Question

n a 2008​ survey, people were asked their opinions on astrology​ - whether it was very​ scientific, somewhat​ scientific, or not at all scientific. Of 1438 who​ responded, 76 said astrology was very scientific. a. Find the proportion of people in the survey who believe astrology is very scientific. b. Find a​ 95% confidence interval for the population proportion with this belief. 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? Explain your answer. a. The proportion of people in the survey who believe astrology is very scientific is . 0529. ​(Round to four decimal places as​ needed.) b. Construct the​ 95% confidence interval for the population proportion with the belief that astrology is very scientific. left parenthesis nothing comma nothing right parenthesis ​(Round to three decimal places as​ needed.) Enter your answer in the edit fields and then click Check Answer.

Answer 1

x                    =				76
sample size		n                    =		1438.0
sample proportion     p̂		x/n=		0.0529
std error       =Se		=√(p*(1-p)/n) =		0.0059
for 95 % CI value of z=				1.96
margin of error E=z*std error                            =				0.0116
lower confidence bound=sample proportion-margin of error				0.0413
Upper confidence bound=sample proportion+margin of error				0.0645

a)

   proportion of people in the survey who believe astrology is very scientific =0.0529

b)

95% confidence interval for the population proportion =0.041 , 0.064

c)

Yes as 5% falls within confidence interval