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 total volume of recycling over a 10-week period was measured for each of the households. The average total volumes were 382 and 415 gallons for the households with the 60- and 75-gallon bins, respectively. The sample standard deviations were 52.5 and 43.8 gallons, respectively. Assume that the 10-week total volumes of recycling are approximately normally distributed for both groups and that the population standard deviations are 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 volume of all households that have 75-gallon containers?