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A random sample of Oak County residents was selected and asked, "To attract new employment to our area, are you in favor of giving incentives to industries that build plants that are environmentally friendly?" A 90 percent confidence interval for the proportion of residents in favor of the incentives was found to be 0.62 ± 0.06. Which statement is true?

User Khalik
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Final answer:

The correct interpretation of the given 90 percent confidence interval is that if many samples were taken and the procedure was repeated, about 90 percent of such confidence intervals would contain the true population proportion of residents in favor of giving incentives to industries for building environmentally friendly plants.

Step-by-step explanation:

The statement 'A 90 percent confidence interval for the proportion of residents in favor of the incentives was found to be 0.62 ± 0.06' means that we are 90 percent confident that the true proportion of Oak County residents who are in favor of giving incentives to industries for building environmentally friendly plants is between 0.56 and 0.68 (0.62 - 0.06 and 0.62 + 0.06).

The true statement related to this confidence interval is that if we were to take many samples and build a confidence interval for each sample, then approximately 90 percent of these intervals would contain the true population proportion of residents in favor of the incentives. This does not guarantee that the particular interval from this sample definitely includes the true proportion; rather, it is a statement about the reliability of the interval construction process over many repetitions.

User Novae
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