Question

Use the given information to find the minimum sample size required to estimate an unknown population mean μ

Answer 1

Answer:

94

Step-by-step explanation:

Margin of error = E = $ 120

Confidence Level = 95%

The z-score for 95% confidence level from the z-table = z = 1.96

Population standard deviation = σ = $593

Sample size = n  = ?

The formula to calculate the margin of error is:

$E=\frac{z \sigma}{\sqrt{n} }$

Re-arranging the equation, we get:

$\sqrt{n}=\frac{z \sigma}{E}\\\\ n = (\frac{z \sigma}{E})^{2}$

Using the given values in above equation, we get:

$n=(\frac{1.96 \times 593}{120} )^{2}\\\\ n = 93.8$

Rounding of to next higher integer, we get n = 94

Thus, we need a sample size of 94 to estimate an unknown population mean μ