33. Consider the pooled t variable which has a t distribution with m  n  2 df when both population distributions are normal with s1 

s2 (see the Pooled t Procedures subsection for a description of Sp).

a. Use this t variable to obtain a pooled t con dence interval formula for m1  m2.

b. A sample of ultrasonic humidi ers 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 the second brand gave output values 12.1, 13.6, 11.9, and 11.2 ( Multiple Comparisons of Means Using Simultaneous Con dence Intervals, J. Qual. Techn., 1989: 232—241). Use the pooled t formula from part

(a) to estimate the difference between true average outputs for the two brands with a 95%
con dence interval.

c. Estimate the difference between the two m s using the two-sample t interval discussed in this section, and compare it to the interval of part (b).