Find the minimum sample size needed to estimate the population proportion:

Margin of error: .015
Confidence level: 96%
p ˆ ,q ˆ : unknown

Question

Find the minimum sample size needed to estimate the population proportion:

Margin of error: .015
Confidence level: 96%
p ˆ ,q ˆ  : unknown

amistre64 · Answer

$$\hat p\  \text{and}\ \hat q\ \text{are unknown}$$

amistre64 · Answer

i keep getting 4687, but it isnt one of my options ....

either im doing it wrong, or the study guide is off

amistre64 · Answer

$$n=\cfrac{(z_{\alpha/2})^2(.25)}{Error^2}$$

blacksteel · Answer

It's been a while since I did stats, but wouldn't that be $$\alpha = 0.96 => \alpha/2 = 0.48$$$$z_{0.48} = 0.6844$$$$n = 0.6844^2 * 025 / 0.015^2 \approx521$$

blacksteel · Answer

*0.25

amistre64 · Answer

looks good; you zscore number is off tho ...

I get it by doing (.5 + (.CI)/2)

amistre64 · Answer

either way it gets to .48 with a zscore = 2.05

blacksteel · Answer

Yeah, that looks right - like I said, it's been a while. So then your equation should be$$n = (.9798)^2*0.25/0.015^2 \approx 1067$$
right?

amistre64 · Answer

my choices, albeit wrong as they may be, are :

4670
4519
3667
6669

amistre64 · Answer

(.9798)^2 is where you are off at; the rest is good

amistre64 · Answer

should be (2.05)^2 according to the text I have

blacksteel · Answer

Yeah, never mind, I'm an idiot. You're using the zscore, not the z table entry. When I run the numbers with (2.05)^2, I get 4670.

amistre64 · Answer

4670 is good; i was using the calculators inverseNorm function which has a higher degree of accuracy than 2.05 which thew the answer off from the choices

blacksteel · Answer

Yup, that would do it.

amistre64 · Answer

2.053748911 doesnt fit good in the answer choices :)