Suppose that a bottled water plant wants to determine if the bacteria count in their water supply exceeds the safety threshold of \(100 \mathrm{cfu} / \mathrm{mL}\) (colony-forming units per milliliter). Ten different samples were taken at random points in the water supply and the bacterial count was measured in \(\mathrm{cfu} / \mathrm{mL}\). The data is presented in Table 4.6.

a. Can you conclude whether the plant water supply exceeds the safety threshold for the bacteria count?

b. How big of a sample would be needed to detect at least a 2 -cfu/mL difference?

c. The plant wants to be able to detect a bacteria count of at least \(105 \mathrm{cfu} / \mathrm{mL}\). How big of a sample would be needed to determine if the bacteria count exceeds 105 \(\mathrm{cfu} / \mathrm{mL}\) ?

Table 4.6

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Bacteria Count (in cfu/mL) 104 102 100 97 93 105 102 97 96 102