Question

1,600 college freshmen were randomly selected for a national survey. Among survey participants, the mean grade-point average (GPA) was 3 , and the margin of error was 0.0343% for the 95% confidence interval. If we want to get a 85% confidence interval with a small margin of error 15%. How many students do you need to select? Remember that our answer is about actual people -- to answer this question you must round your number up to the nearest whole number (if you need 100.1 people, you really need 101 people). symbolic expression

Answer 1

Answer:

Given,

n = 1600

E = +/- 0.0343%

Here for 95% confidence interval , z value is 1.96

Now consider,

n = (z*s/E)^2

from this,

E = z*s/sqrt(n)

substitute values

0.000343 = 1.96*s/sqrt(1600)

0.000343 = 1.96*s/40

s = 0.000343*40 / 1.96

s = 0.007

Now to give the sample size for 85% confidence interval & E = 0.05

consider,

n = (z*s/E)^2

Here for 85% confidence interval , z value is 1.44

n = (1.44*0.007 / 0.05)^2

= 0.04064

= 4*10^-2