The Employment and Training Administration reported the U.S. mean unemployment i

Question

The Employment and Training Administration reported the U.S. mean unemployment insurance benefit was $238 per week (The World Almanac 2003). A researcher in the state of Virginia anticipated that sample data would show evidence that the mean weekly unemployment insurance benefit in Virginia was below the national level. a. Develop appropriate hypotheses such that rejection of H0 will support the researcher's contention. H0: Ha: b. For a sample of 90 individuals, the sample mean weekly unemployment insurance benefit was $231 with a sample standard deviation of $80. The p-value is c. Using = .05, can you conclude that the mean weekly unemployment insurance benefit in Virginia is below the national level? Answer the next three questions using the critical value approach. d. Using = .05, what is the critical value for the test statistic (to 2 decimals)? e. State the rejection rule: Reject H0 if t is the critical value. f. Using = .05, can you conclude that the mean weekly unemployment insurance benefit in Virginia is below the national level?

Explanation / Answer

A) H0:= 238 vs Ha: < 238

B) T = (x0)/(s/n)=(231238)/(80/90)=0.83
Degrees of freedom = 90-1 = 89.

The p-value is 0.2044

P-value>0.05. We can’t reject H0. Cannot conclude mean weekly benefit in Virginia is less than the national mean.

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