Records of 749 students who are enrolled in the faculties of Humanities & Educat

Question

Records of 749 students who are enrolled in the faculties of Humanities & Education, SocialSciences, Science & Agriculture and Engineering on the St. Augustine Campus of the University of the West Indies were compiled and tabulated in a 2-way contingency table. These students were classified according to their status/gender and faculty; Status being recorded as Level III or Level III. The data so gathered were analysed by a statistician using MINITAB, the results are shown below Expected counts are printed below observed counts Hum & Ed Soe Sci Ss, & AgE. Eog Total Level III Male 8 17.74 10 27 43 26.20 23.62 Level III Female 29 38 23.18 26.72 34.24 30.86 Level I/II Male 32 50.88 72 65.20 82 58.77 219 44.15 Level I/II Female 81 106 86 54 65.92 75.97 97.36 87.75 327 Total 151 223 201 749 Chi- 5.343 + + 0.024 + 15.912 + 1.459 t 0.019 0.413 2.544 2.816 7.003 + 0.709 + 9.182 + 3.448 + 11.875 ± 1.325 + 12.983 80.395 DE- , P-value= No cells with expected counts less than 5. i. Name the random variables present in the table above. ii. Carefully define the null and alternative hypotheses of the Chi Square test underlying the generation of the above table. iii. iv. Fill in the gaps marked by 't,'t , and 4 , , What is the assumption on which these calculations are based. What is relevance of the statement" No cells with expected counts less than 5. Do the records suggest a relationship or independence between faculty and v. vi. status/gender for students at UWI, St. Augustine? Give reason(s) for your answer. vii. State the limitations of this Chi Square Test

Explanation / Answer

i) Faculties and Status/gender are two independent variables

ii) H0: There is no association between Faculties and status/gender

H1:There is association between Faculties and status/gender

iii) * = 29+26+38+22 = 115

** = 10+26+32+106 = 174

*** = (88*75.97)/749 = 26.7156

**** = (10-26.7156)^2/26.7156 = 20.443

df = 9

P-Value: 0.0000

iv) Sum of the observed frequencies and sum of the expected frequenies are equal

v)  an expected value in a cell is not less than 5

vi) There is association between Faculties and status/gender

vii)

Chi-square is also sensitive to small frequencies in the cells of tables. Generally when the expected frequency in a cell of a table is less than 5, chi-square can lead to erroneous conclusions. The rule of thumb here is that if either (i) an expected value in a cell is less than 5 or (ii) more than 20% of the expected values in cells are less than 5, then chi-square should not and usually is not computed.

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