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

(A) The massage therapist feels that she has a technique that can reduce the frequency and intensity of migraine headaches, So it is left tailed hypothesis

Population proportion p = 15.2/100 = 0.152

Null hypothesis (proportion is equal to 0.152)

Alternate hypothesis (proportion is reduced or less than 0.152)

(2) If the null hypothesis is rejected, then we can conclude that "there is enough evidence to support the claim that the massage therapist has a technique which recuces the frequency and intensity of migraine headaches". This is the alternate hypothesis statement.

(3) We know that the type I error is the rejection of true null hypothesis, i.e. rejecting the null hypothesis when it is true.

In this case, if null hypothesis is true then we will say that the proportion is same, i.e. proportion is 0.152

but rejecting the null hypothesis means we are concluding that the proportion is reduced.(type I error)

So, the statement for type I error will be that "The massage therapist has a technique which recuces the frequency and intensity of migraine headaches, even when there is no change in the frequency and intensity of migraine headaches"

(4) we know that the type II error is failing to reject a false null hypothesis, i.e. accepting the null hypothesis when it is false

In this case, False null hypothesis means that the proportion is not equal to 0.152

but failing to reject false null hypothesis means we are concluding that the proportion is equal to 0.152

So, the statement for type II error will be that "We will conclude that there is no change in the intensity and frequency of migraine headaches, when actually the frequency is reduced by masage therapist technique"