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.)

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 \(\boxed{0.056}\).