Question 1181555: You are a researcher studying the lifespan of a certain species of bacteria. A preliminary sample of 30 bacteria reveals a sample mean of x = 74 hours with a standard deviation of s = 5 hours. You would like to estimate the mean lifespan for this species of bacteria to within a margin of error of 0.45 hours at a 95% level of confidence.
What sample size should you gather to achieve a 0.45 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 half-interval or 0.45=t(0.975,df=unknown)*s/sqrt(n); t=2.045
start using z and 1.96 to estimate: 0.45=1.96*5/sqrt(n)
sqrtIn)=9.8/0.45=21.78
n=474.27 or 475
The t-value for this is very close to 1.96 but maybe a percentage poignant away, or a sample size of 5-9
At 475, the error is 0.451; at 480, 0.448
It is exactly 0.45 at n=477.
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