How large of a sample size is required? Round up to nearest whole number.n =

Question

You want to obtain a sample to estimate a population mean. Based on previous evidence, you believe the population standard deviation is approximately . You would like to be 98% confident that your estimate is within 10 of the true population mean. How large of a sample size is required? Round up to nearest whole number.n = 

Answer 1

We need to use

Margin of Error = z^*(σ/√n) We use z^* because we know the population standard deviation.

Margin of Error = 10 since you want to the answer to be within 10 units of the true population mean.

z^* = 2.33, which is how many standard deviations are required in order to have 98% confidence. (Let me know if you need help finding this critical value.)

We also know σ = 59.3.

Let's look at our formula and plug in the values.

Margin of Error = z^*(σ/√n)

10 = 2.33(59.3/√n) First divide both sides by 2.33.

4.29185 = 59.3/√n Now multiply both sides by √n to get it out of the denominator.

4.29185√n = 59.3 Now divide both sides by 4.29185.

√n = 13.8169 Now square both sides to undo the square root.

n = 190.907 Now we round up to the next whole number.

n = 191

Answer 2

Since this is 2-sided, you use z_.01 z.₀₁² 59.3²/10² = in Excel, NORMSINV(0.99)² 59.3²/10² = 190.3087, which we round up to 191.