Question

Suppose you believe that the true average daily trade volume for General Electric stock is 49,829,719 shares and a standard deviation of 21,059,637 shares. Considering a 95% confidence level: What is the minimum required sample size if you would like your sampling error to be limited to 1,000,000 shares

Answer 1

Answer:

The minimum sample size is 1,704.

Step-by-step explanation:

We have to find our $\alpha$ level, that is the subtraction of 1 by the confidence interval divided by 2. So:

$\alpha = \frac{1 - 0.95}{2} = 0.025$

Now, we have to find z in the Z-table as such z has a p-value of $1 - \alpha$.

That is z with a p-value of $1 - 0.025 = 0.975$, so Z = 1.96.

Now, find the margin of error M as such

$M = z\frac{\sigma}{\sqrt{n}}$

In which $\sigma$ is the standard deviation of the population and n is the size of the sample.

Standard deviation of 21,059,637 shares

This means that $\sigma = 21059637$

What is the minimum required sample size if you would like your sampling error to be limited to 1,000,000 shares?

This is n for which $M = 1000000$, so:

$M = z\frac{\sigma}{\sqrt{n}}$

$1000000 = 1.96\frac{21059637}{\sqrt{n}}$

$1000000\sqrt{n} = 1.96*21059637$

$\sqrt{n} = \frac{1.96*21059637}{1000000}$

$(\sqrt{n})^2 = (\frac{1.96*21059637}{1000000})^2$

$n = 1703.8$

Rounding up:

The minimum sample size is 1,704.