Question

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You want to obtain a sample to estimate a population mean. Based on previous evidence, you
believe the population standard deviation is approximately 25.1. You would like to be 99%
confident that your estimate is within 0.5 of the true population mean. How large of a sample size is
required?


Do not round mid-calculation. However, use a critical value accurate to three decimal places - this
is important for the system to be able to give hints for incorrect answers.

Answer 1

The formula for calculating the sample size needed to estimate a population mean with a specified margin of error and confidence level is:

n = [(z*σ)/E]^2

where:

n = sample size

z = critical value

σ = population standard deviation

E = margin of error

In this case, we want to be 99% confident that our estimate is within 0.5 of the true population mean, and we believe the population standard deviation is approximately 25.1. Therefore:

E = 0.5

σ = 25.1

Confidence level = 99%, so alpha = 0.01 (two-tailed test)

Using a z-table or calculator, we can find the critical value z to be 2.576.

Substituting these values into the formula, we get:

n = [(2.576*25.1)/0.5]^2

n = 3297.47

Therefore, we need a sample size of at least 3298 to be 99% confident that our estimate is within 0.5 of the true population mean.