Suppose that a study is designed to choose between the hypotheses: Null hypothesis: Population proportion is 0.25. Alternative hypothesis: Population proportion is higher than 0.25. On the basis of a sample of size 500, the sample proportion is 0.29. The null standard error for the potential sample proportions in this case is about 0.02.
a. Compute the standardized score corresponding to the sample proportion of 0.29, assuming the null hypothesis is true.
b. What is the percentile for the standardized score computed in part (a)?
c. What is the p-value for the test?
d. Based on the results of parts (a) to (c), make a conclusion. Be explicit about the wording of your conclusion and justify your answer.
e. To compute the standardized score in part (a), you assumed the null hypothesis was true. Explain why you could not compute a standardized score under the assumption that the alternative hypothesis was true.