Confidence Interval: Basics

1. A Gallup Poll in November 2014 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 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.

2. The admissions director from Florida International University found that (107.8, 116.2) is a 95% confidence interval for the mean IQ score of all freshmen. Comment on whether or not each of the following explanations is correct.

(a) There is a 95% probability that the interval from 107.8 to 116.2 contains . (b) There is a 95% chance that the interval (107.8, 116.2) contains X.

(c) This interval was constructed using a method that produces intervals that capture the true mean in 95% of all possible samples.

(d) 95% of all possible samples will contain the interval (107.8, 116.2).

(e) The probability that the interval (107.8, 116.2) captures is either 0 or 1, but we don't know which.

3. How do Confidence Intervals Change... (a) How does the shape of the confidence interval change if the confidence level increases from 90% to

95%?

(b) How would the shape of a confidence change if the sample size was decreased? Assume the new, smaller sample size still meets all of the normality conditions.