You are testing the claim that the mean GPA of night students is different from the mean GPA of day students. You sample 55 night students, and the sample mean GPA is 2.08 with a standard deviation of 0.86 . You sample 45 day students, and the sample mean GPA is 1.68 with a standard deviation of 0.79 . Test the claim using a $5 \%$ level of significance. Assume the population standard deviations are unequal and that GPAs are normally distributed. Give answer to at least 4 decimal places.
What are the correct hypotheses?
\[
\begin{array}{l}
\mathrm{H}_{0}: \text { Select an answer } v=\text { Select an answer } v \\
\mathrm{H}_{1}: \text { Select an answer } v \text { ? } v \text { Select an answer } v
\end{array}
\]
Answer
The correct hypotheses are: \(\mathrm{H}_{0}: \mu_{\text{night}} = \mu_{\text{day}}\) and \(\mathrm{H}_{1}: \mu_{\text{night}} \neq \mu_{\text{day}}\)
Step 1 ：The null hypothesis (H0) is the statement that there is no difference between the two groups, while the alternative hypothesis (H1) is the statement that there is a difference.
Step 2 ：Since the question is asking if the mean GPA of night students is different from the mean GPA of day students, the null hypothesis would be that the means are equal, and the alternative hypothesis would be that the means are not equal.
Step 3 ：The correct hypotheses are: \(\mathrm{H}_{0}: \mu_{\text{night}} = \mu_{\text{day}}\) and \(\mathrm{H}_{1}: \mu_{\text{night}} \neq \mu_{\text{day}}\)
