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 1440 who​ responded, 71 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.

Answer 1

a)

Sample proportion = 71 / 1440 = 0.049

b)

Margin of error = Z/2 * sqrt [ ( 1 - ) / n ]

= 1.96 * sqrt [ 0.049 * ( 1 - 0.049) / 1440 ]

= 0.011

95% confidence interval for p

- E < p < + E

0.049 - 0.011 < p < 0.049 + 0.011

0.038 < p < 0.060

95% CI is ( 0.038 , 0.060 )

c)

Since 0.05 contained in confidence interval, it is plausible.