Question

A research scientist wants to know how many times per hour a certain strand of bacteria reproduces. He wants to construct a 99% confidence interval with a maximum error of 0.17 reproductions per hour. Assuming that the mean is 15.1 reproductions and the standard deviation is known to be 2.6, what is the minimum sample size required for the estimate? Round your answer up to the next integer.

Answer 1

Solution :

Given that,

standard deviation =s =  σ =2.6

Margin of error = E = 0.17

At 99% confidence level the z is,

= 1 - 99%

= 1 - 0.99 = 0.01

/2 = 0.005

Z/2  = 2.58

sample size = n = [ Z/2 *  σ/ E]2

n = ( 2.58*2.6 / 0.17 )2

n =1556.99

Sample size = n =1557