Question

2. The U.S. Bureau of Labor Statistics publishes a variety of unemployment statistics, including the number of individuals who are unemployed and the mean length of time the individuals have been unemployed. For November 1998, the Bureau of Labor Statistics reported that the national mean length of time of unemployment was 14.5 weeks.

The mayor of Chicago has requested the study on the status of unemployment in City of Chicago. A sample of 60 unemployed residents shows the sample mean is 15.7 and the sample standard deviation is 9.0. Test whether the length of time in Chicago is long than national average.

Answer 1

H0: <= 14.5

Ha: > 14.5

Test statistics

t = - / (S / sqrt(n) )

= 15.7 - 14.5 / (9 / sqrt(60))

= 1.03

This is test statistics value

df = n - 1 = 60 - 1 = 59

t critical value at 0.05 level with 59 df = 1.671

Since test statistics falls in non-rejection region, do not reject H0.

We conclude at 0.05 level that we fail to support the claim.