I have no idea what do do here please explain HW 11 Q 17 A b

I have no idea what do do here, please explain! HW 11 Q 17

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 = 15 cm^2 and that he has a sample size of 35 with sample mean equal to 114 cm^2. Assume all conditions are met. (a) What is the the t* value needed to construct a 99% confidence interval for the mean? (b) Let mu denote the population mean amount of bacteria present per plate of culture. Calculate the 99% confidence interval for mu. (Use 3 decimal places)

Solution

(a) The degree of freedom =n-1=35-1=34

Given a=1-0.99=0.01, t(0.005, df=34) =2.728 (from student t table)

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(b) So the lower bound is

xbar - t*s/vn =114-2.728*15/sqrt(35) =107.083

So the upper bound is

xbar +t*s/vn=114+2.728*15/sqrt(35) =120.917