Question

HYPOSIS TEST EXERCISE

Two teachers in a school want to compare the performance of eighth-year students who have been mobile (population 1) with the scores of students who have not been mobile (population 2). Can it be concluded with the sample data if the average performance score is different in the two groups?

Group 1: n. 15 Average 85 variances - 30

Group 2: n. 22 Average 87 variances - 25

MOBILE: Students who attended two or more schools

NON-MOBILE: Students who remain in the same school

Answer:

1) 1) Are there homogeneous variances?

2) 2) Answer the research question

Answer 1

1] NULL HYPOTHESIS H0:

ALTERNATIVE HYPOTHESIS Ha:

Testing for Equality of Variances

A F-test is used to test for the equality of variances. The following F-ratio is obtained:

F=s1^2/s2^2

F= 30/25

F= 1.2

The critical values are FL​=0.354 and FU​=2.564, and since F=1.201, then the null hypothesis of equal variances is not rejected.

Therefore Variances are EQUAL.

2] NULL HYPOTHESIS H0:

ALTERNATIVE HYPOTHESIS Ha:

LEVEL OFSIGNIFICANCE =0.05

Based on the information provided, the significance level is α=0.05, and the degrees of freedom are df=35. In fact, the degrees of freedom are computed as follows, assuming that the population variances are equal:

Hence, it is found that the critical value for this two-tailed test is tc​=2.03, for α=0.05 and df=35.

The rejection region for this two-tailed test is R={t:∣t∣>2.03}.

DECISION: DO NOT REJECT H0.

COCNLUSION: WE DONT HAVE SUFFICIENT EVIDENCE TO CONCLUDE THAT THERE IS DIFFERENCE IN MEANS.