Question

A random sample is selected form a population with μ =80 and σ = 20. How large must the sample be to ensure a standard error of 2 points or less?

Answer 1

Answer:

The sample has to be at least 100.

Step-by-step explanation:

We can find the samples size to ensure a standard error of 2 points or less by using the sampling distribution's standard error formula:

$\boxed{SE=\frac{\sigma}{\sqrt{n} } }$

where:

• SE = standard error
• σ = standard deviation
• n = samples size (number of samples)

Given:

• σ = 20
• SE ≤ 2

$SE\leq 2$

$\displaystyle\frac{\sigma}{\sqrt{n} } \leq 2$

$\displaystyle\frac{20}{\sqrt{n} } \leq 2$

$2\sqrt{n} \geq 20$

$4n\geq 400$

$\bf n\geq 100$