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=5.4 hours. You would like to estimate the mean lifespan for this species of bacteria to within a margin of error of 0.65 hours at a 99% level of confidence.

What sample size should you gather to achieve a 0.65 hour margin of error? Round your answer up to the nearest whole number.

Question

Mathematics

Jaylin Kirk

8 December, 16:10

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=5.4 hours. You would like to estimate the mean lifespan for this species of bacteria to within a margin of error of 0.65 hours at a 99% level of confidence.

What sample size should you gather to achieve a 0.65 hour margin of error? Round your answer up to the nearest whole number.

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Answers (1)

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Janelle Wilkinson · Answer 1

458

Step-by-step explanation:

Margin of error = critical value * standard error

At 99% confidence, the critical value is z = 2.576.

The standard error is σ/√n = 5.4/√n.

Given the desired margin of error is 0.65:

0.65 = 2.576 * 5.4/√n

n = 458