Question

According to the local union president, the mean gross income of plumbers in the Salt Lake area

follows the normal probability distribution with a mean of $45,000 and a standard deviation of $3,000. A

recent investigative report for KYAK TV found, for a sample of 120 plumbers, the mean gross income was $45,500. At the .10 significance level, is it reasonable to conclude that the mean income is not equal to $45,500? Use the 5-step process; show your work.

Answer 1

Solution :

This is the two tailed test .

The null and alternative hypothesis is ,

H₀ :   = 45500

H_a :    45500

Test statistic = z

= ( - ) / / n

= (45000 - 45500) / 3000 / 120

= -1.83

P(z < -1.83) = 0.0336

P-value = 0.0674

= 0.10

P-value <

Reject the null hypothesis .

There is sufficient evidence to conclude that the mean income is not equal to $45,500 .