You are testing the claim that the mean GPA of night students is different from the mean GPA of day students. You sample 35 night students, and the sample mean GPA is 2.72 with a standard deviation of 0.54. You sample 60 day students, and the sample mean GPA is 3.19 with a standard deviation of 0.32. Test the claim using a 1% level of significance. Assume the population standard deviations are unequal and that GPAs are normally distributed. Give answer to at least 4 decimal places.

Question

What are the correct hypotheses?

H0:
Select an answer
=
Select an answer

H1:
Select an answer

?

Select an answer

Answer 1

To set up the hypotheses for testing whether the mean GPA of night students is different from the mean GPA of day students, we can define them as follows:

1. \( H_0 \) (null hypothesis): The mean GPA of night students is equal to the mean GPA of day students.
2. \( H_1 \) (alternative hypothesis): The mean GPA of night students is different from the mean GPA of day students.

In mathematical terms, we can express the hypotheses as:

• \( H_0: \mu_n = \mu_d \) (where \( \mu_n \) is the mean GPA of night students, and \( \mu_d \) is the mean GPA of day students)
• \( H_1: \mu_n \neq \mu_d \)

You might want to select " = " for \( H_0 \) and " \neq \ " for \( H_1 \).

Thus, the correct hypotheses are:

H0: \( \mu_n = \mu_d \)

H1: \( \mu_n \neq \mu_d \)