Question

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 cm² and that he has a sample size of 35 with sample mean equal to 111 cm². Assume all conditions are met.

(a) What is the 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.

Answer 1

a)

df = n -1 = 35 - 1 = 34

t critical value at 0.01 level at 34 df = 2.728

b)

99% confidence interval for is

- t * S / sqrt( n) <   < + t * S / sqrt( n)

111 - 2.728 * 15 / sqrt(35) < < 111 + 2.728 * 15 / sqrt(35)

104.08 < < 117.92

99% CI is ( 104.08 , 117.92 )