From the image provided, here's the analysis based on the hypothesis testing details:

1. Alpha used in the study: The significance level ($\alpha$) used is 0.05.

2. Test statistic for the mean: The test statistic for the hypothesis regarding the mean age of online students being 32 years is 2.445339 (rounded to 2 decimal places as 2.45).

3. p-value for the mean: The p-value corresponding to this test statistic is 0.01404 (rounded to 4 decimal places).

4. Decision in the hypothesis: The null hypothesis ($H_0$) that the average age of online students is 32 years was rejected. This decision was made because the p-value (0.01404) is less than the significance level ($\alpha = 0.05$). Since the p-value is small, it provides enough evidence to reject $H_0$.

5. Interpretation of the hypothesis results: A complete sentence to interpret the result would be:

   • "We reject the null hypothesis that the average age of online students is 32 years because the p-value (0.01404) is less than the significance level (0.05), providing sufficient evidence that the average age of online students is not equal to 32 years."

Do you want further details on any aspect or need additional clarification?

Here are 5 relative questions to deepen your understanding:

1. What is the importance of setting the significance level ($\alpha$) before conducting hypothesis tests?
2. How does the p-value compare to the significance level to guide decision-making in hypothesis testing?
3. What assumptions are typically made when performing a test on population means?
4. Can you explain why rejecting the null hypothesis does not mean proving the alternative hypothesis?
5. How would increasing the sample size affect the outcome of this hypothesis test?

Tip: Always ensure that the assumptions of normality or sample size requirements are satisfied before relying on the p-value in hypothesis testing.