As mentioned in Exercise 10.26, a town that recently started a single-stream recycling program provided 60-gallon recycling bins to 25 randomly selected households and 75-gallon recycling bins to 22 randomly selected households. The average total volumes of recycling over a 10-week period were 382 and 415 gallons for the two groups, respectively, with standard deviations of 52.5 and 43.8 gallons, respectively. Suppose that the standard deviations for the two populations are not equal.
a. Construct a 98% confidence interval for the difference in the mean volumes of 10-week recycling for the households with the 60- and 75-gallon bins.
b. Using a 2% significance level, can you conclude that the average 10-week recycling volume of all households having 60-gallon containers is different from the average 10-week recycling volume of all households that have 75-gallon containers?
c. Suppose that the sample standard deviations were 59.3 and 33.8 gallons, respectively. Redo parts a and b. Discuss any changes in the results.