Problem

The test statistic of $z=1.59$ is obtained when testing the claim that $p>0.5$. a. Identify the hypothesis test as being two-tailed, left-tailed, or right-tailed. b. Find the P-value. c. Using a significance level of $\alpha=0.01$, should we reject $\mathrm{H}_{0}$ or should we fail to reject $\mathrm{H}_{0}$ ? Click here to view page 1 of the standard normal distribution table. b. $P$-value $=$ (Round to three decimal places as needed.)

Solution

Step 1 :The test statistic of \(z=1.59\) is obtained when testing the claim that \(p>0.5\).

Step 2 :This is a right-tailed hypothesis test because we are testing the claim that \(p>0.5\).

Step 3 :The P-value is the probability of obtaining a result as extreme as, or more extreme than, the observed result, under the null hypothesis.

Step 4 :In a right-tailed test, this is the probability of obtaining a result greater than the observed test statistic.

Step 5 :We can find this probability using the standard normal distribution table or a z-score calculator.

Step 6 :The P-value is approximately 0.056. This is the probability of obtaining a test statistic as extreme as, or more extreme than, \(z=1.59\) under the null hypothesis.

Step 7 :Final Answer: The P-value is approximately \(\boxed{0.056}\).

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