Question

1. A hospital’s human resources department is comparing work performance with work shift times (Shifts A, B, C).
   1. What are the two qualitative variables? Classify each of them as nominal or ordinal.

2. Write the hypotheses for a chi-square test of homogeneity.

3. The data from the study is shown below. Fill in the empty table with the row percentages for each shift. Round to the nearest tenth of a percent.

	Exceptional	Satisfactory	Needs Improving	Unsatisfactory
A	12	24	13	9
B	22	16	14	8
C	18	19	12	15

	Exceptional	Satisfactory	Needs Improving	Unsatisfactory
A
B
C

4. Does there seem to be a difference in the distribution of work performance among the shifts? Why or why not?

5. The p-value from a chi-square test of homogeneity on the performance data is 0.304. Does the conclusion, based on the p-value, match your intuition in part b)? Give a thorough explanation.

Answer 1

a)Two qualitative Variables are work performance and time shifts . Now we can rank the levels of work performance from exceptional at 1 st rank and unsatisfactory as last . Therefore work performance is ordinal .but work shift times we can just categorize but cannot put in order like work performance . Therefore work shift is nominal data.

a)chi square test is used to test if two attributes (qualitative Variables ) are related or not . We test the hypothesis

Null hypothesis : work performance is not related to work shift timings

Alternative hypothesis : work performance is related to work shift timings .

	Exceptional(E)	statisfactory(S)	needs improvement(N)	unsatisfactory(U)	Total
A	12	24	13	9	58
B	22	16	14	8	60
C	18	19	12	15	64

Percentage table ( number / Row total)

	E	S	N	U
A	20.69	41.38	22.41	15.51
B	36.67	26.67	23.33	13.33
C	28.13	29.69	18.75	23.44

By looking at the performance values we can't see that performance is very poor for some shift or very exceptional for some other. Values look evenly distributed for work performance levels across shifts.

p- value of 0.304 suggests that we should not reject Null hypothesis at 5% level of significance . ( If p value is greater than level of significance we fail to reject Null)

Therefore we can conclude that work performance is not related to shift timings and hence it is homogeneous across all shifts