The uniform length of nails is very important to a carpenter—the length of the nails being used are matched to the materials being fastened together, thereby making a small standard deviation an important property of the nails. A sample of 35 randomly selected 2-inch nails is taken from a large quantity of Nails, Inc.’s, recent production run. The resulting length measurements have a mean length of 2.025 inches and a standard deviation of 0.048 inch.
a. Determine whether an assumption of normality is reasonable. Explain.
b. Is the sample evidence sufficient to reject the idea that the nails have a mean length of 2 inches? Use a = 0.05
c. Is there sufficient evidence, at the 0.05 level, to show that the length of nails from this production run has a standard deviation greater than the advertised 0.040 inch?
d. Write a short report outlining the findings and recommendations as to whether or not the carpenter should use these nails for an application that requires 2-inch nails.