You are a researcher studying the lifespan of a certain species of bacteria. A preliminary sample of 40 bacteria reveals a sample mean of 64 hours with a standard deviation of 4.2 hours. You would like to estimate the mean lifespan for

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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 64 hours with a standard deviation of 4.2 hours. You would like to estimate the mean lifespan for this species of bacteria to within a margin of error of .65 hours at a 95% level of confidence.

What sample size should you gather to achieve a .65 hour margin of error? Round your answer up to the nearest whole number.

Expert Solution
Step 1

From the available information,

Sample size, n= 40

Sample Mean,x¯ = 64

The estimate of population standard deviation is the Sample standard deviation. That is, σ^ =s =4.2

The margin of error is given as ,

E =0.65

The confidence level is,

C = 95%=95/100= 0.95

The level of significance Is,

α= 1-C= 1-0.95=0.05

From standard normal table at 0.05 level of significance the two- tailed critical value is,

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