5. I wanted to see if a student at Messiah’s class year is related to whether th

Question

5. I wanted to see if a student at Messiah’s class year is related to whether they live in a dorm or apartment. I went in the dining hall and randomly surveyed students there and got the following results.

First year Dorm 20, First year apartment 1

Sophomore Dorm 18, Sophomore apartment 2

Junior Dorm 14, Junior apartment 3

Senior Dorm 12, Senior apartment 4

A.Produce the right statistic and determine if it is significant at the .05 level (Do the statistic even if it does not meet all the assumptions).

B. Can I accept my hypothesis that class is related to living in an apartment in that as you are here longer you are more likely to be in an apartment?

C. What problems may be present with my methodology and calculations as it stands now (refer to assumptions and my way of getting participants) (Mention at least 2 problems)?

Explanation / Answer

Null Hypothesis : Whether student live in a dorm or apartment is independent of Class year student study.

Alternative Hypothesis : whether student live in a dorm or apartment is dependent on the class year student study.

Observed Table

Expected Table

Here Right Statistic is Chi - square test

X2= Sum of [ Ei- Oi] 2 / Ei

Chi - square contribution table

Test Static

X2 = sum of all above given chi - square contribution = 3.642

Here X 2 Crtical at alpha = 0.05 and dF = (2-1) * (4-1) = 3 is  X 2 Crtical = 7.815

so X2 < X 2 Crtical , so we can not reject the null hypothesis and can conclude that there is no relation between year of study and whether it affect a student live in dorm or apartment.

(B) No, we can not the given hypothesis that class is related to living in an apartment in that as one is here longer so more likely to be in an apartment. We cannot reject the null hypothesis so this alternative hypothesis is automatically rejected.

(C) (a) Sample size is very small as students living in apartments are having very meager number like 1,2,3,4 in comparison to students in Dorms. In totality also the sample size is very small. Survey must not be done based on a mess student result. It should have a heterogeneous group representing more students.

(b) This random survey is pertaining result of a dining hall at a particular time so may be it is highly possible that apartment people eat somewhere else instead of dining halls. Similarly, First year students tend to eat more in dining halls instead of outside.The survey must be taken in the classes not in some particular segment like dining hall or basketball court because then it will produce biased result.

Dorm Apartment Total First Year 20 1 21 Sophomore 18 2 20 Junior 14 3 17 Senior 12 4 16 total 64 10 74

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