Question

You are a researcher studying the lifespan of a certain species of bacteria. A preliminary sample of 35 bacteria reveals a sample mean of ¯x=64x¯=64 hours with a standard deviation of s=4.8s=4.8 hours. You would like to estimate the mean lifespan for this species of bacteria to within a margin of error of 0.45 hours at a 90% level of confidence.

What sample size should you gather to achieve a 0.45 hour margin
of error? Round your answer *up* to the nearest whole
number.

Answer #1

Solution :

Given that,

standard deviation =s = =4.8

Margin of error = E = 0.45

At 90% confidence level

= 1 - 90%

= 1 - 0.90 =0.10

/2
= 0.05

Z/2
= Z0.05 = 1.645

sample size = n = [Z/2* / E] 2

n = ( 1.645 *4.8 /0.45 )2

n =307.8

Sample size = n =308

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