Question

You are going to estimate how long a person holds down a button on their calculator by randomly selecting people and asking them to do something on your calculator (which has a special timer to record how long the enter button is pressed). You practiced on the people at work and found a standard deviation of about 0.37 seconds. You want to get a 94% confidence interval that is only 0.06 in width. How many people do you need to have in your study

Answer 1

Answer:

You need to have 538 people in your study.

Step-by-step explanation:

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

$\alpha = \frac{1 - 0.94}{2} = 0.03$

Now, we have to find z in the Ztable as such z has a pvalue of $1 - \alpha$.

That is z with a pvalue of $1 - 0.03 = 0.97$, so Z = 1.88.

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.

You practiced on the people at work and found a standard deviation of about 0.37 seconds.

This means that $\sigma = 0.37$

You want to get a 94% confidence interval that is only 0.06 in width.

This means that $M = \frac{0.06}{2} = 0.03$

How many people do you need to have in your study?

This is n for which M = 0.03. So

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

$0.03 = 1.88\frac{0.37}{\sqrt{n}}$

$0.03\sqrt{n} = 1.88*0.37$

$\sqrt{n} = \frac{1.88*0.37}{0.03}$

$(\sqrt{n})^2 = (\frac{1.88*0.37}{0.03})^2$

$n = 537.6$

Rounding up:

You need to have 538 people in your study.