SOLUTION: A researcher studying the lifespan of a certain species of bacteria. A preliminary sample of 30 bacteria reveals a sample mean of ¯ x = 64 hours with a standard deviation

Question 1166620: A researcher studying the lifespan of a certain species of bacteria. A preliminary sample of 30 bacteria reveals a sample mean of
¯
x
=
64
hours with a standard deviation of
s
=
5.8
hours. He would like to estimate the mean lifespan for this species of bacteria to within a margin of error of 0.8 hours at a 98% level of confidence.
What sample size should you gather to achieve a 0.8 hour margin of error?
He would need to sample
bacteria.
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
start with z0.99 since we aren't sure yet of df for t
that is 2.326
the half-interval is 0.8 and is equal to z*s/sqrt(n) for the first approximation
0.8=2.326*5.8/sqrt(n)
0.8sqrt*n=2.326*5.8
square both sides
0.64n=182.00
n=284.375 or 285
At this point the t-value is a few more df than 285. From the calculator, n=288 or df=287 gives the desired margin of error, and that is the answer.

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