Fabco, a precision machining shop, uses statistical process control (SPC) techniques to ensure quality and consistency of their steel shafts. The control limits used in their SPC charts are based on the assumption that shaft diameters are normally distributed. To verify this assumption, a quality engineer has measured the diameters for a sample of 50 of its popular 1∕2-inch shafts.

a. Using the Jarque-Bera test, state the competing hypotheses in order to determine whether or not the data follow the normal distribution.

b. Calculate the value of the Jarque-Bera test statistic. Use Excel to calculate the p-value.

c. At α = 0.10, can you conclude that the shaft diameters are not normally distributed?

d. Would your conclusion change at the 5% significance level?