Use the one-proportion plusfour z-interval procedure, as...

Use the one-proportion plusfour z-interval procedure, as discussed on page $551,$ to find the required confidence interval. Interpret your results. In the May 2008 New York Times article "More Mothers Breast-Feed, in First Months at Least," G. Harris reported that $77 \%$ of new mothers breast-feed their infants at least briefly, the highest rate seen in the United States in more than a decade. His report was based on data for 434 infants from the National Health and Nutrition Examination Survey, which involved in-person interviews and physical examinations. Find a $90 \%$ confidence interval for the percentage of all new mothers who breast-feed their infants at least briefly.

Use the one-proportion plusfour z-interval procedure, as discussed on page $551,$ to find the required confidence interval. Interpret your results.
In the May 2008 New York Times article "More Mothers Breast-Feed, in First Months at Least,"
G. Harris reported that $77 \%$ of new mothers breast-feed their infants at least briefly, the highest rate seen in the United States in more than a decade. His report was based on data for 434 infants from the National Health and Nutrition Examination Survey, which involved in-person interviews and physical examinations. Find a $90 \%$ confidence interval for the percentage of all new mothers who breast-feed their infants at least briefly.

Key Concepts

One-Proportion Z-Interval

This procedure is used in statistical inference to estimate a population proportion based on sample data. It relies on the normal approximation to the binomial distribution when the sample size is sufficiently large, and it provides a method to construct confidence intervals for proportions.

Plus-Four Method

The plus-four method is a correction used in constructing confidence intervals for proportions, particularly when sample sizes are small or moderate. It involves adding two successes and two failures to the data before calculating the interval, which results in more accurate estimates by reducing bias and improving coverage probability.

Confidence Interval

A confidence interval is a range of values derived from sample data that is likely to contain the true population parameter. The confidence level, such as 90%, indicates that if many samples were taken, approximately 90% of the intervals would be expected to include the true proportion.

Interpretation of the Interval

Interpreting a confidence interval involves understanding that it provides a range within which we are reasonably certain, given our chosen level of confidence, that the true population parameter lies. This does not mean there is a 90% probability that the interval contains the true value; rather, it indicates the long-run success rate of the interval estimation method.

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