Question

1) Do students change their study habits in classes where they achieve a higher midterm score? A researcher wants to explore this question for a particular macroeconomics class. She recruits 8 students who performed well on the midterm exam and compares their before and after weekly hours studying as below:

Students	1	2	3	4	5	6	7	8
Before	15	14	17	17	19	14	13	16
After	9	9	11	10	19	10	14	10

Assuming differences in study time are generally normally distributed, use a 1% significance level to determine if study times after the midterm have changed in high performing students (use critical values).

Answer 1

(a) Null and Alternative Hypotheses

t-Test: Paired Two Sample for Means
	Before	After
Mean	15.625	11.5
Variance	3.982142857	11.71428571
Observations	8	8
Pearson Correlation	0.491533925
Hypothesized Mean Difference	0
df	7
t Stat	3.892951269
P(T<=t) one-tail	0.00297635
t Critical one-tail	2.997951567
P(T<=t) two-tail	0.005952699
t Critical two-tail	3.499483297

TS = 3.892951269 > critical value (3.499483297)

hence we reject the null hypothesis