Question

The job type distribution in the state are summarized in the table below.

Job Type	Percent in State	Expected Frequency
Blue-Collar	23%
White-Collar	26%
Pink-Collar	43%
Unemployed	8%

Suppose a random sample of 3000 adults from your town are surveyed. The table below shows the results of the survey. Fill in the expected frequencies in the above table.

Job Type	Frequency
Blue-Collar	598
White-Collar	883
Pink-Collar	1219
Unemployed	300

Test the if the distribution is as expected at the 5% significance level.

Test statistic (round to 2 decimal places):

p-value:

Answer 1

Applying chi square test:

	relative	observed	Expected	residual	Chi square
category	frequency	Oi	Ei=total*p	R2i=(Oi-Ei)/√Ei	R2i=(Oi-Ei)2/Ei
Blue-Collar	0.230	598	690.00	-3.50	12.267
White-Collar	0.260	883	780.00	3.69	13.601
Pink-Collar	0.430	1219	1290.00	-1.98	3.908
Unemployed	0.080	300	240.00	3.87	15.000
total	1.000	3000	3000		44.776

Test statistic X² =44.78

p value =0.0000

Reject Ho ; we have sufficient evidence at 0.05 level to conclude that the distribution is not as expected.