d the survey udents were asked if they formed study groups to prepare for tests.

Question

d the survey udents were asked if they formed study groups to prepare for tests. In a recent study, Each student in the study was asked if they had regularly participated in a study group. The results obtained from the aske 10) was classified according to academic performance at school and survey are summarized in the table. a 5% level of significance, can you conclude that school performance and Using participation in study groups? Group Study Yes 38 27 13 No 38 45 28 Excellent School Performance Average Below Average

Explanation / Answer

Here the hypothesis tests are
H0: School performance and group study are indpendent
H1: School performance and group study are not indpendent

Observed and expected frequency tables are as follows

Expected frequency, Ei = sum(coli)*sum(rowi)/total

test statistic, chi-square = Sum((Oi - Ei)^2/Ei) = 4.3587

df = (3-1)(2-1) = 2

p-value = 0.1131

As p-value is less than the significance level of 0.05, we fail to reject the null hypothesis.

This means school performance and group study are independent.

Observed Yes No total Excellent 38 38 76 Average 27 45 72 Below Avg. 13 28 41 Total 78 111 189 Expected Yes No Excellent 31.365 44.635 Average 29.714 42.286 Below Avg. 16.921 24.079

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