The Department of Economic and Community Development (DECD) reported that in 200

Question

The Department of Economic and Community Development (DECD) reported that in 2005 the average of new jobs created per county was 450. The department also provided the following information regarding a sample of 5 counties in 2006.

County New Jobs Created in 2006
Bradley 410
Rhea 480
Marion 407
Grundy 428
Sequatchie 400

a. Compute the sample average and the standard deviation for 2006.

b. We want to determine whether there has been a significant decrease in the average number of jobs created. Provide the null and alternative hypotheses.

c. Compute the test statistic

d. Compute the p-value; and at 95% confidence, test the hypotheses. Assume the population is normally distributed

Explanation / Answer

Given xbar = 425, s = 32.435, n = 5
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b.The test hypothesis is
Ho:>=450
Ha:<450
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c. test statistic:

t =(xbar-)/(s/n)

=(425 - 450)/(32.435/sqrt(5))
= -1.724

---------------------------------------------------------

d. The p-value is P(t with df=n-1=4 <-1.72)= 0.0803 (check student t table)

Since the p-value is larger than 0.05, we do not reject HO.

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