Question

You are a researcher studying the lifespan of a certain species of bacteria. A preliminary sample of 40 bacteria reveals a sample mean of ¯ x = 74 x¯=74 hours with a standard deviation of s = 4.6 s=4.6 hours. You would like to estimate the mean lifespan for this species of bacteria to within a margin of error of 0.4 hours at a 99% level of confidence.

What sample size should you gather to achieve a 0.4 hour margin of error? Round your answer up to the nearest whole number.

n = bacteria

Answer 1

Solution :

Given that,

standard deviation =s = 4.6

Margin of error = E = 0.4

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* / E] ²

n = ( 2.58* 4.6/0.4 )²

n =880

Sample size = n =880