The national institute of standards and technology (nist) offers standard reference materials to aid in the calibration of measurement instruments and verify the accuracy of measurements. suppose a medical researcher wants to verify that the distances he measures with his computed tomography machine are not too large, so he orders a dimensional standard for medical computed tomography from nist.

this standard consists of 18 plastic balls held in place by a plastic support structure. the certified distance between the balls numbered 1 and 2 is 15.96 mm, and nist determines that measurement errors are normally distributed with a standard deviation of 0.05 mm. upon receiving the standard reference material, the researcher measured the distance between balls 1 and 2 five times. take these five measurements to be a simple random sample of all measurements made on this device under carefully controlled conditions. the researcher then calculated the summary statistics, where is the mean distance between balls 1 and 2, as measured by his computed tomography machine.

test of =15.96 vs > 15.96the assumed standard deviation=0.05