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).
(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
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