Question

According to the Bureau of Labor Statistics, citizens remain unemployed for an average of 15.9 weeks before finding their next job (June, 2008). Suppose you want to show that Louisiana has been effective in getting their unemployed back to work sooner by testing the hypothesis, H₀: μ ≥ 15.9 vs H₁: μ < 15.9, at 0.10 level of significance. You take a random sample of 50 citizens who were unemployed six months earlier and ask them to report the duration. You find that the average time spent unemployed was 13.9 with a sample standard deviation of the time unemployed is 6.7 weeks. The test statistic for testing the hypothesis is _____________.

Select one:

-2.64

-2.32

-2.11

-1.28

none of these are correct

Answer 1

Solution :

The null and alternative hypothesis is ,

H0 :   ≥ 15.9

Ha : < 15.9  

= 13.9

s = 6.7

n = 50

Test statistic = t =

= ( - ) / s / n

= (13.9 - 15.9 ) / 6.7 / 50

Test statistic = t = -2.11