Question

A warehouse manager wants to investigate the productivity of her employees. It is expected that an employee will complete 100 orders in one day. Five employees are assessed and the following data are collected:

Employee A: 120 orders completed
Employee B: 88 orders completed
Employee C: 93 orders completed
Employee D: 117 orders completed
Employee E: 97 orders completed

a) Which chi-square hypothesis test is best for this situation?
b) Conduct the hypothesis test you selected in part (a). Based on your test, are employees perfoming as expected?

Answer 1

Solution:-

Given data:

It is expected that an employee will complete 100 orders in one day.

Employee A: 120 orders completed
Employee B: 88 orders completed
Employee C: 93 orders completed
Employee D: 117 orders completed
Employee E: 97 orders completed

a) Which chi-square hypothesis test is best for this situation?

In one sample tests for a discrete outcome, we set up our hypotheses against an appropriate comparator.

We can write the Null and alternative hypothesis as,

b) Conduct the hypothesis test you selected in part (a). Based on your test, are employees performing as expected?

	Observed (O)	Expected (E)
A	120	100	= = 4
B	88	100	= 1.44
C	93	100	= 0.49
D	117	100	=2.89
E	97	100	=0.09

Test statistic,

Here, Degrees of freedom, Df = K -1 = 5 - 1 = 4

Now consider the chi-squared critical value with Df=4 and level of significance = 0.05.

= 9.488 ( From critical values of chi-square distribution table )

Hence we can say that, .

Hence we can conclude that as" there is a significant results that the employees are performing as expected".