In Example 2 from Section 10.3, the quality-control engineer for M\&MMars tested whether the mean weight of fun-size Snickers was 20.1 grams. Suppose that the standard deviation of the weight of the candy was 0.75 gram before a machine recalibration. The engineer wants to know if the recalibration resulted in more consistent weights. Conduct the appropriate test at the \(\alpha=0.05\) level of significance. The data are reproduced in Table 2.

Approach If the recalibration results in more consistent weights, then the standard deviation weight should be less than it was prior to recalibration. We want to test if \(\sigma

Data from Example 2 from Section 10.3

The "fun size" of a Snickers bar is supposed to weigh 20 grams. Because the penalty for selling candy bars under their advertised weight is severe, the manufacturer calibrates the machine so the mean weight is 20.1 grams. The quality-control engineer at M\&M-Mars, the Snickers manufacturer, is concerned about the calibration. He obtains a random sample of 11 candy bars, weighs them, and obtains the data shown in Table 1. Should the machine be shut down and calibrated? Because shutting down the plant is very expensive, he decides to conduct the test at the \(\alpha=0.01\) level of significance.

Table 2 19.68 20.66 19.56 19.98 20.65 19.61 20.55 20.36 21.02 21.50 19.74