Tilton Athletic Gear is planning to conduct surveys in Los Angeles and New York in an effort to determine whether consumer awareness of the Tilton Athletic brand differs among consumers in these two major markets. Sample results will be used in a hypothesis test testing H0: π The proportion of Los Angeles consumers who are aware of the brand is no greater than the proportion of New York consumers. Ha: π The proportion of Los Angeles consumers who are aware of the brand is greater than the proportion of New York consumers. Design the hypothesis test using a significance level of 5%. For the test, you want the probability of failing to reject the null hypothesis to be no more than 10% if the Los Angeles population brand awareness proportion is actually .05 (five percentage points) greater than the New York population brand awareness proportion. Report the sample size and explain exactly how the test would work. (Assume that in a preliminary sample, the Los Angeles brand awareness proportion was .36 and the New York proportion was .32.)
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