Question

Question 2 A study is done to compare the height of students from two selected school in Cheras. 6 students from each school are chosen at random and the mean height and the standard deviation are recorded as follows: Sekolah A Sekolah B Mean 179.67 181 Variance 5.47 5.40 Test the hypothesis that the mean height of students in Sekolah A is less than that in Sekolah B at 5% level of significance. Assuming that the i. Two population variances are not equal. ii. Two population variances are equal.

Answer 1

Null hypothesis: H: 4242 The mean height of students in Sekolah A is same as that in Sekolah B. Alternative hypothesis: H:4<42 The mean height of students in Sekolah A is less than that in Sekolah B. Rejection rule: If p-value sal=0.05), then reject the null hypothesis H.

EXCEL (Mega Stat) output: Hypothesis Test: Independent Groups (t-test, unequal variance) Sekolah A Sekolah B 179.67 1 81 mean 2.3388 2.3238 std. dev. 6n 9 df -1.33000 difference (Sekolah A - Sekolah B) 1.34598 standard error of difference 0 hypothesized difference -0.99 1745 p-value (one-tailed, lower) The value of the test statistic is t=-0.99 P-value = 0.1745. Conclusion: Use a significance level, a = 0.05. Here, p-value is 0.1745, which is greater than the value of a = 0.05. That is, p-value = 0.1745) > a{=0.05). Therefore, by the rejection rule, do not reject the null hypothesis H.

Interpretation: There is insufficient evidence at level of significance a = 0.05. We cannot conclude that the mean height of students in Sekolah A is less than that in Sekolah B. EXCEL (Mega Stat) output:

Hypothesis Test: Independent Groups (t-test, pooled variance) Sekolah A Sekolah B 179.67 181 mean 2.3388 2.3238 std. dev. 6 6n 10 df -1.33000 difference (Sekolah A - Sekolah B) 5.43502 pooled variance 2.33131 pooled std. dev 1.34598 standard error of difference 0 hypothesized difference -0.99 t .1732 p-value (one-tailed, lower) The value of the test statistic is t = -0.99. P-value = 0.1732. Conclusion: Use a significance level, a = 0.05. Here, p-value is 0.1732, which is greater than the value of a = 0.05. That is, p-value (= 0.1732) > a{=0.05). Therefore, by the rejection rule, do not reject the null hypothesis H.

Interpretation: There is insufficient evidence at level of significance a = 0.05. We cannot conclude that the mean height of students in Sekolah A is less than that in Sekolah B.