Nuclear power, and coal power plus carbon sequestration, are two options for gen

Question

Nuclear power, and coal power plus carbon sequestration, are two options for generating electricity without emitting CO_2 to the atmosphere. (Sequestration is a method of storing CO_2 underground after it is removed from exhaust gas.) About half of the electricity generated in Illinois is produced by nuclear power. In 2011, Morgan County, Illinois was selected as the site for the FutureGen facility. FutureGen will be the first full-scale carbon sequestration project. (See: futuregenalliance. g). Both nuclear power and carbon sequestration have risks. A sample of 900 residents, conducted around Morgan County in 2008, suggests that 61% of people support construction of a new nuclear power plant. How many people stated that they supported new nuclear power? Enter your answer to the nearest integer. What is the 90% 2-sided confidence interval for the percentage of people who support a new nuclear power plant? Enter the lower bound here. Give the value as a percentage, not a fraction. Enter your answer to one decimal place (XX.X) Enter the upper bound of the 90% 2-sided confidence interval for the percentage of people who support nuclear power. Enter your answer to one decimal place (XX.X) You would like to determine public opinion about the FutureGen facility, as the risks of sequestration are not fully understood. How large a sample is needed for you to be at least 90% confident that the estimate is within 0.03 of the true proportion of residents who favor the construction of the facility? Enter your answer to the nearest integer. 5) Suppose you sample 1, 052 residents and find that 66% support the CO2 storage facility. What is the 90% lower confidence interval (one-sided) for the difference between the percentage that support CO_2 storage and the percentage that support nuclear power? Enter your answer to two decimal places (X.XX). Turn this on paper only. Comment on the statement: "More people support coal power with CO_2 sequestration than nuclear power."

Explanation / Answer

Question 1

We are given total sample size = n = 900

Sample proportion = 61%

We have to find the value X, the number of people support the construction of a new nuclear power plant.

p = X/n

So, X = n*p = 900*0.61 = 549

Required answer = 549

Question 2

Here, we have to find the lower limit for the 90% two sided confidence interval for the population proportion.

We are given p = 0.61, n = 900, c = 0.90, so Z = 1.6449 (by using z-table or excel)

Confidence interval = p -/+ Z*sqrt(p*q/n)

Where, q = 1 – p = 1 – 0.61 = 0.39

Confidence interval = 0.61 -/+ 1.6449*sqrt(0.61*0.39/900)

Confidence interval = 0.61 -/+ 1.6449*0.0163

Confidence interval = 0.61 -/+ 0.0267

Lower limit = 0.61 – 0.0267

Lower limit = 0.5833

Lower limit = 58.3%

Question 3

Upper limit = 0.61 + 0.0267

Upper limit = 0.6367

Upper limit = 63.7%

Question 4

Here, we have to find the sample size.

We are given

Confidence level = 90%

So, Z = 1.6449

p = 0.61

Margin of error = E = 0.03

q = 1 – p = 1 – 0.61 = 0.39

Sample size = n =p^2*q^2*(Z/E)^2

n = 0.61*0.39*(1.6449/0.03)^2

n = 715.2056

Required sample size = 716

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