At a large university, 20% of a random sample of male students have an overall grade point average (GPA) of 3.5 or higher. A random sample of female student records found that 25% had a GPA of 3.5 or higher. The president of the university wants to determine whether there is evidence of a difference in grades between males and females. What would she write as the null and alternative hypotheses for this situation?
Answer choices
H0:p1 − p2 = 0 and Ha:p1 − p2 ≠ 0
H0:p1 − p2 = 0 and Ha:p1 − p2 > 0
H0:p1 − p2 = 0 and Ha:p1 − p2 < 0
H0:p1 − p2 > 0 and Ha:p1 − p2 = 0
H0:p1 − p2 > 0 and Ha:p1 − p2 ≠ 0

Answer:

H0:p1 − p2 = 0 and Ha:p1 − p2 ≠ 0

Explanation:

Null hypothesis would be there not being a difference, so the difference would be 0.

Alternative hypothesis would be that there is a difference. However, the president of the university does not want to determine whether more males than females, or more females than males, get a GPA of 3.5 or higher, so the alternative hypothesis is =/= 0.

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