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

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

Explanation / Answer

Solution :

Given that mean x = 115 , standard deviation s = 15 , n = 35

=> df = n-1 = 34

(a) => t-value with df = 34 for a 99% confidence interval is 2.728

(b) => The 99% confidence interval for the mean if x +/- t*s/sqrt(n)

=> 115 +/- 2.728*15/sqrt(35)

=> (108.083 , 121.917)

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