The octane number Y of refined petroleum is related to the

Chapter 11, Problem 30E

(choose chapter or problem)

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

\(\bar{y}=9.360+.155 x\)

with \(n=31, V\left(\bar{\beta}_{1}\right)=(.0202)^{2}\), and SSE = 2.04. An independent experiment with a large particle catalyst gave

\(\bar{y}=4.265+.190 x\)

with \(n=11, V\left(\widetilde{\beta_{1}}\right)=(.0193)^{2}\), and \(S S E=1.86^{7}\)

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.)

Equation transcription:

Text transcription:

bar{y}=9.360+.155 x

n=31, V{\beta}{1})=(.0202)^{2}

bar{y}=4.265+.190 x

n=11, V(\widetilde{\beta{1})=(.0193)^{2}

S S E=1.86^{7}