The octane number, Y, of refined petroleum is related to the temperature, x, of the refining process. An experiment with sample size n = 11 gave a fitted least-squares line of with V(1) = (0.0193)². ŷ = 4.265+0.190x, a. Give the test statistic you should use to test H0: ẞ₁ = ẞ1,0 vs. Ha: ẞ₁ ẞ1,0 for some fixed value ẞ1,0. Briefly explain your choice. [Hint: with the information provided, determine whether you should use a Z or a t statistic.] b. Use your result from part (a) to test the hypothesis that the slope coefficient, B₁, is significantly different from 0 at significance level α = 0.05.

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The octane number, Y, of refined petroleum is related to the temperature, x, of the
refining process. An experiment with sample size n = 11 gave a fitted least-squares
line of
with V(1) (0.0193)².
=
ŷ = 4.265+0.190x,
a. Give the test statistic you should use to test Ho: B₁ = 1,0 vs. Ha: ẞ₁ ẞ1,0 for
some fixed value ẞ1,0. Briefly explain your choice. [Hint: with the information
provided, determine whether you should use a Z or at statistic.]
b. Use your result from part (a) to test the hypothesis that the slope coefficient,
ẞ1, is significantly different from 0 at significance level α = 0.05.
Transcribed Image Text:The octane number, Y, of refined petroleum is related to the temperature, x, of the refining process. An experiment with sample size n = 11 gave a fitted least-squares line of with V(1) (0.0193)². = ŷ = 4.265+0.190x, a. Give the test statistic you should use to test Ho: B₁ = 1,0 vs. Ha: ẞ₁ ẞ1,0 for some fixed value ẞ1,0. Briefly explain your choice. [Hint: with the information provided, determine whether you should use a Z or at statistic.] b. Use your result from part (a) to test the hypothesis that the slope coefficient, ẞ1, is significantly different from 0 at significance level α = 0.05.
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