Question

Use the information to find the minimum sample size required to estimate an unknown population mean µ. Margin of error: $110, confidence level: 95%, σ = $500. Group of answer choices

Answer 1

Answer:

The minimum sample size required is 79.

Step-by-step explanation:

The following are given in the question:

e = Margin of error = 110

σ = Standard deviation = 500

Confidence level = 95%

n = Minimum sample size = ?

Therefore, we have:

Zσ = 1.96 at 95% confidence level

s.e. = Standard error = σ / $\sqrt{n}$ = 500 /

Alternatively, margin of error can be calculated as follows:

e = s.e. * Zσ = 110 ................... (1)

Substituting the other values into equation (1) and solve for n, we have:

500 / $\sqrt{n}$ * 1.96 = 110

500 / $\sqrt{n}$  = 110 / 1.96

500 / $\sqrt{n}$  = 56.1224489795918

500 = 56.1224489795918 *  $\sqrt{n}$  

$\sqrt{n}$  = 500 / 56.1224489795918

$\sqrt{n}$  = 8.90909090909092

$n^{\frac{1}{2}$ = 8.90909090909092

Squaring both sides, we have:

($n^{\frac{1}{2}$)^2 = (8.90909090909092)^2

n = 79.3719008264465

Approximating to a whole number, we have:

n = 79

Therefore, the minimum sample size required is 79.