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=78x¯=78 hours with a standard deviation of s=4.4s=4.4  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 99% 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

MATLAB: An Introduction with Applications
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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=78x¯=78 hours with a standard deviation of s=4.4s=4.4  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 99% 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

Expert Solution
Step 1

Given sample standard deviation

s=4.4

We know that margin of error for mean is given by zα2*sn

But margin of error is given as 0.45.

Then

zα2*sn=0.45n=zα2*s0.452=2.58*4.40.452=636.3847637

 

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