# 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
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:

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:

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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