The test statistic of $$ z=-1.18 $$ is obtained when testing the claim that $$ p
eq 0.513 $$. This is a two-tailed test. Using a 0.05 significance level, complete parts (a) and (b). Click here to view the standard normal distribution table for negative $$ z $$ scores. Click here to view the standard normal distribution table for positive $$ z $$ scores. a. Find the critical value(s) Select the correct choice below and fill in the answer box(es) within your choice. (Round to two decimal places as needed.) A. There are two critical values; the lower critical value is -1.96 and the upper critical value is 1.96 . B. There is one critical value, the critical value is A. Should we reject $$ H_{0} $$ or should we fail to reject $$ H_{0} $$ ? B. $$ H_{0} $$ should be rejected, since the test statistic is in the critical region. B. $$ H_{0} $$ should not be rejected, since the test statistic is not in the critical region. C. $$ H_{0} $$ should be rejected, since the test statistic is not in the critical region. D. $$ H_{0} $$ should not be rejected, since the test statistic is in the critical region.

Question

The test statistic of $$ z=-1.18 $$ is obtained when testing the claim that $$ p 
eq 0.513 $$. This is a two-tailed test. Using a 0.05 significance level, complete parts (a) and (b). Click here to view the standard normal distribution table for negative $$ z $$ scores. Click here to view the standard normal distribution table for positive $$ z $$ scores. a. Find the critical value(s) Select the correct choice below and fill in the answer box(es) within your choice. (Round to two decimal places as needed.) A. There are two critical values; the lower critical value is -1.96 and the upper critical value is 1.96 . B. There is one critical value, the critical value is A. Should we reject $$ H_{0} $$ or should we fail to reject $$ H_{0} $$ ? B. $$ H_{0} $$ should be rejected, since the test statistic is in the critical region. B. $$ H_{0} $$ should not be rejected, since the test statistic is not in the critical region. C. $$ H_{0} $$ should be rejected, since the test statistic is not in the critical region. D. $$ H_{0} $$ should not be rejected, since the test statistic is in the critical region.

UpStudy AI · Accepted Answer

**Step 1. Determine the Critical Values**

For a two-tailed test at a significance level of $$\alpha = 0.05$$, we split the significance level between the two tails. Each tail has an area of  
$$
\frac{\alpha}{2} = \frac{0.05}{2} = 0.025.
$$

The z-value corresponding to an upper tail probability of $$0.025$$ is approximately $$1.96$$. Since the test is two-tailed, the lower critical value is the negative of this value:  
$$
-1.96.
$$

Thus, the two critical values are:
- Lower critical value: $$-1.96$$
- Upper critical value: $$1.96$$

This corresponds to choice:

**A. There are two critical values; the lower critical value is $$-1.96$$ and the upper critical value is $$1.96$$.**

---

**Step 2. Decision Based on the Test Statistic**

The test statistic provided is:
$$
z = -1.18.
$$

We compare this value to the critical values:
- If $$z \leq -1.96$$ or $$z \geq 1.96$$, we would reject $$H_{0}$$.
- Since $$-1.96 < -1.18 < 1.96$$, the test statistic does not fall in the critical region.

Thus, we do not have sufficient evidence to reject $$H_{0}$$.

This corresponds to choice:

**B. $$H_{0}$$ should not be rejected, since the test statistic is not in the critical region.**
**a. Critical Values:** - Lower critical value: $$-1.96$$ - Upper critical value: $$1.96$$ **b. Decision:** - $$H_{0}$$ should not be rejected, since the test statistic $$-1.18$$ is not in the critical region.

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