Question

A college prep school advertises that their students are more prepared to succeed in college than other schools. To verify this, they categorize GPA’s into 4 groups and look up the proportion of students at a state college in each category. They find that 7% have a 0-0.99, 21% have a 1-1.99, 37% have a 2-2.99, and 35% have a 3-4.00 in GPA. They then take a random sample of 200 of their graduates at the state college and find that 19 has a 0-0.99, 28 have a 1-1.99, 82 have a 2-2.99, and 71 have a 3-4.00. Can they conclude that the grades of their graduates are distributed differently than the general population at the school? Test at the 0.05 level of significance. A. yes because the p-value is .0620 B. no because the p-value is .0620 C. yes because the p-value is .9379 D. no because the p-value is .9379

Answer 1

Category	Observed Frequency (O)	Proportion, p	Expected Frequency (E)	(O-E)²/E
0-0.99	19	0.07	200 * 0.07 = 14	(19 - 14)²/14 = 1.7857
1-1.99	28	0.21	200 * 0.21 = 42	(28 - 42)²/42 = 4.6667
2-2.99	82	0.37	200 * 0.37 = 74	(82 - 74)²/74 = 0.8649
3-4	71	0.35	200 * 0.35 = 70	(71 - 70)²/70 = 0.0143
Total	200	1.00	200	7.3315

Test statistic:  

χ² = ∑ ((O-E)²/E) = 7.3315

df = n-1 = 3

p-value = CHISQ.DIST.RT(7.3315, 3) = 0.0620   

answer: B. no because the p-value is .0620