A university admissions committee looked at students' entrance grades to see if a certain university was lowering their grade requirements for students with athletic scholarships. A random sample of 23 first year students were selected from this university. Eight were offered basketball scholarships, seven were offered football scholarships, and the rest were non-athletes.

Is there evidence of a difference in mean entrance grades between the groups?

Which of the following is(are) correct about the hypotheses? (Check all that apply)

The alternative hypothesis is that non-athletes have a higher true mean entrance grade than students with basketball and football scholarships.

The alternative hypothesis is that the 8 non-athlete students have a higher mean entrance grade than the 8 students with basketball scholarships and 7 students with football scholarships.

The alternative hypothesis is that not all of the true mean entrance grades between these groups are equal.

The null hypothesis is that not all of the means are equal.