If a p-value for your hypothesis testing about the population mean is 0.073 , and the level of significance used was 5%, then the conclusion would be to: Select one: a. Reject the null hypothesis H subscript o b. Don’t Reject the null hypothesis H subscript o c. Not enough information to make conclusion d. Accept the alternative hypothesis H subscript a If a p-value for your hypothesis testing about the population mean is 0.073 , and the level of significance used was 5%, then the conclusion would be to: Select one: a. Reject the null hypothesis H subscript o b. Don’t Reject the null hypothesis H subscript o c. Not enough information to make conclusion d. Accept the alternative hypothesis H subscript a
The Correct Answer and Explanation is :
The correct answer is:
b. Don’t Reject the null hypothesis H₀
Explanation:
In hypothesis testing, the p-value represents the probability of obtaining results at least as extreme as the observed data, assuming the null hypothesis (H₀) is true. The level of significance (α) is the threshold set to determine whether the null hypothesis should be rejected.
Step 1: Compare the p-value to α
- Given p-value = 0.073
- Given α = 0.05 (5%)
- The rule states: If p-value ≤ α, reject H₀. Otherwise, do not reject H₀.
Since 0.073 > 0.05, the p-value is greater than the significance level. This means that there is not enough statistical evidence to reject the null hypothesis at a 5% significance level.
Step 2: Interpreting the Decision
- “Do not reject H₀” means that the evidence is insufficient to conclude that the alternative hypothesis (Hₐ) is true.
- This does NOT mean that H₀ is accepted as true—only that we do not have strong enough evidence against it.
Step 3: Common Misconceptions
- Rejecting H₀ means that we have strong statistical evidence supporting Hₐ. Since p = 0.073 is slightly higher than 0.05, the evidence is not strong enough to reject H₀.
- Failing to reject H₀ does not prove H₀ is true—it just means we lack enough evidence to conclude otherwise.
Conclusion:
Since the p-value (0.073) is greater than the significance level (0.05), we do not reject the null hypothesis. This means there is not enough evidence to support the alternative hypothesis.
Thus, the correct choice is: b. Don’t reject the null hypothesis H₀.
Here is an illustration of hypothesis testing decision-making, showing the process of comparing the p-value to the significance level (α) and concluding whether to reject or not reject the null hypothesis. Let me know if you need any modifications!
