Question

10 Yeartage aroup. Use critical policies In a certain region, 17% of people over age 50 didn't graduate from high school. We would like to know if this percentage is the same among the 25- 30 year age group. Use critical values to exactly 3 decimal places. (a) How many 25-30 year old people should be surveyed in order to estimate the proportion of non-grads to within 9% with 98% confidence? (b) Suppose we wanted to cut the margin of error to 3%. How many people should be sampled now? (c) What sample size is required for a margin of error of 10%?

Answer 1

given that

p=0.17

a)

the margin of error =E=0.09

confidence level =98%

now margin of error is given by

$E=Z_{0.01}*\sqrt{\frac{p(1-p)}{n}}=2.326*\sqrt{\frac{0.17*(1-0.17)}{n}}=0.09\Rightarrow n=(\frac{2.326}{0.09})^2 *0.17*0.83=94.246$

b)

margin of error=E=0.03

now margin of error is given by

$E=Z_{0.01}*\sqrt{\frac{p(1-p)}{n}}=2.326*\sqrt{\frac{0.17*(1-0.17)}{n}}=0.03\Rightarrow n=(\frac{2.326}{0.03})^2 *0.17*0.83=848.211$

c)

Margin of error =E=0.1

now

$E=Z_{0.01}*\sqrt{\frac{p(1-p)}{n}}=2.326*\sqrt{\frac{0.17*(1-0.17)}{n}}=0.1\Rightarrow n=(\frac{2.326}{0.1})^2 *0.17*0.83=76.339$