## Related questions with answers

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 measurec 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 $\alpha=0.10$, can you conclude that the shaft diameters are not normally distributed?

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

Solution

Verified**(a)** First let us state the two competing hypotheses for the problem. First we have the null hypotheses $H_0$

$H_0:S=0 \text{ and } K=0.$

where $S$ is the skewness coefficient and $K$ is the kurtosis coefficient. The null hypotheses states that the data follows the normal distribution.

Next we have the alternative hypotheses $H_A$

$H_A:S\ne0 \text{ or } K\ne0.$

The alternative hypotheses states that the data does not follow the normal distribution.

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