Reconsider the situation of Exercise 73, in which x = retained austenite content using a garnet abrasive and y = abrasive wear loss were related via the simple linear regression model Y = β0 + β1x + ε. Suppose that for a second type of abrasive, these variables are also related via the simple linear regression model Y = γ0 + γ0x + ε and that V(ε) = (2 for both types of abrasive. If the data set consists of n1 observations on the first abrasive and n2 on the second and if SSE1 and SSE2 denote the two error sums of squares, then a pooled estimate of (2 is 2 = (SSE1 + SSE2) / (n1 + n2 - 4). Let SSx1 and SSx2 denote
((xi - x̅)2 for the data on the first and second abrasives, respectively. A test of H0: β1 - γ1 = 0 (equal slopes) is based on the statistic

When H0 is true, T has a t distribution with n1 + n2 - 4 df. Suppose the 15 observations using the alternative abrasive give SSx2 = 7152.5578, 1 = .006845, and SSE2 = .51350. Using this along with the data of Exercise 73, carry out a test at level .05 to see whether expected change in wear loss associated with a 1% increase in austenite content is identical for the two types of abrasive?

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