Aid Home Near Home Far

You are studying the attrition of entering college freshmen (those students who enter college as freshmen but do no stay to graduate). You find the following relationships between attrition, aid, and distance of home from college (see chart below). What is your interpretation? Consider all variables and relationships.

Aid Home Near Home Far

Receiving Aid Receiving Aid

Yes No Yes No Yes No

(%) (%) (%) (%) (%) (%)

Drop out 25 20 5 15 30 40

Stay 75 80 95 85 70 60

For relationship between Attrition and Aid,

Chi-square = 0.72, p-value = 0.3972.

So, there seems no significant relationship between attrition and whether the student receives aid or not.

For relationship between Attrition and “Home Near Receiving Aid”

Chi-square = 5.56, p-value = 0.0184.

So, at significance level of 0.05, there is significant relationship between attrition and aid for students with home near the college.

For relationship between Attrition and “Home Far Receiving Aid”,

Chi-square = 2.20, p-value = 0.1382.

So, there seems no significant relationship between attrition and aid for students with home far from the college.

So, overall, aid is related with attrition only for the students who have home near the college.

Question # 2

You decide to conduct a survey of a sample of 25 members of this year's graduating class and find that the average GPA is 3.2. The standard deviation of the sample is 0.4. Over the last ten years, the average GPA has been 3.0. Is this year's class significantly different from the long-run average? At what alpha level would it be significant?

H0: µ = 3

H1: µ ≠ 3

t = (3.2-3)/(0.4/sqrt(25)) = 2.5

Degree of freedom = 25-1 = 24

P-value = 0.0197

At alpha 0.01, the difference is not significant.

There would be significant difference at any alpha greater than 0.0197 (say alpha = 0.05).

Questions # 3

You are curious about whether the professors and students at your school are of different political persuasions, so you take a sample of 20 professors and 20 students drawn randomly from each population. You find that 10 professors say they are conservative, and 6 students say they are conservative. Is this a statistically significant difference?

H0: p1 = p2

H1: p1 ≠ p2

p1 = 10/20 = 0.5, p2 = 6/20 = 0.3

Pooled proportion = (10+6)/(20+20) = 0.4

z = (0.5-0.3)/sqrt(0.4*(1-0.4)*(1/20+1/20)) = 1.291

P-value = 0.1967

Since p-value is considerably high (greater than 0.05), there isn’t a statistically significant difference.