You are testing the claim that the mean GPA of night students is less than the mean GPA of day students. You sample 25 night students, and the sample mean GPA is 2.18 with a standard deviation of 0.9 You sample $35 \mathrm{~d} A$ students, and the sample mean GPA is 2.53 with a standard deviation of 0.85 Calculate the test statistic, rounded to 2 decimal places Question Help: $\square$ Message instructor Submit Question

Step 1 ：Given that the sample mean GPA of night students (\(\bar{X}_1\)) is 2.18, the standard deviation of the GPA of night students (\(s_1\)) is 0.9, and the number of night students sampled (\(n_1\)) is 25.

Step 2 ：Also, the sample mean GPA of day students (\(\bar{X}_2\)) is 2.53, the standard deviation of the GPA of day students (\(s_2\)) is 0.85, and the number of day students sampled (\(n_2\)) is 35.

Step 3 ：We are testing the claim that the mean GPA of night students is less than the mean GPA of day students, so we can set \(\mu_1 - \mu_2\) to 0 in the formula for the test statistic.

Step 4 ：Substitute these values into the formula for the test statistic: \[Z = \frac{(\bar{X}_1 - \bar{X}_2) - (\mu_1 - \mu_2)}{\sqrt{\frac{s_1^2}{n_1} + \frac{s_2^2}{n_2}}}\]

Step 5 ：Calculate the test statistic to get \(Z = -1.52\)

Step 6 ：Final Answer: The test statistic, rounded to 2 decimal places, is \(\boxed{-1.52}\)