Question

An statistics Instructor is trying to figure out the percentage of students that still listen to Nirvana. The statistics Instructor is pretty out of touch, so he doesn't know what

percentage of students listen to Nirvana. How many students should the statistics instructor sample if he wants to be within 2% of the actual percentage of students who listen to
Nirvana with a 98% confidence level. (Round the z value to 2 decimal places)

Answer 1

Given:

Confidence level = 98%

Margin of error, E = 2% = 0.02

Let's find the number of students the instructor should sample.

Here, we are to find the sample size (n).

We have:

`P^{^(\prime)}=1-P^(\prime)=0.5`

At 98% confidence level, we have:

`\alpha=1-\text{ 98\%= 2\% = 0.02}`
`(\alpha)/(2)=(0.02)/(2)=0.01`

Using the z-score table, we have:

`Z_{(\alpha)/(2)}=Z_(0.01)=2.33`

To find the sample size(number of students) n, we have:

`n=(\frac{Z_{(\alpha)/(2)}}{E})^2\ast P^(\prime)\ast(1-P^(\prime))`

Thus, we have:

`\begin{gathered} n=((2.33)/(0.02))^2\ast0.5\ast0.5 \\ \\ n=(116.5)^2\ast0.5\ast0.5 \\ \\ n=13572.25\ast0.5\ast0.5 \\ \\ n=3393.06\approx3393 \end{gathered}`

Therefore, the statistics instructor should sample 3393 students.

ANSWER:

3393