Question

You are a researcher studying the lifespan of a certain species of bacteria. A preliminary sample of 25 bacteria reveals a sample mean of ¯x=72x¯=72 hours with a standard deviation of s=5.8s=5.8 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 1

The following information has been provided:

The critical value for the significance level α=0.05 is zc​=1.96. The following formula is used to compute the minimum sample size required to estimate the population mean μ within the required margin of error:

Therefore, the sample size needed to satisfy the condition n≥638.16, and it must be an integer number, we conclude that the minimum required sample size is n = 639

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