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 UII or Level III. The data so gathered were analysed by a statistician using MINITAB; the results are shown below: 6. Expected counts are printed below observed counts Hum & Ed Soc Sci Sc & Agr. Eng Total 43 26.20 23.62 Level III Malee 8 17.74 10 27 26 23.1826.72 38 34.24 Level III Female29 30.86 Level I/II Male 32 72 219 44.15 50.88 65.20 58.77 Level I/II Female 106 86 327 54 65.92 75.97 97.36 87.75 81 Total 151 223 201 749 Chi-Sg= 5.348 + + 0.024 + 15.912 + 1.459 + 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. Fill in the gaps marked by.*,,,**, ,' , , ‘ , and '* What is the assumption on which these calculations are based. What is relevance of the statement" No cells with expected counts less than iii. iv. v. vi. Do the records suggest a relationship or independence between faculty and status/gender for students at UWI, St. Augustine? Give reason(s) for your answer

Explanation / Answer

i. The random variables present are number of male students in Level I/II, number of female students in Level I/II, number of male students in Level III, number of female students in Level III.

ii. Null Hypothesis: Faculty and gender/status of the students are independent

Alternate Hypothesis: The Faculty and gender/status are independent.

iii. * = 115. this is the sum of 29,26,38 & 22.

** = 174. This is the number required to make the bottom row equal to 749, the other elements in the sum being 151, 223 & 201.

*** = 20.43. This is the number required to make the total expected count equal to 749, the othe values being 17.74, 26.2, 23.62, 23.18, 26.72, 34.24, 30.86, 44.15, 50.88, 65.20, 58.77, 65.92, 75.97, 97.36, 87.75.

**** = 5.335. This can be easily found by subtracting the sum of the individual chi-square values from the total Chi-Sq value. Otherwise, this can be found as ((10-20.43)^2)/20.43.

***** = degrees of freedom = (4-1) x (4-1) = 9

****** = p-value = 1.36149 x 10^(-13). This can be found in Excel by using the CHITEST function and then providing the range of actual counts and expected counts.

iv. The usual assumptions are: The population has a normal distribution; the test statistic has a chi-squared distribution of degrees of freedom (n-1) x (k-1), where n and k denote the number of rows and columns.

v. No cell has expected counts less than 5 signifies that samples are not very small, and hence Chi-square approximation can be applied.

vi. The p-value is 1.36149 x 10^(-13), so the Null Hypothesis can be rejected.

Also from a Ch-square table, the critical value for 9 degrees of freedom = 16.91898.

Our value of test statistic = 80.395.

Since the test statistic is too larger than the critical value, the Null Hypothesis of independence can be rejected.

We can accept the alternate hypothesis of existence of a relationship between the Faculty and gender/status of the students at the UWI, St. Augustine.

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