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.
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.
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter1: Functions
Section1.2: The Least Square Line
Problem 5E
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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.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd3cc4b1e-ed91-4330-9eca-3239f006dbcf%2F20257dbb-0a09-44b1-9ad4-5a02190aeb9e%2F1tj6kf_processed.png&w=3840&q=75)
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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