The test statistic of $$ z=1.67 $$ is obtained when testing the claim that $$ p
eq 0.334 $$. 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 $$ \alpha=0.05 $$, 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.)

Question

The test statistic of $$ z=1.67 $$ is obtained when testing the claim that $$ p 
eq 0.334 $$. 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 $$ \alpha=0.05 $$, 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.)

UpStudy AI · Accepted Answer

**a. Identify the hypothesis test type:**

Since the claim is that $$ p \neq 0.334 $$, the alternative hypothesis involves a “not equal to” statement. This indicates a two-tailed test.

**b. Finding the P-value:**

The test statistic is given as $$ z = 1.67 $$.

For a two-tailed test, the P-value is computed as:
$$
\text{P-value} = 2 \times P(Z > 1.67)
$$

Using the standard normal distribution table, we find:
$$
P(Z < 1.67) \approx 0.9525
$$

Thus,
$$
P(Z > 1.67) = 1 - 0.9525 = 0.0475
$$
and so,
$$
\text{P-value} = 2 \times 0.0475 = 0.095
$$

**c. Decision at $$ \alpha = 0.05 $$:**

Compare the P-value with $$ \alpha $$:
$$
0.095 > 0.05
$$

Since the P-value exceeds the significance level, we fail to reject the null hypothesis $$ \mathrm{H}_0 $$.
**a. This is a two-tailed test.** **b. P-value $$ = 0.095 $$** **c. Fail to reject $$ \mathrm{H}_0 $$ at $$ \alpha = 0.05 $$.**

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