The article from which the data in Exercise 1 was extracted also gave the accompanYing strength observations for cylinders:

Prior to obtaining data, denote the beam strengths by X1,..., Xm and the cylinder strengths by Y1, . . . , Yn. Suppose that the Xi's constitute a random sample from a distribution with mean µ1 and standard deviation σ1 and that the Yi's form a random sample (independent of the Xi's) from another distribution with mean σ2 and standard deviation σ2.
a. Use rules of expected value to show that - is an unbiased estimator of µ1 - µ2. Calculate the estimate for the given data.
b. Use rules of variance from Chapter 5 to obtain an expression for the variance and standard deviation (standard error) of the estimator in part (a), and then compute the estimated standard error.
c. Calculate a point estimate of the ratio σ1/σ2 of the two standard deviations.
d. Suppose a single beam and a single cylinder are randomly selected. Calculate a point estimate of the variance of the difference X - Y between beam strength and cylinder strength.

6.1 5.8 7.8 7.1 7.2 9.2 6.6 8.3 7.0 8.3 7.8 8.1 74 8.5 8.9 9.8 9.7 14.1 12.6 11.2