Nuclear power, and coal power with carbon sequestration, are two options for gen
ID: 3055150 • Letter: N
Question
Nuclear power, and coal power with carbon sequestration, are two options for generating electricity without emitting CO2 to the atmosphere. A sample of 870 people found that 47% of people supported the construction of a new nuclear power plant for their city.
A) Determine the 95%, two-sided confidence interval for the fraction of people who support a new nuclear power plant.
B) You would like to determine public opinion about a potential carbon sequestration facility for the city. What sample size is needed for you to be at least 90% confident that the estimate is within 0.03 of the true proportion of residents who support the construction of the facility?
C) Now you want to advocate the carbon sequestration facility's construction over the nuclear power plant. Suppose that you sample 1098 people and find that 552 support the construction of the carbon sequestraton facility. What is the best estimate of the difference between the fraction that support CO2 sequestration and the fraction that support nuclear power?
D) What is the 95%, one-sided lower confidence interval between the fraction that support CO2 sequestration and the fraction that support nuclear power? Is the statement, "More people support coal power with CO2 sequestration than nuclear power" true?
Please show all work, and I'll give the thumbs up for a correct answer. Thanks.
Explanation / Answer
Given that,
sample size (n) = 870
sample proportion (p^) = 47% = 0.47
A) Determine the 95%, two-sided confidence interval for the fraction of people who support a new nuclear power plant.
95% confidence interval for p^ is,
p^ - E < p < p^ + E
where E is margin of error.
E = Zc * sqrt [p^ * (1-p^) / n ]
Zc is the critical value for normal distribution.
Zc we can find in excel.
syntax :
=NORMSINV(probability)
where probability = 1 - a/2
where a = 1 - C
C is confidence level = 95%
Zc = 1.96
E = 1.96 * sqrt[ 0.47*(1-0.47) / 870] = 1.96 * 0.017 = 0.033
95% confidence interval for p is,
0.47-0.033 < p < 0.47+0.033
95% confidence interval for p is (0.437, 0.503)
B) You would like to determine public opinion about a potential carbon sequestration facility for the city. What sample size is needed for you to be at least 90% confident that the estimate is within 0.03 of the true proportion of residents who support the construction of the facility?
Here we have to find sample size when c = 90% = 0.90 and E = 0.03
The formula for sample size is,
n = p*(1-p) * (Zc / E)^2
Zc = 1.645
n = 0.47* (1-0.47) * (1.645 / 0.03)^2 = 748.83 or approximately equal to 749.
C) Now you want to advocate the carbon sequestration facility's construction over the nuclear power plant. Suppose that you sample 1098 people and find that 552 support the construction of the carbon sequestraton facility. What is the best estimate of the difference between the fraction that support CO2 sequestration and the fraction that support nuclear power?
The estimate of the difference between the fraction that support CO2 sequestration and the fraction that support nuclear power is p1^ - p2^ .
where p1^ = 552 / 1098 = 0.50
p2^ = 0.47
p1^-p2^ = 0.50 - 0.47 = 0.03
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