Consider the pooled t variableT 5(X 2 Y) 2 (m1 2 m2)SpB1m 11nwhich has a t distribution

Chapter 9, Problem 34

(choose chapter or problem)

Consider the pooled t variableT 5(X 2 Y) 2 (m1 2 m2)SpB1m 11nwhich has a t distribution with df when bothpopulation distributions are normal with (see thePooled t Procedures subsection for a description of Sp).a. Use this t variable to obtain a pooled t confidence intervalformula for .b. A sample of ultrasonic humidifiers of one particularbrand was selected for which the observations on maximumoutput of moisture (oz) in a controlled chamberwere 14.0, 14.3, 12.2, and 15.1. A sample of the secondbrand gave output values 12.1, 13.6, 11.9, and 11.2(Multiple Comparisons of Means Using Simultaneousm1 2 m2s1 5 s2m 1 n 2 2 Confidence Intervals, J. of Quality Technology, 1989:232241). Use the pooled t formula from part (a) to estimatethe difference between true average outputs for thetwo brands with a 95% confidence interval.c. Estimate the difference between the two ms using thetwo-sample t interval discussed in this section, and compareit to the interval of part (b).