Question

Suppose your boss wants you to obtain a sample to estimate a population mean. Based on previous analyses, you estimate that 49 is the approximate value of the population standard deviation. You would like to be 99% confident that your estimate is within 38 of the true population mean. What is the minimum sample size required

Answer 1

Answer:

the minimum sample size n = 11.03

Step-by-step explanation:

Given that:

approximate value of the population standard deviation $\sigma$ = 49

level of significance ∝ = 0.01

population mean = 38

the minimum sample size n = ?

The minimum sample size required can be determined by calculating the margin of error which can be re[resented by the equation ;

Margin of error = $Z_{ \alpha /2}} \times \dfrac{\sigma}{\sqrt{n}}$

$38 = \dfrac{2.576 \times 49}{\sqrt{n}}$

$\sqrt{n} = \dfrac{2.576 \times 49}{38}$

$\sqrt{n} = \dfrac{126.224}{38}$

$\sqrt{n} = 3.321684211$

$n= (3.321684211)^2$

n ≅ 11.03

Thus; the minimum sample size n = 11.03