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MCS,PHD
Argosy University/ Phoniex University/
Nov-2005 - Oct-2011
Professor
Phoniex University
Oct-2001 - Nov-2016
The octane number Y of refined petroleum is related to the temperature x of the refining process, but it is also related to the particle size of the catalyst. An experiment with a small-particle catalyst gave a fitted least-squares line of

a Test the hypotheses that the slopes are significantly different from zero, with each test at the significance level of
.05.
*b Test at the .05 significance level that the two types of catalyst produce the same slope in the relationship between octane number and temperature. (Use the test that you developed in Exercise 11.29.)
Exercise 11.29
Let Y1, Y2, . . . , Yn be as given in Exercise 11.28. Suppose that we have an additional set of independent random variables W1,W2, . . . ,Wm, where Wi is normally distributed with E(Wi ) = γ0 + γ1ci and V(Wi ) =σ2, for i = 1, 2, . . . ,m. Construct a test of H0 : β1 = γ1 against the Ha : β1 ≠γ1.6
Â
Exercise 11.28
Suppose that Y1, Y2, . . . , Yn are independent, normally distributed random variables with E(Yi ) = β0 + β1xi and V(Yi ) = σ2, for i = 1, 2, . . . , n. Show that the likelihood ratio test of H0 : β1 = 0 versus Ha : β1 = 0 is equivalent to the t test given in this section
Â
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