The article "Withdrawal Strength of Threaded Nails" (D. Rammer, S.Winistorfer, and D. Bender, Journal of Structural Engineering, 2001:442-449) describes an experiment to investigate the relationship between the diameter of a nail (x) and its ultimate withdrawal strength (y). Annularly threaded nails were driven into Douglas fir lumber, and then their withdrawal strengths were measured in N/mm. The following results for 10 different diameters (in mm) were obtained.
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x
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2.52 2.87 3.05 3.43 3.68 3.76 3.76 4.50 4.50 5.26
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y
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54.74 59.01 72.92 50.85 54.99 60.56 69.08 77.03 69.97 90.70
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a. Compute the least-squares line for predicting strength from diameter.
b. Compute the error standard deviation estimate s.
c. Compute a 95% confidence interval for the slope.
d. Find a 95% confidence interval for the mean withdrawal strength of nails 4 mm in diameter.
e. Can you conclude that the mean withdrawal strength of nails 4 mm in diameter is greater than 60 N/mm? Perform a hypothesis test and report the P-value.
f. Find a 95% prediction interval for the withdrawal strength of a particular nail whose diameter is 4 mm.