Consider the pooled t variable which has a t distribution with m = n - 2 df when both population distributions are normal with Ï1

Consider the pooled t variable

which has a t distribution with m = n - 2 df when both population distributions are normal with σ1 = σ2 (see the Pooled t Procedures subsection for a description of Sp).
a. Use this t variable to obtain a pooled t confidence interval formula for µ1-µ2
b. 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 the second brand gave output values 12.1, 13.6, 1 9, and 11.2 ("Multiple Comparisons of Means Using Simultaneous Confidence Intervals," J. of Quality Technology, 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% confidence interval.
c. Estimate the difference between the two µ's using the two-sample t interval discussed in this section, and compare it to the interval of part (b).

- (, ) - T=