Math please help

Question

A highway construction zone has a posted speed limit of 40 miles per hour. Workers working at the site claim that the mean speed of vehicles passing through this construction zone is at least 50 miles per hour. A random sample of 40 vehicles passing through this zone produced a mean speed of 48 miles per hour with a standard deviation of 4 miles per hour. Do you think the sample information is consistent with the workers’ claim? Use α = 0.025.

Answer 1

Ho: mu >= 50

Ha: mu < 50

z = (mean - mu)/(SD/sqrt(sample size)) = (48-50)/(4/sqrt(40)= -3.16

P(z < -3.16) = 0.001.

p-value = 0.001, which is less than alpha = 0.025, so would reject Ho (the worker's claim) and conclude the sample information is not consistent with the worker's claim.