Acidity and alkalinity of soil are typically measured on the \(\mathrm{pH}\) scale, which has a range from \(0-14\). A pH of 7 is considered neutral, a \(\mathrm{pH}\) of \(0-7\) is acidic, and a \(\mathrm{pH}\) of 7-14 is alkaline. Lawns should have a \(\mathrm{pH}\) of between 6.3 and 6.7 , where a \(\mathrm{pH}\) of 6.5 is considered optimal. A landscaper needs to test a customer's lawn \(\mathrm{pH}\) to see if the lawn needs to be treated to adjust the \(\mathrm{pH}\) balance. Random soil samples were taken from nine different locations and the \(\mathrm{pH}\) readings are presented in Table 4.12.

a. Is the mean soil pH significantly different from the measure of 6.5 that is considered optimal?

b. Is the standard deviation of the soil \(\mathrm{pH}\) significantly different from 0.20 ?

c. Find and interpret a \(99 \%\) confidence interval for the population standard deviation.

Table 4.12

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pH Readings for a Random Sample of Nine Locations 6.2 6.8 6.3 6.9 6.2 6.5 6.0 6.9 6.3