Question

The probability that a woman in the United States, aged 40–59, has a stroke is 0.317 (31.7%). Consider the claim that following a particular diet decreases the likelihood of developing a stroke, so that the probability is less than 0.317 (31.7%). At a significance level of 0.05, if the proportion of people who follow a particular diet and develop a stroke is 0.312 or less, the power to reject the null hypothesis is 0.06. Determine the probability of each kind of error for this hypothesis test. probability of type I error: probability of type II error:

Answer 1

For any hypothesis test, we have:

Probability of type I error = Significance level

[Since, P(type I error) = P(rejecting null hypothesis | null hypothesis is true) = signficance level]

Now, we are given in question that the singificance level is 0.05, thus we get:

Probability of type I error = 0.05 [ANSWER]

Moreover, in any hypothesis test, we have:

Probability of type II error = 1 - Power of the test

[This is because P(Type II error) = P(not rejecting null hypothesis | null hypothesis is false) and Power = P(rejecting null hypothesis | null hypothesis is false)]

Now, we are given in question that the power of the test is 0.06, thus we get:
Probability of Type II error = 1 - 0.06 = 0.94 [ANSWER]

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