Question

5. L. Wallace, the president of a major public university, believes students’ grade-point-averages [GPAs] decline when students transition from high school to college, on average. To test President Wallace’s belief, you selected a random sample of 41 students enrolled in BMGT 230 this semester and conducted a test to compare each student’s high school GPA [HS_GPA] to their current college GPA [COLL_GPA]. Use the MS Excel output below to answer/complete Parts a through d:

t-Test: Paired Two Sample for Means
	HS_GPA	COLL_GPA
Mean	3.67	3.42
Variance	0.1083	0.1749
Observations	41	41
Pearson Correlation	0.161
Hypothesized Mean Difference	0
df	40
t Stat
P(T<=t) one-tail
t Critical one-tail
P(T<=t) two-tail	0.0030
t Critical two-tail

a. State the null and alternative hypotheses associated with the test.
b. What is the p-VALUE for the test (please use FOUR decimal places)?
c. If α = 0.05, state your decision regarding the null hypothesis by comparing α to the p-VALUE (from Part b).
d. State your conclusion (meaning, describe what the decision means in this problem).

Answer 1

5. a) Null and Alternative hypothesis: decline from high school to college mean it was higher in high school

Ho : µd = 0

Ha : µd > 0

b) p-value for a one tailed test = half of the p-value for two tailed test

= 0.0030/2 = 0.0015

c) As p-value = 0.0015 < 0.05, we reject the null hypothesis.

d) There is enough evidence to conclude that the grade point average decline when student transition from high school to college at 0.05 significance level.