The Cadet is a popular model of sport utility vehicle, known for its relatively high resale value. For a random sample of 31 Cadets, each bought "new" two years ago and each sold "used" within the past month, the least-squares regression equation relating the two variables mileage, x (in thousands), and used selling price, y (in thousands of dollars), was y = 38.73 – 0.54x. The standard error of the slope of this least-squares regression line was approximately 0.34. Based on this information, test for a significant linear relationship between the two variables by doing a hypothesis test regarding the population slope B,. (Assume that the variable y follows a normal distribution for each value of x and that the other regression assumptions are satisfied.) Use the 0.05 level of significance, and perform a two-tailed test. Then complete the parts below.
The Cadet is a popular model of sport utility vehicle, known for its relatively high resale value. For a random sample of 31 Cadets, each bought "new" two years ago and each sold "used" within the past month, the least-squares regression equation relating the two variables mileage, x (in thousands), and used selling price, y (in thousands of dollars), was y = 38.73 – 0.54x. The standard error of the slope of this least-squares regression line was approximately 0.34. Based on this information, test for a significant linear relationship between the two variables by doing a hypothesis test regarding the population slope B,. (Assume that the variable y follows a normal distribution for each value of x and that the other regression assumptions are satisfied.) Use the 0.05 level of significance, and perform a two-tailed test. Then complete the parts below.
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.CR: Chapter 1 Review
Problem 86CR
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Transcribed Image Text:The Cadet is a popular model of sport utility vehicle, known for its relatively high resale value. For a random sample of 31 Cadets, each bought "new" two years
ago and each sold "used" within the past month, the least-squares regression equation relating the two variables mileage, x (in thousands), and used selling
price, y (in thousands of dollars), was y = 38.73 – 0.54x. The standard error of the slope of this least-squares regression line was approximately 0.34. Based on
this information, test for a significant linear relationship between the two variables by doing a hypothesis test regarding the population slope B. (Assume that
the variable y follows a normal distribution for each value of x and that the other regression assumptions are satisfied.) Use the 0.05 level of significance, and
perform a two-tailed test. Then complete the parts below.
(If necessary, consult a list of formulas.)
Transcribed Image Text:(a) State the null hypothesis H, and the alternative hypothesis H,.
Ho :0
H, 0
O=0
OSO
(b) Determine the type of test statistic to use.
(Choose one)
O<O
(c) Find the value of the test statistic. (Round to three or more decimal places.)
(d) Find the two critical values at the 0.05 level of significance. (Round to three or more decimal places.)
O and I
(e) Based on the information, can we conclude (using the 0,05 level) that there is a significant linear
relationship between mileage and used selling price for two-year-old Cadets?
OYes ONo
Ix
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