Losing weight A Gallup Poll in November 2008 found that 59%...

Losing weight A Gallup Poll in November 2008 found that 59% of the people in its sample said “Yes” when asked, “Would you like to lose weight?” Gallup announced: “For results based on the total sample of national adults, one can say with 95% confidence that the margin of (sampling) error is $\pm 3$ percentage points." the margin of (sampling) error is $\pm 3$ percentage points." (a) Explain what the margin of error means in this setting. (b) State and interpret the 95% confidence interval. (c) Interpret the confidence level.

Losing weight A Gallup Poll in November 2008 found that 59% of the people in its sample said “Yes”
when asked, “Would you like to lose weight?” Gallup announced: “For results based on the total sample of national adults, one can say with 95% confidence that the margin of (sampling) error is $\pm 3$ percentage points." the margin of (sampling) error is $\pm 3$ percentage points."
(a) Explain what the margin of error means in this setting.
(b) State and interpret the 95% confidence interval.
(c) Interpret the confidence level.

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Key Concepts

Margin of Error

The margin of error quantifies the range in which the true population parameter is expected to lie based on the sample estimate. It represents the maximum expected difference between the sample statistic (e.g., the proportion of people wishing to lose weight) and the actual population value due to sampling variability.

Confidence Interval

A confidence interval is a range of values derived from the sample data that, according to the confidence level, is believed to contain the true population parameter. In this context, the interval is built around the sample proportion (59%) and extends by the margin of error on both sides, providing a set range where the true proportion is likely to be found.

Confidence Level

The confidence level indicates the degree of certainty associated with the confidence interval. A 95% confidence level means that if the same sampling procedure were repeated many times, approximately 95% of the calculated confidence intervals would be expected to contain the true population parameter.

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