SOLUTION: A researcher studying the lifespan of a certain species of bacteria. A preliminary sample of 30 bacteria reveals a sample mean of ¯ x = 80 hours with a standard deviation

Question 1184846: A researcher studying the lifespan of a certain species of bacteria. A preliminary sample of 30 bacteria reveals a sample mean of
¯
x
=
80
hours with a standard deviation of
s
=
4.2
hours. He 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?
He would need to sample_____ bacteria.
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
error=t*s/sqrt(n), but we don't know what the sample size is so can't use t initially. Use z
0.45=1.645*4.2/sqrt(n)
square both sides and move sqrt(n) over after squaring it
0.2025 n=47.73
n=235.72 or 236
t (0.95, df=236)=1.651
at this point one would try n=237 and n=238.
0.45 is between the two for the error, so the answer is n=238.

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