Question

According to the Centres for Disease Control, 15.2% of American adults experience migraine headaches. Stress is a major contributor to the frequency and intensity of headaches. A massage therapist feels that she has a technique that can reduce the frequency and intensity of migraine headaches. (a) Determine the null and alternative hypotheses that would be used to test the effectiveness of the massage therapists techniques. (b) A sample of 500 American adults who participated in the massage therapists program results in data that indicate that the null hypothesis should be rejected. Provide a statement that supports the massage therapists program. (c) Explain what it would mean to make Type I error. (d) Explain what it would mean to make a Type II error.

Answer 1

Given,

Population proportion, P = 0.152

(a) Our hypothesis is,

H₀ : P = 0.152 i.e. 15.2% of american adults experience migraine headaches.

H₁ : P < 0.152 i.e. The therapy techniquereduce the frequency of migraine headaches.

(b) Result is that H0 is rejected (Given)

Since, H0 is rejected, therefore we say that there is enough evidence to support the claim that massage therapy program reduce the frequency and intensity of migraine headaches.

(c) If type 1 error occure : Type 1 error is that reject H0 when H0 is true, so if type 1 error occur means therapy program is not effective but we wrongly conclude that it is effective.