Suppose a researcher collected data to assess if a \"majority\" of all residents

Question

Suppose a researcher collected data to assess if a "majority" of all residents of a particular city were in favor of a newly proposed city ordinance. Her hypotheses are H0: p = 0.5 versus H_a: p > 0.5. A large enough random sample of residents was obtained and the resulting sample proportion was 0.41. Think about the test statistic value: Consider the formula for the z test statistic. Although its exact value cannot be computed without knowing the actual sample size n, it can be determined that the resulting test statistic value will be: Think about the p-value: Consider the sign of the resulting test statistic value and the hypotheses that are to be tested and 'picture' thep-value. (It is recommended that you actually sketch the picture of the p-value -- draw the model for your z statistic assuming the null hypothesis is true, and then shade the area that would be the p-value.) What can you say about that p-value?

Explanation / Answer

a. negative. z=(ps-pu)/(s/sqrtn)

b. It is less than 0.50. Area corresponding to any negative z score is 0.5-(area between mean and z)

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