In a hypothesis test with a = 0.05 the p-value is calculated to be 0.02. What decision should be made about the null hypothesis? Reject the Null Hypothesis Fail to reject the Null Hypothesis

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### Hypothesis Testing Decision-Making

In a hypothesis test with \(\alpha = 0.05\), the p-value is calculated to be 0.02. What decision should be made about the null hypothesis?

- \( \bigcirc \) Reject the Null Hypothesis

- \( \bigcirc \) Fail to reject the Null Hypothesis

### Explanation

In hypothesis testing, the p-value is compared to the significance level \(\alpha\) to determine whether to reject or fail to reject the null hypothesis.

**Key Points:**
1. **Significance Level (α):** This is the threshold set by the researcher which for this test is 0.05.
2. **P-value:** In this case, the p-value is 0.02.

To make a decision:
- If the p-value is less than or equal to \(\alpha\), we reject the null hypothesis.
- If the p-value is greater than \(\alpha\), we fail to reject the null hypothesis.

**Given:**
- \(\alpha = 0.05\)
- p-value = 0.02

Since 0.02 < 0.05, we **reject the Null Hypothesis**.
Transcribed Image Text:### Hypothesis Testing Decision-Making In a hypothesis test with \(\alpha = 0.05\), the p-value is calculated to be 0.02. What decision should be made about the null hypothesis? - \( \bigcirc \) Reject the Null Hypothesis - \( \bigcirc \) Fail to reject the Null Hypothesis ### Explanation In hypothesis testing, the p-value is compared to the significance level \(\alpha\) to determine whether to reject or fail to reject the null hypothesis. **Key Points:** 1. **Significance Level (α):** This is the threshold set by the researcher which for this test is 0.05. 2. **P-value:** In this case, the p-value is 0.02. To make a decision: - If the p-value is less than or equal to \(\alpha\), we reject the null hypothesis. - If the p-value is greater than \(\alpha\), we fail to reject the null hypothesis. **Given:** - \(\alpha = 0.05\) - p-value = 0.02 Since 0.02 < 0.05, we **reject the Null Hypothesis**.
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