Question

For each problem, follow these steps.

1. State the hypotheses and identify the claim.

2. Find the critical values(s).

3. Compute the test value.

4. Make the decision.

5. Summarize the results.

1. The reasons that workers in the 25-54 year old category were displaced are listed below.

Plant closed/moved 44.8%

Insufficient work 25.2%

Position eliminated 30.0%

A random sample of 180 displaced workers (in this age category) found that 40 lost their jobs due to their position being eliminated, 53 due to insufficient work, and the rest due to the company being closed or moving. At the 0.01 level of significance, are these proportions different from those from the U.S. Department of Labor?  

Answer 1

Null hypothesis : the proportions are as stated :

Plant closed/moved 44.8%

Insufficient work 25.2%

Position eliminated 30.0%

Alternate hypothesis: At least one proportion is different from others

Day	Number of crime	Expected proportion.	Expected Frequency ( E)	( O-E)^2	( O-E)^2/E
Plant closed/moved	87	0.448	80.64	40.4496	0.501607143
Insufficient work	53	0.252	45.36	58.3696	1.28680776
Position eliminate	40	0.3	54	196	3.62962963
Total	180	1	180	294.8192	5.418044533

The test statistic:

= 5.418

The critical value is given by at df = n - 1 = 3 - 1 = 2

and alpha = 0.01

= 9.2

As the <

Do not reject the null hypothesis.

Hence

the proportions of loosing jobs are as stated :

Plant closed/moved 44.8%

Insufficient work 25.2%

Position eliminated 30.0%