Final Answer:
The assumption of normality is crucial when conducting hypothesis tests on means. In this case, Jennifer is attempting to make inferences about the average volunteer hours of TC3 students based on a sample mean and standard deviation.
b) No, assumption of normality not satisfied
Step-by-step explanation:
The assumption of normality is crucial when conducting hypothesis tests on means. In this case, Jennifer is attempting to make inferences about the average volunteer hours of TC3 students based on a sample mean and standard deviation.
The assumption of normality is violated if the sample distribution of the mean is not approximately normal. A mean of 6.75 hours is only slightly above the target of 6 hours, and the standard deviation of 3.30 hours is relatively large. These factors, along with the relatively small sample size of 100, suggest that the distribution of volunteer hours may not be normal.
Without a normal distribution, the results of hypothesis testing may not be valid, and Jennifer cannot confidently assert that TC3 students average more than six hours a week in volunteer work at the 0.05 significance level.
It's worth considering alternative methods or conducting additional tests to address the violation of the normality assumption. This could involve using non-parametric tests or collecting a larger and more representative sample to improve the robustness of the analysis.
Without addressing the normality assumption, the validity of the statistical conclusions drawn from the data is compromised, and Jennifer's case for TC3 students averaging more than six hours in volunteer work lacks statistical support.