Question

Does anyone still believe the earth is flat? To answer this, a random sample of 55 U.S. adults were asked if they believe the earth is flat. Based on the results of the survey, a 95% confidence interval is (0.124, 0.348).

(a) What is the estimate of the proportion of all U.S. adults that believe the earth is flat?  

(b) Interpret the confidence interval:

We are 95% confident the proportion of all U.S. adults that believe the earth is flat is between 0.124 and 0.348.We are 95% confident that of the 55 people sampled, the proportion that believe the earth is flat falls in the above interval.    We are 95% confident that the percent of U.S. adults that believe the earth is flat is 23.6%.We are 95% confident the proportion of all U.S. adults in the sample that believe the earth is flat is between 0.124 and 0.348.

(c) A follow-up study is being considered. Using the proportion from this sample as an estimate, how many U.S. adults need to be sampled in order to be 95% confident the sample proportion is within 5% of the true proportion?

Answer 1

(a)

Estimate of proportion = is given by:

So,

Answer is:

0.236

(b)

Correct option:

We are 95% confident that the proportion of all U.S. adults that believe the earth is flat is between 0.124 and 0.348.

(c)

Number of U.S. adults needed to be sampled (n) is given by:

Given:

= 0.05

From Table critical values of Z = 1.96

p = 0.236

e = 0.05

Substituting, we get:

So,

Answer is:

278