Question

In the 2008 General Society Survey, people were asked their opinions on astrology – whether it was very scientific, somewhat scientific, or not at all scientific. Of 1438 who responded, 84 said astrology was very scientific.

1. Find a 99% confidence interval for the population proportion of all people with this belief.
2. Suppose a TV news anchor said that 5% of people in the general population think astrology is very scientific. Would you say that it is plausible? Explain your answer.

Answer 1

Given In the 2008 General Society Survey, people were asked their opinions on astrology – whether it was very scientific, somewhat scientific, or not at all scientific. Of n = 1438 who responded, X = 84 said astrology was very scientific.

a) Hence a 99% confidence interval for the population proportion of all people with this belief is calculated as:

Where the sample proportion is calculated as:

and the critical score at 99% confidence level is calculated using the excel formula for normal distribution which is =NORM.S.INV(0.995), thus the Zc is computed as 2.576.

Now the confidence interval at 995 confidence level is computed as:

b) Given that a TV news anchor said that 5% of people in the general population think astrology is very scientific, thus the percentage is transformed to proportion as 5/100 = 0.05.

As we can see from the confidence interval that 0.05 can be inside the 99% confidence level hence you say that it is plausible.