SOLUTION: You are a researcher studying the lifespan of a certain species of bacteria. A preliminary sample of 40 bacteria reveals a sample mean of ¯x=72 hours with a standard deviation of

Question 1157904: You are a researcher studying the lifespan of a certain species of bacteria. A preliminary sample of 40 bacteria reveals a sample mean of ¯x=72 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 0.55 hours at a 99% level of confidence.
What sample size should you gather to achieve a 0.55 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!
half-interval is t (df=unknown, 0.995)*s/sqrt(n). Use z first
=2.576*5.2/sqrt(n)=0.55 units hours
13.3952/sqrt(n)=.55
so 13.3952/0.55=sqrt(n)
n=593.16 round to 594

t df=594 should be close to z
divide t 0.995/z 0.995 and multiply by 594
that gives 596 rounded upward.
can check
t=2.584
t*s/sqrt(586)=.55
596 is the sample size needed.

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