SOLUTION: #6 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=78 hours with a standard deviation

Question 1120076: #6
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=78 hours with a standard deviation of s=6.2
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 90% 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!
Use a z first to get an idea and then look at the t-value
the margin of error is equal to t(df=unknown)*s/sqrt)(n) and that is equal to 0.45
Start with sample size of 100
t=1.66
1.66*6.2/sqrt(100)=1.029
let n=500
1.645*6.2/sqrt(n)=0.45
10.199=0.45 sqrt(n)
22.664=sqrt (n)
n=513.67 or 514

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