The town of Charlotte recently started a single-stream recyclingprogram. The town provided 60-gallon recycling bins to 25 randomlyselected households and 75-gallon recycling bins to 22 randomlyselected households. The total volume of recycling over a 10-weekperiod was measured for each of the households. The average totalvolumes were 382 and 415 gallons for the households with the 60-and 75-gallon bins, respectively. The sample standard deviationswere 52.5 and 43.8 gallons, respectively. Assume that the 10-weektotal volumes of recycling are approximately normally distributedfor both groups and that the population standard deviations areequal. Using a test statistic of -2.321 and a 2% significancelevel, can you conclude that the average 10-week recycling volumeof all households having 60-gallon containers is different from theaverage volume of all households that have 75-galloncontainers?

Then reconsider the town of Charlotte's recycling program. If weassume that the population standard deviations are different, wewill have a test statistic of -2.348. We will also now have 44degrees of freedom. Re-test the hypothesis given thesecalculations.

These are sample two population t-tests. Please show ALL thework up to the answers.