A large manufacturing firm believes that its market share is 45%. From time to time, a statistical hypothesis test is carried out to check whether the assertion is true. The test consists of gathering a random sample of 500 products sold nationally and finding what percentage of the sample constitutes brands made by the firm. Whenever the test is carried out, there is no suspicion as to the direction of a possible change in market share, that is, increase or decrease; the company wants to detect any change at all. The tests are carried out at the α = 0.01 level of significance. What is the probability of being able to statistically determine a true change in the market share of magnitude 5% in either direction? (That is, find the power at p = 0.50 or p = 0.40.
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