Per-trade profit has standard deviation s = 15. You want the half-width of the interval h = 2 × s/√n to be at most 1.5. What is the smallest integer n that works?

Learn / Library / Statistics

Sample size for precision

StatisticsMedium

Per-trade profit has standard deviation $s = 15$ . You want the half-width of the interval $h = 2 \times \frac{s}{n}$ to be at most $1.5$ . What is the smallest integer $n$ that works?

Checking an answer needs JavaScript. The hint and the solution open without it.

Hint

Solve the inequality for $n$ and then square it.

Solution

We need $2 \times \frac{15}{n} \leq 1.5$ .
This gives $n \geq \frac{30}{1.5} = 20$ .
Squaring gives $n \geq 400$ .
At $n = 400$ the half-width is exactly $1.5$ , so it is allowed.
So the smallest $n$ is $400$ .

Answer: $400$

Next question Back to the library