11-25. Two soda vending machines in two separate wings of an office building are tested monthly for average fill. Each machine is set to dispense 8 oz. of soda. On a particular day a service technician obtains the following results (in ounces):
Machine 1 8.5 8.1 8.3 8.7 8.4 8.5 Machine 2 8.2 7.9 8.1 8.0 7.7 Find a 90% confidence interval for the mean difference in the amount that each machine dispenses. First assume that it is known that σ2 1 = σ2 2 = σ2. If this assumption cannot be legitimately made, recalculate the said interval.