Question

Carl Cornfield has been wondering whether he should plant white corn this year. He decides to sample 100 customers. 38% say they would purchase white corn. Carl wants to have a 95% confidence interval for this proportion. The confidence interval is from 33% to 43% (to the nearest percent). Truth Or False

Answer 1

The answer is false

This should be the interval:

.285 to .475

Hope this helps

-AaronWiseIsBae

Answer 2

Answer is false

Here sample size = 100

Sample propotion = 38%

i.e. p =0.38 and q = 1-p =0.62

p follows a normal with mean = 0.38 and std error = $\sqrt{}\frac{pq}{n} =0.0485$

For 95% z value = 1.96

Hence margin of error = 1.96 (std error) = 0.0951

Confidence interval = (0.38-0.0951, 0.38+0.0951)

=(0.2949, 0.4751)

= (29.49%, 47.51%)

Hence given confidence interval is from 33% to 43% (to the nearest percent).

False