The table to the right shows the results of a survey in whic

The table to the right shows the results of a survey in which 2565 adults from Country A 1102 adults from Country B: and 1087 adults from Country C were asked if human activity contributes to global warming. Complete parts (a), (b), and (c). Construct a 90% 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.)

ACTIVITY CONTRIBUTES GLOBAL WARMING

Country A........63%

Country B........89%

Country C........92%

Solution

A:

p = 0.63

q = 0.37

n = 2565

m = n*p = 1615.95

sd = sqrt(npq) = 24.45

P(-x<X<x) = 0.90

P(-z<Z<z) = 0.90

P(0<Z<z) = 0.45

z = 1.645

x = m +- 1.645 * sd

x = 1615.95 -1.645*24.45 to 1615.95 +1.645*24.45

x = 1575.73 to 1656.17

B.

p = 0.89

q = 0.11

n = 1102

m = n*p = 980.78

sd = sqrt(npq) = 10.38

P(-x<X<x) = 0.90

P(-z<Z<z) = 0.90

P(0<Z<z) = 0.45

z = 1.645

x = m +- 1.645 * sd

x = 980.78 -1.645*10.38 to 980.78 +1.645*10.38

x = 963.70 to 997.85

C.

p = 0.92

q = 0.08

n = 1087

m = n*p = 1000.04

sd = sqrt(npq) = 8.94

P(-x<X<x) = 0.90

P(-z<Z<z) = 0.90

P(0<Z<z) = 0.45

z = 1.645

x = m +- 1.645 * sd

x = 1000.04 -1.645*8.94 to 1000.04 +1.645*8.94

x = 1985.33 to 1014.74