A company receives a large shipment of bolts. The bolts will be used in an application that requires a torque of 100 J. Before the shipment is accepted, a quality engineer will sample 12 bolts and measure the torque needed to break each of them. The shipment will be accepted if the engineer concludes that fewer than 1% of the bolts in the shipment have a breaking torque of less than 100 J.
a. If the 12 values are 107, 109, 111, 113, 113, 114, 114, 115, 117, 119, 122, 124, compute the sample mean and sample standard deviation.
b. Assume the 12 values are sampled from a normal population, and assume the sample mean and standard deviation calculated in part (a) are actually the population mean and standard deviation. Compute the proportion of bolts whose breaking torque is less than 100 J. Will the shipment be accepted?
c. What if the 12 values had been 108, 110, 112, 114, 114, 115, 115, 116, 118, 120, 123, 140? Use the method outlined in parts (a) and (b) to determine whether the shipment would have been accepted.
d. Compare the sets of 12 values in parts (a) and (c). In which sample are the bolts stronger?
e. Is the method valid for both samples? Why or why not?