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 population standard deviation of $3,000. A recent investigative reporter 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 $45,000? Determine the p-value.

Please write neatly to full understand the material, please and thank you!

Answer 1

n = 120

significance level = 0.1

H0 :

H1 :

z for normal destribution =

since x = mean in this hence  

hence z =

1.825

p value for 1.825(from normal destribution table) = 0.0672

p value < significance level

hence we can reject the null hypothesis

yes it is reasonable to conclude mean is not 45000