A sample of ultrasonic humidifiers of one particular brand was selected for which the observations on maximum output of moisture (oz) in a controlled chamber were 14.0, 14.3, 12.2, and 15.1. A sample of a second brand gave output values 12.1, 13.6, 11.9, and 11.2 ("Multiple Comparisons of Means Using Simultaneous Confidence Intervals", J. Qual. Techn., 1989). Assume that both brands have maximum moisture distributions with equal variances. (a) Is there a difference in mean maximum output of moisture between the two brands? Set up the relevant hypotheses and test at the a = .05 level, using the pooled procedure. Make sure to interpret your results in the context of the problem.
(b) Construct and interpret a 95% confidence interval to support your decision from (a).