Question: The sample mean is found to be 0.498 in. Assume that the standard deviation of all such lengths is 0.12 in, and use a 0.05 significance level to test the chain that the screws have a mean length equal to 1/2in [or 0.5 in], as indicated on the package labels. Do the screw length appear to be consistent with the package label?

H0:μ =0.05
H1:μ ≠0.05
What is the test statistic?  Edit

Answer: H0: μ =0.5
H1:μ ≠0.5
test statistic, z= (x bar - mu)/sigma= (x bar - 0.498)/0.12
x bar=0.5
z= (0.5-0.498)/0.12=0.016

z-critical at 0.05 level of significance= 1.96

hence, z computed < z-critical

so, fail to reject null .
so, the screw length appear to be consistent with the package label.  Edit