The test statistic of z = - 1.81 is obtained when testing the claim that p = 2/3. a. Using a significance level of a = 0.05, find the critical value(s). b. Should we reject Họ or should we fail to reject H, ? 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. The critical value(s) is/are z = (Round to two decimal places as needed. Use a comma to separate answers as needed.)

MATLAB: An Introduction with Applications
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**Title: Hypothesis Testing and Critical Values**

**Problem Statement:**

The test statistic of z = -1.81 is obtained when testing the claim that p = 2/3.

**Tasks:**

a. Using a significance level of α = 0.05, find the critical value(s).

b. Should we reject H₀ or should we fail to reject H₀?

**Resources:**

- Click here to view page 1 of the standard normal distribution table.
- Click here to view page 2 of the standard normal distribution table.

**Solution:**

a. The critical value(s) is/are z = [____].

*(Round to two decimal places as needed. Use a comma to separate answers as needed.)* 

---

**Explanation:**

This problem involves hypothesis testing using a standard normal distribution. To find the critical value(s), refer to the standard normal distribution table to determine the z-value that corresponds to the significance level, α = 0.05.

In hypothesis testing:

1. **Null Hypothesis (H₀):** p = 2/3

2. **Alternative Hypothesis (H₁):** p ≠ 2/3 (assuming a two-tailed test)

The critical value(s) help determine the rejection region for testing the null hypothesis. If the test statistic falls in the rejection region, we reject H₀; otherwise, we fail to reject H₀.

For further exploration, use the provided links to the standard normal distribution table, which will aid in identifying the corresponding critical z-value(s).
Transcribed Image Text:**Title: Hypothesis Testing and Critical Values** **Problem Statement:** The test statistic of z = -1.81 is obtained when testing the claim that p = 2/3. **Tasks:** a. Using a significance level of α = 0.05, find the critical value(s). b. Should we reject H₀ or should we fail to reject H₀? **Resources:** - Click here to view page 1 of the standard normal distribution table. - Click here to view page 2 of the standard normal distribution table. **Solution:** a. The critical value(s) is/are z = [____]. *(Round to two decimal places as needed. Use a comma to separate answers as needed.)* --- **Explanation:** This problem involves hypothesis testing using a standard normal distribution. To find the critical value(s), refer to the standard normal distribution table to determine the z-value that corresponds to the significance level, α = 0.05. In hypothesis testing: 1. **Null Hypothesis (H₀):** p = 2/3 2. **Alternative Hypothesis (H₁):** p ≠ 2/3 (assuming a two-tailed test) The critical value(s) help determine the rejection region for testing the null hypothesis. If the test statistic falls in the rejection region, we reject H₀; otherwise, we fail to reject H₀. For further exploration, use the provided links to the standard normal distribution table, which will aid in identifying the corresponding critical z-value(s).
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