Question

The proportion of California residents who reported insufficient rest or sleep during each of the preceding 30 days is 8.0%, while this proportion is 8.8% for Oregon residents. These data are based on simple random samples of 11,545 California and 4,691 Oregon residents.

(a) Conduct a hypothesis test to determine if these data provide strong evidence the rate of sleep deprivation is different for the two states.
(b) It is possible the conclusion of the test in part (a) is incorrect. If this is the case, what type of error was made?

Answer 1

Explanation:

We start by stating the null hypothesis

H0: p1 = p2

No difference is existent

H1: p2 not equal to p2

There is a difference

We find the z statistic using microsoft excel or using the formula in the attachment

= -1.68

From the normal table, p value = 0.099

The p value is greater than 0.05 so we fail to reject the null hypothesis and conclude there is no difference

B. If answer in part a is incorrect then we have made a type ii error. A type 2 error occurs when we accept a false null hypothesis.