Question

Two placement exams are available that students can take to determine which math class they should begin with in their freshman year. It is believed that there is no difference in the mean scores that would be received for the two tests. To test this using a 0.05 level of significance, a randomly selected group of students took both tests and had their scores recorded. The following data were obtained: Student Test A Test B 1 78 82 2 86 74 3 74 79 4 72 93 5 75 80 6 68 82 7 77 99 Determine: 1. Point estimate 2. Pooled standard deviation sp. 3. Calculate test statistics 4. State the decision rule 5. Decision. 6.Conclusion

Student Test A Test B 1 78 82 NI 86 74 3 74 79 72 93 5 75 80 6 68 82 7 77 99

Answer 1

Test A	Test B
75.71	84.14	mean
5.62	8.71	std. dev.
7	7	n

To Test :-

H0 :- µ1 = µ2
H1 :- µ1 ≠ µ2

Point Estimate = X̅1 - X̅2 = - 8.4286

Pooled standard deviation

Sp=(V(n1 – 1)S? + (n2 – 1)53)/(n1+ n2 – 2)

Sp = 7.327

Test Statistic :-
t = (X̅1 - X̅2) / SP √ ( ( 1 / n1) + (1 / n2))
t = - 2.15

Test Criteria :-
Reject null hypothesis if | t | > t(α/2, n1 + n2 - 2)
Critical value t(α/2, n1 + n1 - 2) = t(0.05 /2, 7 + 7 - 2) = 2.179
t > < -2.179 OR t > 2.179

| t | > t(α/2, n1 + n2 - 2) = - 2.15 > -2.179
Result :- Fail to reject Null Hypothesis

There is sufficient evidence to support the claim that there is no difference in the mean scores that would be received for the two tests.