A machine packs cereal into boxes, and you don’t want too much variation from box to box. You decide that a standard deviation of no more than five grams (about 1/6 ounce) is acceptable. The default assumption is that the machine is working fine, but from time to time, to determine whether the machine is operating within specification, you randomly select 45 boxes and check their weights. On one such test, a sample standard deviation of 6.42 grams was obtained. At a 5% significance level, conduct the appropriate hypothesis test and determine if the machine is malfunctioning.

Question

A machine packs cereal into boxes, and you don’t want too much variation from box to box. You decide that a standard deviation of no more than five grams (about 1/6 ounce) is acceptable. The default assumption is that the machine is working fine, but from time to time, to determine whether the machine is operating within specification, you randomly select 45 boxes
and check their weights. On one such test, a sample standard deviation of 6.42 grams was obtained. At a 5% significance level, conduct the appropriate hypothesis test and determine if the machine is malfunctioning.

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Hypothesis Testing

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