Question

You want to obtain a sample to estimate a population mean. Based on previous evidence, you believe the population standard deviation is approximately
σ=39.7. You would like to be 95% confident that your estimate is within 3 of the true population mean. How large of a sample size is required?

Answer 1

Answer:

673 people

Step-by-step explanation:

Statistics<3

Use the margin of error formula.

ME = t*$\frac{s}{\sqrt{n} }$

• Margin of error or ME = 3
• Critical t or t* with a confidence level of 95% on the calculator is invNorm(.975) = 1.96. You would use invt, except you don't have the degrees of freedom, so you can approximate with invNorm. It's close enough.
• Standard deviation or s = 39.7
• Solve for n!

3 = 1.96*$\frac{39.7}{\sqrt{n} }$

3/1.96 = $\frac{39.7}{\sqrt{n} }$

1.531 = $\frac{39.7}{\sqrt{n} }$

39.7/1.531 = $\sqrt{n}$

25.937 = $\sqrt{n}$

25.937^2 = $\sqrt{n}$^2

672.7 = n

You need at least 673 people to be confident!