therapist believes that she has a technique that can reduce the frequency and intensity of migraine headaches. The following hypotheses are used to test the effectiveness of the massage therapist’s claim.

Ho: The true proportion of adults who experience migraine headaches after massage therapy is 0.152.

HA: The true proportion of adults who experience migraine headaches after massage therapy is less than 0.152 A.

Describe Type 1 error in the context of this situation. (4 points)

We conclude that proportion of adults who experience migraines after therapy is less than 0.152 when it is not less than 0.152. (We think the therapy is helping but it really is not).

1 pt correct conclusion – “concludes proportion has decreased” 1 pt correct truth – “proportion has not decreased” 2 pts – context for both conclusion and truth Deductions: deduct 1 point if the word proportion is not used

From my understanding a type 1 error is when p > ? and we fail to reject the null hypothesis. Following this mindest Ho cannot be reject. So why is the answer less than 0.152 when it is not less than 0.152? I thought it would be the proportion equals .152 cannot be rejected.

Answer 1

Type 1 error is the case when we reject the null hypothesis when actually it should not have been rejected. Incorrect rejection of null hypothesis gives rise to type 1 error. In this case it is given that type 1 error has occurred.

This means that although the data shows at first that the proportion has decreased after the therapy, but the truth is that it has actually not decreased. The decrease in proportion shown by the data is a chance occurrence, and not of any significance.

In your solution, although the proportion you calculate is less than 0.152 for the particular sample, but this does not mean that we should reach to the big conclusion that the propotion for the population is also less than 0.152

The proportion is less just for the sample, and in this case it has occurred by chance. We cannot make any conclusions about the population from this sample data, because the p-value is greater than the significance level. If the p-value had been less than the significance level, then it would have been correct to make that conclusion.