## Confidence Interval for Difference of Two Means Exercise

1. A sample of 40 pine trees grown on the north side of a hill has a mean of 25.4 metres and a standard deviation of 2.1 metres.

A second sample of 40 trees from the south side has a mean of 23.2 metres and a standard deviation of 1.7 metres.

Find the 95% confidence interval for the difference in the mean heights of the two populations of trees.

2. Below are summary statistics for data sets of the tar content of two brands of cigarettes.

 Sample size Sample mean (mg) Sample standard deviation (mg) Brand A 30 4.716 0.0824 Brand B 30 4.675 0.1200

a. Find a 95% confidence interval for the difference between the two brand means μA and μB.

b. It is claimed that there is no difference between the mean tar content of Brand A (μA) and the mean tar content of Brand B (μB). Do the random samples give us evidence against this claim? Using the 95% confidence interval from part a., justify your answer.

c. Assuming that there is no difference between the mean tar content of Brand A (μA) and the mean tar content of Brand B (μB), calculate the probability of obtaining a difference between the sample means at least as large as that obtained for the random samples above.

d. Explain how the probability calculated in part c. can be used to determine whether these random samples give us evidence against the claim of no difference between the mean tar content levels for the two brands.

3. The life expectancy of people in two different countries is surveyed. Two samples of 80 people were taken in each country.

In country A, the mean life expectancy was found to be 66.2 years with a standard deviation of 7.3 years. In country B, the mean life expectancy was found to be 71.9 years with a standard deviation of 8.3 years.

a. Find a 90% confidence interval for the difference between the mean life expectancy of the two countries.

b. State any assumptions made when constructing these confidence intervals.

c. Does the confidence interval from part a. suggest that there is a significant difference in life expectancy between the two countries? Justify your answer.