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Sample size and confidence interval for proportion

The Star Tribune, a Min.-St. Paul newspaper sponsored a poll designed to reveal opinions about the "photocop" which consist of cameras positioned to catch drivers who run red lights. The cameras photograph the license plates of cars passing through red lights, and those car owners are later mailed traffic violations. The newspaper sponsored the poll because of pending Min. legislation that would approve the use of cameras for issuing traffic violations. Pollsters surveyed 829 adult Minnesotans and found that 51% were opposed to the photo-cop legislation.

ANALYZING THE DATA

1. Use the survey results to construct a 95% confidence interval estimate of the percentage of all Minnesotans opposed to a photo-cop legislation.

2.Given that 51% of the 829 Minnesotans surveyed were opposed to the photo-cop legislation,explain why it would or would not be okay for a newspaper to make this statement: "Based on results from recent survey,the majority of Minnesotans are opposed to the photo-cop legislation.

3.A common criticism of surveys is that they poll only a very small percentage of the population and therefore cannot be accurate. Is a sample of only 829 people taken from a population of 3.4 million adult Minnesotans a sample size that is too small?Write an explanation of why the sample size is of 829 is or is not too small.

4.In reference to another survey,the president of a company wrote to the associate press about a nation wide survey of 1223 subjects.

The writer of that letter then proceeds to claim that because the sample size of 1223 people represents 120 million people, his single letter represents 98,000 (120 million divided by 1223) who share the same views.

Solution Preview

Please see the attached file.

1. The 95% CI proportion is given by .Given n =829 , p =0.51
[0.47624, 0.5442823] . Margin of error E = = 0.034029. Thus 95% confidence interval estimate of the percentage of all Minnesotans opposed ...

Solution Summary

The solution gives step by step procedure with formula for the calculation of sample size and confidence interval for population proportion.

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