In a poll of 1,004 adults,934 indicated that restaurants and bars should refuse service to patrons who have had too much to drink.The 90% confidence interval for the proportion of all adults who feel the same way would be _____.
A)[.078,.108]
B)[.914,.946]
C)[.920,.940]
D)[.917,.943]
E)[.910,.950]

Question

Quizplus · Accepted Answer

We can use the formula for a confidence interval for a proportion:
CI = p ± Z*sqrt((p(1-p))/n)
where p is the sample proportion, n is the sample size, and Z is the appropriate z-score for the desired confidence level. For a 90% confidence interval, Z=1.645.
Using the values given in the problem:
p = 934/1004 = 0.929
n = 1004
Z = 1.645
Plugging these values into the formula, we get:
CI = 0.929 ± 1.645*sqrt((0.929(1-0.929))/1004)
Simplifying, we get:
CI = 0.929 ± 0.015
So the 90% confidence interval is (0.914, 0.944). The closest choice is D, which has a range of (0.917, 0.943), so D is the best choice.

In a Poll of 1,004 Adults,934 Indicated That Restaurants and Bars