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(x-bar)=74 hours with a standard devia

Question 1157324: 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(x-bar)=74 hours with a standard deviation of s=6 hours. You 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? 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!
0.7=t*s/sqrt(n)
problem is that t is dependent on the sample size which isn't known. So start with z
0.7=1.96*6/sqrt(n)
square both sides
0.49=3.8416*36/n
282.24 or 283
t (df=282)=1.968
recalculate using that and n=284.5 round to 285
This sample size will give exactly 0.7 margin of error

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