1. Many people consider themselves “green”, meaning they are supportive (in theo
ID: 3358073 • Letter: 1
Question
1. Many people consider themselves “green”, meaning they are supportive (in theory) when it comes to environmental issues. But, how do they act in practice? For instance, Americans’ per capita use of energy is roughly double that of Western Europeans. If you live in North America, would you be willing to pay the same price for gas that Europeans do (often about $6 or more per gallon), if the government proposed a significant price hike as an incentive for conservation and for driving more fuel-efficient cars to reduce air pollution and its impact on global warning?
In 2000, the General Social Survey asked subjects if they would be willing to pay much higher prices in order to protect the environment. Of n=1154 respondents, 518 indicated a willingness to do so. That is, the sample proportion p= 518/1154= 0.4489.
a) [10pts] Find a 95% confidence interval for the population proportion of adult Americans willing to do so at the time of that survey.
b) [10pts] Interpret the interval.
c) [10pts] Suppose the survey result of p=0.4489 had resulted from a sample of size n=288.
Calculate the 95% confidence interval for this sample size. Assess the effects of sample size on the interval.
Explanation / Answer
a) here std error =(p(1-p)/n)1/2 where n=1154
=0.0146
for 95% confidence interval ; crtiical value of z =1.96
therefore 95% confidence interval for the population proportion=sample proportion -/= z*Std error
=0.4489 -/+ 0.0146*1.96 =0.4202 to 0.4776
b) above interval provide 95% confidence to contain true population proportion of adult Americans willing to pay much higher prices in order to protect the environment..
c)
std error =(p(1-p)/n)1/2 where n=288
=0.0293
for 95% confidence interval ; crtiical value of z =1.96
therefore 95% confidence interval for the population proportion=sample proportion -/= z*Std error
=0.4489 -/+ 0.0293*1.96 =0.3914 to 0.5063
we can see that decreasing the sample size increase the width of confidence interval due to increase in standard error of sample proportion
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