Question

A survey showed that 720 of the 1000 adult respondents believe in global warming. (a) Construct a 90% confidence interval estimate of the proportion of adults believing in global warming. (Round the lower bound and upper bound of the confidence interval to three decimal places) Include description of how confidence interval was constructed. (b) Describe the results of the survey in everyday language.

Answer 1

a)

Sample proportion = 720 / 1000 = 0.72

90% confidence interval for p is

- Z/2 * sqrt( ( 1 - ) / n) < p < + Z/2 * sqrt( ( 1 - ) / n)

0.72 - 1.645 * sqrt( 0.72 * 0.28 / 1000) < p < 0.72 + 1.645 * sqrt( 0.72 * 0.28 / 1000)

0.697 < p < 0.743

The 90% CI is (0.697 , 0.743)

b)

We are 90% confident that the true proportion of adult respondents believe in global warming is

between 0.697 and 0.743.