Question

A researcher studying the lifespan of a certain species of bacteria. A preliminary sample of 40 bacteria reveals a sample mean of ¯ x = 78 hours with a standard deviation of s = 4.6 hours. He would like to estimate the mean lifespan for this species of bacteria to within a margin of error of 0.7 hours at a 95% level of confidence. What sample size should you gather to achieve a 0.7 hour margin of error? He would need to sample_____ bacteria.

Answer #1

Solution :

Given that,

Population standard deviation = = 4.6

Margin of error = E = 0.7

At 95% confidence level the z is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

Z/2 = Z0.025 = 1.96

sample size = n = (Z/2* / E) 2

n = (1.96 * 4.6/ 0.7)2

n = 165.89

n = 166

**Sample size = 166**

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