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 2 to test the hypotheses H_0: p = 0.5 versus H_a: 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, Ohm_0 (b) the power of the test (c) the probability of making a Type 1 error (think carefully about this one!) (d) the probability of making a Type 2 error

Explanation / Answer

(a) Null hypothesis:0.5

(b) The power of the test 0.791

(c) Probability of making a Type I error

Ans:0,because a type I error can only be made when the null hypothesis is true,and we have been told that the alternative hypothesis is true

(d) the probability of making a type 2 error

Ans: type 2 error=1-power of the test

                         =1-0.791

                        =0.209

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