The test statistic of \( z=1.72 \) is obtained when testing the claim that \( p \neq 0.486 \). 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. Click here to view page 2 of the standard normal distribution table. a. This is a two-tailed test. b. P-value \( =\square \) (Round to three decimal places as needed.)

To address your questions step by step: ### a. Identify the hypothesis test as being two-tailed, left-tailed, or right-tailed. Since the claim is that \( p \neq 0.486 \), this indicates that we are testing for a difference in either direction (greater than or less than). Therefore, this is a **two-tailed test**. ### b. Find the \( P \)-value. To find the \( P \)-value for a two-tailed test with a test statistic of \( z = 1.72 \), we need to find the area in both tails of the standard normal distribution. 1. First, we find the area to the right of \( z = 1.72 \): - Using the standard normal distribution table or a calculator, we find the cumulative probability for \( z = 1.72 \). - The cumulative probability \( P(Z < 1.72) \) is approximately \( 0.9573 \). 2. The area to the right of \( z = 1.72 \) is: \[ P(Z > 1.72) = 1 - P(Z < 1.72) = 1 - 0.9573 = 0.0427. \] 3. Since this is a two-tailed test, we need to double this area to account for both tails: \[ P\text{-value} = 2 \times P(Z > 1.72) = 2 \times 0.0427 = 0.0854. \] Thus, the \( P \)-value is approximately **0.085** (rounded to three decimal places). ### c. Using a significance level of \( \alpha=0.01 \), should we reject \( \mathrm{H}_{0} \) or should we fail to reject \( \mathrm{H}_{0} \)? To make a decision: - The \( P \)-value we calculated is \( 0.085 \). - The significance level \( \alpha \) is \( 0.01 \). Since \( 0.085 > 0.01 \), we **fail to reject \( \mathrm{H}_{0} \)**. ### Summary of Answers: a. This is a **two-tailed test**. b. \( P \)-value \( = 0.085 \) (rounded to three decimal places). c. We **fail to reject \( \mathrm{H}_{0} \)**.