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10.15 National public opinion polls are often based on as few as 1,500 persons in a randomsampling of public sentiment on issues of public interest. These surveys are often done in personbecause the response rate for a mailed survey is very low and telephone interviews tend to reach alarger proportion of older persons than would be represented in the public as a whole. Suppose arandom sample of 1,500 registered voters was surveyed about energy issues.a. If 230 of the 1,500 responded that they would favor drilling for oil in nationalparks, estimate the proportion r of registered voters who would favor drilling foroil in national parks. Use a 95% confidence intervalb. How many persons must the survey include to have 95% confidence that the sam-ple proportion is within.01 of r?c. A congressman has claimed that over half of all registered voters would supportdrilling in national parks. Use the survey data to evaluate the congressman's claim.Use α .05.

Question
10.15 National public opinion polls are often based on as few as 1,500 persons in a random
sampling of public sentiment on issues of public interest. These surveys are often done in person
because the response rate for a mailed survey is very low and telephone interviews tend to reach a
larger proportion of older persons than would be represented in the public as a whole. Suppose a
random sample of 1,500 registered voters was surveyed about energy issues.
a. If 230 of the 1,500 responded that they would favor drilling for oil in national
parks, estimate the proportion r of registered voters who would favor drilling for
oil in national parks. Use a 95% confidence interval
b. How many persons must the survey include to have 95% confidence that the sam-
ple proportion is within.01 of r?
c. A congressman has claimed that over half of all registered voters would support
drilling in national parks. Use the survey data to evaluate the congressman's claim.
Use α .05.
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10.15 National public opinion polls are often based on as few as 1,500 persons in a random sampling of public sentiment on issues of public interest. These surveys are often done in person because the response rate for a mailed survey is very low and telephone interviews tend to reach a larger proportion of older persons than would be represented in the public as a whole. Suppose a random sample of 1,500 registered voters was surveyed about energy issues. a. If 230 of the 1,500 responded that they would favor drilling for oil in national parks, estimate the proportion r of registered voters who would favor drilling for oil in national parks. Use a 95% confidence interval b. How many persons must the survey include to have 95% confidence that the sam- ple proportion is within.01 of r? c. A congressman has claimed that over half of all registered voters would support drilling in national parks. Use the survey data to evaluate the congressman's claim. Use α .05.

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Step 1

a.

Confidence Interval:

The form of the confidence interval is,

CI = Point estimate ± Margin of error

The approximate 100*(1–α)% confidence interval for the population proportion will be obtained using the formula given below:

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Step 2

Obtain the sample proportion of registered voters who favor drilling for oil in national parks:

It is given that among a sample of 1,500 registered voters in a opinion poll, 230 registered voters responded that they would favor drilling for oil in national parks.

The sample size is n = 1,500.

The number of specified characteristics is x = 230.

The sample proportion of registered voters who favor drilling for oil in national parks is obtained as 0.1533 from the calculation given below:

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Step 3

Obtain the critical value:

The given confidence level is 100*(1–α)% = 95%.

From this, the level of significance value is α = 0.05.

The critical value corres...

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