Confidence Interval for a Single Mean

Example 7: Dark Chocolate for Good Health

Eleven people were given 46 grams (1.6 ounces) of dark chocolate every day for two weeks, and their vascular health was measured before and after the two weeks. Larger numbers indicate greater vascular health, and the mean increase for the participants was 1.3 with a standard deviation of 2.32. Assume a dotplot shows the data are reasonably symmetric with no extreme values. Find and interpret a 90% confidence interval for the mean increase in this measure of vascular health after two weeks of eating dark chocolate.   Can we be 90% confident that the mean change for everyone would be positive? Use t* = 1.812

Example 8: Sample Size and Margin of Error for Dark Chocolate

(a) What is the margin of error for the confidence interval found in Example 7?

(b) What sample size is needed if we want a margin of error within ±0.5, with 90% confidence? (Use the standard deviation from the original sample to estimate σ.)

Confidence Interval for a Single Proportion

Example 2: Movie Goers are More Likely to Watch at Home

In a random sample of 500 movie goers in January 2013, 320 of them said they are more likely to wait and watch a new movie in the comfort of their own home. Find and interpret a 95% confidence interval for the proportion of movie goers who are more likely to watch a new movie from home.

Example 3: Sample Size and Margin of Error for Movie Goers

(a) What is the margin of error for the confidence interval found in Example 2?

(b) What sample size is needed if we want a margin of error within ±2%? (Use the sample proportion from the original sample.)

(c) What sample size is needed if we want a margin of error within ±2%, and if we use the conservative estimate of p = 0.5?