The Employment and Training Administration reported that the

The Employment and Training Administration reported that 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 unemployement insurance benefit in Virginia was below the national average. Develop appropriate hypotheses such that rejection of H_theta will support the researcher\'s contention. For a sample of 100 individuals, the sample mean weekly unemployement insurance benefit was $231 with a sample standard deviation of $80. What is the p-value At a = .05, what is your conclusion Repeat the preceding hypothesis test using the critical value approach.

Solution

27)

a.

Null Hypothesis : mu < 238

Alternate Hypothesis: mu >= 238

b.

n=100

X-bar = 231

SD = 80

z = (231 - 238)/(80/10) = -0.875

P-value = 0.1949 Answer

c.

At alpha =0.05,

Since P-value > 0.05

Failed to reject null hypothesis.

d.

Critical value = 1.96

Since z-value < 1.96 ,

Reject null hypothesis