Question

A study on students drinking habits wants to determine the true average number of alcoholic drinks all UF male students have in a one week period. We know from preliminary studies that the standard deviation is around 5. How many students should be sampled to be within 1 drink of the population mean with 95% probability? Group of answer choicesA. 49 B. 97 C. 25 D. 10

Answer 1

Answer:

B. 97

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 $1-\alpha$.

So it is z with a pvalue of $1-0.025 = 0.975$, so $z = 1.96$

Now, find 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.

How many students should be sampled to be within 1 drink of the population mean with 95% probability?

This is n when $M = 1$

We know from preliminary studies that the standard deviation is around 5, so $\sigma = 5$

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

$1 = 1.96*\frac{5}{\sqrt{n}}$

$\sqrt{n} = 5*1.96$

$(\sqrt{n})^{2} = (5*1.96)^{2}$

$n = 96.04$

We round up, so the correct answer is:

B. 97