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Hypothesis Testing of Population Proportion: P-Value

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Suppose that a company CEO claims that more than ¾ of his employees carry a secondary health insurance. You decide to test his claim using a significance level of a = 0.02. A sample of 200 employees finds that 160 of them carry secondary health insurance. First, you set up your hypotheses as follows:

H0: p ≤ 0.75
H1: p > 0.75 (claim)

Then you compute your sample statistic, and get the following:

(see attached file for formulas)

Compute the probability of getting a sample statistic at least as extreme as z=1.63, and interpret this probability value. Remember that in a one-tailed test such as this, you do not need to multiply your p-value by two.

Choose one of the following:
a. The p-value is small enough to prove the claim
b. The p-value is not small enough to prove the claim

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Solution Summary

The solution provides step by step method for the calculation of p-value. Formulas for the calculation and Interpretations of the results are also included.