Question

A research scientist wants to know how many times per hour a certain strand of bacteria reproduces. He wants to construct the 90% confidence interval with a maximum error of 0.18 reproductions per hour. Assuming that the mean is 10.3 reproductions and the standard deviation is known to be 2.2, 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 = = 2.2

margin of error = E = 0.18

At 90% confidence level the z is ,

= 1 - 90% = 1 - 0.90 = 0.10

/ 2 = 0.10 / 2 = 0.05

Z_/2 = Z_0.05 = 1.645

Sample size = n = [(Z_/2 * ) / E]²

= [(1.645 * 2.2) /0.18]²

= 404.23

Sample size = 405