The P-value for a hypothesis test is shown. Use the P-value to decide whether to reject Ho when the level of significance is (a) a= 0.01, (b) a= 0.05, and (c) a=0.10. P=0.1147 .... (a) Do you reject or fail to reject Ho at the 0.01 level of significance? O A. Fail to reject Ho because the P-value, 0.1147, is greater than a = 0.01. O B. Reject Ho because the P-value, 0.1147, is greater than a = 0.01. OC. Reject Ho because the P-value, 0.1147, is less than a = 0.01. OD. Fail to reject Ho because the P-value, 0.1147, is less than a = 0.01.

MATLAB: An Introduction with Applications
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Chapter1: Starting With Matlab
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Answer A, B, and C questions 

**Interpreting P-Values and Hypothesis Testing**

In hypothesis testing, the P-value is a crucial metric used to decide whether to reject the null hypothesis (\( H_0 \)). The significance level (\( \alpha \)) is the threshold against which the P-value is compared.

The P-value determined from a given test is \( P = 0.1147 \).

Consider the following levels of significance:
  - (a) \( \alpha = 0.01 \)
  - (b) \( \alpha = 0.05 \)
  - (c) \( \alpha = 0.10 \)

### Question:

(a) Do you reject or fail to reject \( H_0 \) at the 0.01 level of significance?

#### Options:
  - **A.** Fail to reject \( H_0 \) because the P-value, 0.1147, is greater than \( \alpha = 0.01 \).
  - **B.** Reject \( H_0 \) because the P-value, 0.1147, is greater than \( \alpha = 0.01 \).
  - **C.** Reject \( H_0 \) because the P-value, 0.1147, is less than \( \alpha = 0.01 \).
  - **D.** Fail to reject \( H_0 \) because the P-value, 0.1147, is less than \( \alpha = 0.01 \).

**Explanation:**
To determine whether to reject \( H_0 \) at \( \alpha = 0.01 \), compare the P-value to \( \alpha \):

Since \( 0.1147 > 0.01 \), we fail to reject \( H_0 \).

**Correct Answer: A.** 
Fail to reject \( H_0 \) because the P-value, 0.1147, is greater than \( \alpha = 0.01 \).
Transcribed Image Text:**Interpreting P-Values and Hypothesis Testing** In hypothesis testing, the P-value is a crucial metric used to decide whether to reject the null hypothesis (\( H_0 \)). The significance level (\( \alpha \)) is the threshold against which the P-value is compared. The P-value determined from a given test is \( P = 0.1147 \). Consider the following levels of significance: - (a) \( \alpha = 0.01 \) - (b) \( \alpha = 0.05 \) - (c) \( \alpha = 0.10 \) ### Question: (a) Do you reject or fail to reject \( H_0 \) at the 0.01 level of significance? #### Options: - **A.** Fail to reject \( H_0 \) because the P-value, 0.1147, is greater than \( \alpha = 0.01 \). - **B.** Reject \( H_0 \) because the P-value, 0.1147, is greater than \( \alpha = 0.01 \). - **C.** Reject \( H_0 \) because the P-value, 0.1147, is less than \( \alpha = 0.01 \). - **D.** Fail to reject \( H_0 \) because the P-value, 0.1147, is less than \( \alpha = 0.01 \). **Explanation:** To determine whether to reject \( H_0 \) at \( \alpha = 0.01 \), compare the P-value to \( \alpha \): Since \( 0.1147 > 0.01 \), we fail to reject \( H_0 \). **Correct Answer: A.** Fail to reject \( H_0 \) because the P-value, 0.1147, is greater than \( \alpha = 0.01 \).
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