SOLUTION: 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 = 70 hours with a standard deviation o

Question 1181556: 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 = 70 hours with a standard deviation of s = 5.2 hours. You would like to estimate the mean lifespan for this species of bacteria to within a margin of error of 0.75 hours at a 95% level of confidence.
What sample size should you gather to achieve a 0.75 hour margin of error? Round your answer up to the nearest whole number.
n = _______ bacteria
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
the margin of error is the half-interval for 95% or t(0.975, df=n-1)*s/sqrt(n)
use z to approximate
0.75=1.96*5.2/sqrt(n)
n=(1.96*5.2)^2/0.75^2=184.67 or 185
t is about 2% larger than z for sample size of 100
that would be 3.78 here for a larger sample size.
I would assume 3 so therefore use 3 more or a sample size of 188.
This produces an interval of (69.252, 70.748) just within 0.75. Try a sample size of 187 to see if that is better.
For n=187, the interval is (69.25, 70.25)

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