Question

In a 2008​ survey, people were asked their opinions on astrology​ - whether it was very​ scientific, somewhat​ scientific, or not at all scientific. Of 1436 who​ responded,71 said astrology was very scientific.

a. Find the proportion of people in the survey who believe astrology is very scientific. Answer ______ (Round to four decimal places as needed)

b. Find a​ 95% confidence interval for the population proportion with this belief. Answer (____, and _____)

c. Suppose a TV news anchor said that​ 5% of people in the general population think astrology is very scientific. Would you say that is​ plausible? Which one is correct?

Choose the correct answer below A,B,C or D Answer ______

A.This is not plausible because​ 5% is outside the interval.

B.This is not plausible because​ 5% is inside the interval.

C.This is plausible because​ 5% is inside the interval.

D.This is plausible because​ 5% is outside the interval.

Answer 1

Solution :

Given that,

n = 1436

x = 71

a) Point estimate = sample proportion = = x / n = 71 / 1436 = 0.0494

1 - = 1 - 0.0494 = 0.9506

b) At 95% confidence level

= 1 - 95%

=1 - 0.95 =0.05

/2 = 0.025

Z/2 = Z0.025 = 1.960

Margin of error = E = Z / 2 * (( * (1 - )) / n)

= 1.96 (((0.0494 * 0.9506) / 1436)

= 0.0112

A 95% confidence interval for population proportion p is ,

± E

= 0.0494   ± 0.0112

= ( 0.0382, 0.0606 )

c) C.This is plausible because​ 5% is inside the interval.