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Suppose that a manufacturer bottling a delicious beverage and the label indicates that the bottle contains 16 fluid ounces. Since providing the customer too little product might cause a significant negative reaction relative to the modest additional cost of providing a little too much, consider the following hypothesis test:
\begin{equation*} H_0 : \mu = 16 \\ H_a: \mu \gt 200. \end{equation*}
To test this hypothesis at significance level \(\alpha = 0.05\text{,}\) you randomly pull out 20 bottles from the production line and accurately measure the amount of produce in each bottle. If the resulting average of these measurements is \(\overline{x} = 16.05\) ounces with a standard deviation of \(s = 0.08\) ounces, determine if you can safely make it known that more product is actually delivered in general to each consumer.
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