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.

b. For a sample of 120 individuals, the sample mean weekly unemployment insurance benefit was $231 with a sample standard deviation of $60. The p-value is:

c. Using level of signifigance = .05, can you conclude that the mean weekly unemployment insurance benefit in Virginia is below the national level?

d. Using   level of signifigance = .05, what is the critical value for the test statistic (to 2 decimals)?

e. State the rejection rule: Reject H₀ if t is - Select your answer -greater than or equal to ,greater than,less than or equal to,less than equal to not equal to Item 6 the critical value.

f. Using  = .05, can you conclude that the mean weekly unemployment insurance benefit in Virginia is below the national level?

Answer 1

a)

Ho :   µ =   238
Ha :   µ <   238

b)

sample std dev ,    s =    60.0000                  
Sample Size ,   n =    120                  
Sample Mean,    x̅ =   231.0000                  
                          
degree of freedom=   DF=n-1=   119                  
                          
Standard Error , SE = s/√n =   60.0000   / √    120   =   5.4772      
t-test statistic= (x̅ - µ )/SE = (   231.000   -   238   ) /    5.4772   =   -1.28
                          
  
p-Value   =   0.1019   [Excel formula =t.dist(t-stat,df) ]              

c)

Level of Significance ,    α =    0.05                  
Decision:   p-value>α, Do not reject null hypothesis   
Conclusion: There is not enough evidence to conclude that the mean weekly unemployment insurance benefit in Virginia is below the national level

d)

critical t value, t* =        -1.6578   [Excel formula =t.inv(α/no. of tails,df) ]          

e)

Reject H₀ if t is greater than -1.28

f)

critical t value, t* =        -1.6578 < -1.28

so

Do not reject null hypothesis   
Conclusion: There is not enough evidence to conclude that the mean weekly unemployment insurance benefit in Virginia is below the national level