Question

Absenteeism of college students from math classes is a major concern to math instructors because missing class appears to increase the drop rate. Three statistics instructors wondered whether the absentee rate was the same for every day of the school week. They took a sample of absent students from three of their statistics classes during one week of the term. The results of the survey appear in the table. Mon. Tues. Wed. Thurs. Fri. # of students absent 28 22 18 20 32 Test at the .01 significance level if there is a difference in the expected number of absences for the different days of the week. a) Research question

) Decision Rule

conclusion

Answer 1

We will apply a chi-square test of goodness of fit test here.

The following table is obtained:

Categories Observed Expected (fo-fe)?/fe Mon. 120*0.2=24 (28-24)2/24 = 0.667 (22-24)2/24 = 0.167 Tues. 120*0.2=24 Wed. 120*0.2=24 (18-24)2/24 = 1.5 Thurs. 120*0.2=24 (20-24)2/24 = 0.667 Fri. 120*0.2=24 (32-24)2/24 = 2.667 Sum = 120 5.667

(1) Null and Alternative Hypotheses

The following null and alternative hypotheses need to be tested:

H. : P1 = 0.2,P2 = 0.2, P3 = 0.2,P4 = 0.2, p = 0.2

Ha​: Some of the population proportions differ from the values stated in the null hypothesis

This corresponds to a Chi-Square test for Goodness of Fit.

(2) Rejection Region

Based on the information provided, the significance level is α=0.01, the number of degrees of freedom is df=5−1=4, so then the rejection region for this test is R={χ2:χ2>13.277}.

(3) Test Statistics

The Chi-Squared statistic is computed as follows:$\chi^2 = \sum_{i=1}^n \frac{(O_i-E_i)^2}{E_i} = 0.667+0.167+1.5+0.667+2.667 = 5.667$

(4) Decision about the null hypothesis

Since it is observed that χ2=5.667≤χc2​=13.277, it is then concluded that the null hypothesis is not rejected.

(5) Conclusion

It is concluded that the null hypothesis Ho is not rejected. Therefore, there is NOT enough evidence to claim that some of the population proportions differ from those stated in the null hypothesis, at the α=0.01 significance level. Hence it seems like the absentee rate was the same for every day of the school week.

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