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A biologist wishes to estimate the effect of an antibiotic on the growth of a particular...

A biologist wishes to estimate the effect of an antibiotic on the growth of a particular bacterium by examining the mean amount of bacteria present per plate of culture when a fixed amount of the antibiotic is applied. Suppose he estimates that s = 12 cm^2 and that he has a sample size of 35 with sample mean equal to 111 cm^2. Assume all conditions are met.

(a) What is the t* value needed to construct a 99% confidence interval for the mean?

(b) Let μ denote the population mean amount of bacteria present per plate of culture. Calculate the 99% confidence interval for μ. (Use 3 decimal places)

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