An airline suspects that a majority of frequent fliers prefer aisle seats. They

Question

An airline suspects that a majority of frequent fliers prefer aisle seats. They define p = proportion of the population of frequent fliers who prefer aisle seats, and plan to test the hypotheses H0: p = 0.5 versus Ha: p > 0.5. The company statistician plans to conduct the test using a significance level of 0.05 based on a random sample of 600 frequent fliers. Suppose in fact 55% of the population of frequent fliers prefer aisle seats. Then the probability that the test will (correctly) result in rejecting the null hypothesis is 0.791. Based on this information, provide numerical values for each of the following.

a) the null set

b)the power of the test

c) the probability of making type 1 error

d) the probability of making type 2 error

Explanation / Answer

a)Null Set = 0.5

b)The probability of not committing a Type II error is called the power of a hypothesis test.

Power = 1 - 0.0142 = 0.9858

c)For type I error:
z = (0.55 - 0.5)/sqrt(0.5*(0.5)/600) = 2.45
P-value = P(z > 2.45) = 1 - 0.9929 = 0.0071

d)For type II error:
z = (0.55 - 0.5)/sqrt(0.5*(0.5)/600) = 2.45
P-value = 2*P(z > 2.45) = 2*(1 - 0.9929) = 0.0142

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