Question

The administration at a university is interested in studying if any relationship exists between satisfaction at the school and whether the student is a freshman or a senior. The school randomly surveys 30 freshmen and 30 seniors and asks them to rate how satisfied they are at the school on a scale of 1-200, where 200 is extremely satisfied and 1 is extremely dissatisfied. He finds that the average level of satisfaction of the freshmen surveyed is 132 with a standard deviation of 5.45. The average satisfaction of seniors is found to be 154 with a standard deviation of 6.81. Is this difference significant at the .01 level of significance? (10 points total)

Answer 1

To Test :-

H0 :- µ1 = µ2
H1 :- µ1 ≠ µ2

Test Statistic :-
t = (X̅1 - X̅2) / SP √ ( ( 1 / n1) + (1 / n2))



t = ( 132 - 154) / 6.1676 √ ( ( 1 / 30) + (1 / 30 ))
t = -13.815

Test Criteria :-
Reject null hypothesis if | t | > t(α/2, n1 + n2 - 2)
Critical value t(α/2, n1 + n1 - 2) = t(0.01 /2, 30 + 30 - 2) = 2.663
| t | > t(α/2, n1 + n2 - 2) = 13.815 > 2.663
Result :- Reject Null Hypothesis

The difference is significant.