Question

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

Margin of error: $120, confidence level: 95%, σ = $593

83

66

94

133

Answer 1

94

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=(z \sigma)/(√(n) )`

Re-arranging the equation, we get:

`√(n)=(z \sigma)/(E)\\\\  n = ((z \sigma)/(E))^(2)`

Using the given values in above equation, we get:

`n=((1.96 * 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