Question

Use the given information to find the minimum sample size required to estimate an unknown population mean μ.

Answer 1

Answer:

151 students must be selected.

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:

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

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 $1 - 0.025 = 0.975$, 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.

The population standard deviation is known to be $25.

This means that $\sigma = 25$

How many students must be randomly selected to estimate the mean weekly earnings of students at one college? Sample mean within $4 of the population mean

This is n for which M = 4. So

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

$4 = 1.96\frac{25}{\sqrt{n}}$

$4\sqrt{n} = 1.96*25$

$\sqrt{n} = \frac{1.96*25}{4}$

$(\sqrt{n})^2 = (\frac{1.96*25}{4})^2$

$n = 150.1$

Rounding up:

151 students must be selected.