Any ideas please?
Simple random sample of voters will be taken in a large state. Researchers will construct an approximate 95% confidence interval for the percent of the state’s voters who will vote for Candidate A. Find the minimum sample size needed to ensure that the width of the interval (right end minus left end) is at most 6%.

Thank you.

Question

Any ideas please? 
Simple random sample of voters will be taken in a large state. Researchers will construct an approximate 95% confidence interval for the percent of the state’s voters who will vote for Candidate A. Find the minimum sample size needed to ensure that the width of the interval (right end minus left end) is at most 6%.

Thank you.

amistre64 · Answer

"an approximate" lends ear to the empirical rule:  z = 2

amistre64 · Answer

100 - 6 is 94;  not 95 tho .... but still an approxiamtion

from the setup:$$CI: p\pm E$$
we get
$$E = z\sqrt{\frac{pq}{n}}$$
solving for n we get
$$n = z^2\frac{pq}{E^2}$$

amistre64 · Answer

without knowing anything about the sample data ... thats as fas as i can get with it

anonymous · Answer

@amistre64 thank you, but what to put for numbers?? Because I have to give a numerical answer!

amistre64 · Answer

You have not given us any numbers to work with.  as such, the best guess I would have for p and q is .5 giving us:$$n = 2^2\frac{.25}{E^2}$$
I might have been forgetful about the E tho ... thats prolly where we want the 6% to go; a .06 error

$$n = 2^2\frac{.25}{.06^2}$$

if we want a more accurate resutl we would have to know more about the standard deviation to address the "pq" setup, and we could use a more accurate 95% z value (1.96)

anonymous · Answer

@amistre64 thank you alot..but it cannon be n=
300...

amistre64 · Answer

attachment

amistre64 · Answer

why cant it be close to 300?  when i use a more accurate Z value of (1.96) the results are still 267

anonymous · Answer

@amistre64  because i tried 300 and was wrong.  the exercise says: "answer with a positive integer; correct to the nearest 50"

amistre64 · Answer

hmmm, the width of the interval is at most 6% ... we might want to halve that then.  use 3% and see how that runs

anonymous · Answer

@amistre64  i did not undersand. You mean to be 1100?

amistre64 · Answer

1068 ... but yes

the Error in the confidence interval seems to be such that it is not more than a .06 span from end to end.  E = .03 in that case

n = .25*(1.96/.03)^2  would be my best guess

anonymous · Answer

1068?  my calculator says 1067.1  ;p  i will try agian later i must leave thank you a lot

amistre64 · Answer

since people are considered not to be divisible .... rnding up to 1068 is perfered

anonymous · Answer

@amistre64  You are absolutely correct.  Thank you!!