Assume a significance level of a = 0.05 and use the given information to complete parts (a) and (b) below. Original claim: Less than 51% of adults would erase all of their personal information online if they could. The hypothesis test results in a P-value of 0.0378. a. State a conclusion about the null hypothesis. (Reject Ho or fail to reject Ho:) Choose the correct answer below.

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### Statistical Hypothesis Testing Example

Assume a significance level of α = 0.05 and use the given information to complete parts (a) and (b) below.

**Original claim:** Less than 51% of adults would erase all of their personal information online if they could. The hypothesis test results in a P-value of 0.0378.

#### a. State a conclusion about the null hypothesis. (Reject H₀ or fail to reject H₀.) Choose the correct answer below.

- **A.** Fail to reject H₀ because the P-value is less than or equal to α.
- **B.** Reject H₀ because the P-value is less than or equal to α.
- **C.** Fail to reject H₀ because the P-value is greater than α.
- **D.** Reject H₀ because the P-value is greater than α.

**Explanation:**
To determine the correct conclusion, compare the P-value to the significance level (α). If the P-value is less than or equal to α, reject the null hypothesis (H₀). If the P-value is greater than α, fail to reject the null hypothesis. In this case, the P-value (0.0378) is less than the significance level (0.05), hence we should reject H₀.

**Correct answer:** **B.** Reject H₀ because the P-value is less than or equal to α.
Transcribed Image Text:### Statistical Hypothesis Testing Example Assume a significance level of α = 0.05 and use the given information to complete parts (a) and (b) below. **Original claim:** Less than 51% of adults would erase all of their personal information online if they could. The hypothesis test results in a P-value of 0.0378. #### a. State a conclusion about the null hypothesis. (Reject H₀ or fail to reject H₀.) Choose the correct answer below. - **A.** Fail to reject H₀ because the P-value is less than or equal to α. - **B.** Reject H₀ because the P-value is less than or equal to α. - **C.** Fail to reject H₀ because the P-value is greater than α. - **D.** Reject H₀ because the P-value is greater than α. **Explanation:** To determine the correct conclusion, compare the P-value to the significance level (α). If the P-value is less than or equal to α, reject the null hypothesis (H₀). If the P-value is greater than α, fail to reject the null hypothesis. In this case, the P-value (0.0378) is less than the significance level (0.05), hence we should reject H₀. **Correct answer:** **B.** Reject H₀ because the P-value is less than or equal to α.
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