The test statistic of $$ z=-1.33 $$ is obtained when testing the claim that $$ \mathrm{p}

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The test statistic of $$ z=-1.33 $$ is obtained when testing the claim that $$ \mathrm{p}<\frac{1}{3} $$. This is a left-tailed test. Using a 0.10 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 and the upper critical value is B. There is one critical value, the critical value is -1.28 . Should we reject $$ H_{0} $$ or should we fail to reject $$ H_{0} $$ ? A. $$ H_{0} $$ 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

**a. Determining the Critical Value**

Since this is a left-tailed test at the $$ \alpha = 0.10 $$ significance level, we find the $$ z $$-value such that the area to the left is $$ 0.10 $$. Consulting the standard normal distribution table, we find:
$$
z_{0.10} \approx -1.28
$$
Thus, there is one critical value:
- The critical value is $$ z = -1.28 $$.

**b. Decision: Reject or Fail to Reject $$ H_0 $$?**

Given the test statistic:
$$
z = -1.33
$$
we compare it to the critical value:
$$
-1.33 < -1.28
$$
Since the test statistic lies in the critical region (i.e., it is more extreme than the critical value), we conclude:

$$
\textbf{Reject } H_0
$$

**Final Answers:**

- **Critical Value:**  
  B. There is one critical value, the critical value is $$ -1.28 $$.

- **Decision:**  
  A. $$ H_0 $$ should be rejected, since the test statistic is in the critical region.
**a. Critical Value:** - There is one critical value: $$ z = -1.28 $$. **b. Decision:** - Reject $$ H_0 $$ because the test statistic $$ z = -1.33 $$ is in the critical region. **Final Answer:** - **Critical Value:** B. $$ z = -1.28 $$ - **Decision:** A. Reject $$ H_0 $$

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