a construct a 90 confidence interval from country A bfrom co

The table to the right shows the results of a survey in Which 2573 adults from Country A, 1115 adults from Country B, and 1075 adults from Country C were asked if human activity contributes to global warming. Complete pails (a), (b), and (c). (a) Construct a 90% confidence interval for the proportion of adults from Country A who say human activity contributes to global warming.

Solution

The formula for a confidence interval for a population proportion:

Phat +/- z*sqrt (phat*(1-phat)/n

The z score you use for a 90% confidence interval is 1.645.

a. 90% confidence interval for country a:

phat = .67, n = 2573

.67 +/- 1.645*sqrt (.67*(1-.67)/2573)

.67 +/- .015

Lower limit: .67 - .015 = 0.655

Upper limit: .67 + .015 = 0.685

90% confidence interval for country A: (0.655, 0.685)

b. 90% confidence interval for country b:

phat = .86, n = 1115

.86 +/- 1.645*sqrt (.86*(1-.86)/1115)

.86 +/- .017

Lower limit: .86 - .017 = 0.843

Upper limit: .86 + .017 = 0.877

90% confidence interval for country B: (0.843, 0.877)

c. 90% confidence interval for country c:

phat = .94, n = 1075

.94 +/- 1.645*sqrt (.94*(1-.94)/1075)

.94 +/- .012

Lower limit: .94 - .012 = 0.928

Upper limit: .94 + .012 = 0.952

90% confidence interval for country C: (0.928, 0.952)