The table to the fight shows the results of a survey in which 2569 adults from C

Question

The table to the fight shows the results of a survey in which 2569 adults from Country A 1125 adults from Country B and 1057 adults from Country C were asked if human activity contributes to global warming Complete parts (a), (D) and (c). (a) Construct a 95% confidence interval for the proportion of adults from Country A who say human activity contributes to global warming. (Round to three decimal places as needed) (b) Construct a 95% confidence interval for the proportion of adults from Country B who say human activity contributes to global warming. (Round to three decimal places as needed) (c) Construct a 95% confidence interval for the proportion of adults from Country C who say human activity contributes to global warming. (Round to three decimal places as needed.)

Explanation / Answer

(a)

n = 2569    

p = 0.63    

% = 95    

Standard Error, SE = {p(1 - p)/n} =    (0.63(1 - 0.63))/2569 = 0.009525529

z- score = 1.959963985    

Width of the confidence interval = z * SE =     1.95996398454005 * 0.00952552858495991 = 0.01866969

Lower Limit of the confidence interval = P - width =     0.63 - 0.0186696929602282 = 0.61133031

Upper Limit of the confidence interval = P + width =     0.63 + 0.0186696929602282 = 0.64866969

The 95% confidence interval is [0.611, 0.649]

(b)

n = 1125    

p = 0.89    

% = 95    

Standard Error, SE = {p(1 - p)/n} =    (0.89(1 - 0.89))/1125 = 0.00932857

z- score = 1.959963985    

Width of the confidence interval = z * SE =     1.95996398454005 * 0.00932857021317963 = 0.01828366

Lower Limit of the confidence interval = P - width =     0.89 - 0.0182836616450852 = 0.87171634

Upper Limit of the confidence interval = P + width =     0.89 + 0.0182836616450852 = 0.90828366

The 95% confidence interval is [0.872, 0.908]

(c)

n = 1057    

p = 0.95    

% = 95    

Standard Error, SE = {p(1 - p)/n} =    (0.95(1 - 0.95))/1057 = 0.006703619

z- score = 1.959963985    

Width of the confidence interval = z * SE =     1.95996398454005 * 0.00670361881399934 = 0.01313885

Lower Limit of the confidence interval = P - width =     0.95 - 0.0131388514415238 = 0.93686115

Upper Limit of the confidence interval = P + width =     0.95 + 0.0131388514415238 = 0.96313885

The 95% confidence interval is [0.937, 0.963]

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