Question

What do Americans do to conserve energy? The Associated Press-NORC Center for Public Affairs Research conducted a survey of 897 adults who had personally done something to try to save energy in the last year, and found the following percentages: Turn off lights: 39% Turn down heat: 26% Install more energy-saving appliances: 23% Drive less/walk more/bicycle more: 18% Unplug things: 16%

A) Construct the 95% confidence interval estimate for the proportion of Americans who turn off lights to conserve energy?

B) what conclusions can you reach concerning what adults do to conserve energy?

Answer 1

Solution:

Part A)

Confidence interval for Population Proportion is given as below:

Confidence Interval = P ± Z* sqrt(P*(1 – P)/n)

Where, P is the sample proportion, Z is critical value, and n is sample size.

We are given

P = 0.39

n = 897

Confidence level = 95%

Z = 1.96

(by using z-table)

Confidence Interval = P ± Z* sqrt(P*(1 – P)/n)

Confidence Interval = 0.39 ± 1.96* sqrt(0.39*(1 – 0.39)/897)

Confidence Interval = 0.39 ± 1.96* 0.0163

Confidence Interval = 0.39 ± 0.0319

Lower limit = 0.39 - 0.0319 = 0.3581

Upper limit = 0.39 + 0.0319 = 0.4219

Confidence interval = (0.3581, 0.4219)

Part B)

We are 95% confident that the population proportion of Americans who turn off lights to conserve energy will lies within 35.81% to 42.19%.