True or False? The margin of error is one-third the width of the confidence interval.

True or False? A researcher wants to estimate the impact prenatal care during pregnancy can have on premature deliveries by conducting a retrospective case-control study on new moms. If the prevalence of premature births is approximately 10.9%, the researcher should enroll a total of 586 women in the study if the researcher wants to construct a 90% confidence interval for the difference in proportions that has a margin of error of no more than 3%.   Please how do i solve the math?

Nielsen ratings are based on televisions in 7000 households. Nielsen estimates that 19,000 people live in these households. Suppose Nielsen reports that American Idol had 75% of the TV audience. Interpret this result with a 95% confidence interval, based on a sample size of 19,000 people. Margin of error = 0.7 % (Round to one decimal place as needed.) Confidence interval is from % to %.

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