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?

Sum of Squares

Group 71.00

Total 226.61

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

Which of the following is(are) correct about the hypotheses?

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.

If applying analysis of variance (ANOVA) to these data, which of the following must we assume?

The sample standard deviations of entrance grades for the different groups are independent.

Entrance grades within each of the groups are independent.

The entrance grades for each group are from a Normal distribution.

None of the statements are correct

Taking that the underlying assumptions of ANOVA hold and that the approach will be applied, what is the estimate of the common variance of the entrance grade for the three groups? Round your answer to 2 decimal places

Under the null hypothesis of equality of population means and given that all ANOVA assumptions are satisfied, what is the appropriate distribution for the test statistic? The notation F(a,b)F(a,b)

F(a,b) represents the F-distribution with aa

a numerator degrees of freedom and bb

b denominator degrees of freedom.

To test the ANOVA null hypothesis at the 5% significance level, what is the test statistic and the decision to reject the null hypothesis?