Consider the pooled t variable Tp from part (b) of the previous exercise.

a. Use this t variable to obtain a pooled t confidence interval formula for μ₁ – μ₂.

b. The article “Effect of Welding on a High-Density Polyethylene Liner” (J. Mater. Civil Engr. 1996: 94–100) reported the following data on tensile strength (psi) of liner specimens both when a certain fusion process was used and when this process was not used.

Use the pooled t formula from part (a) to estimate the difference between true average tensile strength for the two processes with a 95% confidence interval.

c. Estimate the difference between the two l’s using the two-sample t interval discussed in this section, and compare it to the interval of part (b).

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b. Show that the pooled t variable (X-Y)-(H₁-H₂) 1 Tp m + n has a t distribution with m + n - 2 df.