Tar and NicotineEvery year the Federal Trade Commission (FTC) must report tar and nicotine levels in cigarettes to Congress. The FTC obtains the tar and nicotine levels in over 1200 brands of cigarettes. A random sample from those reported to Congress is given in the following table:
|
Brand
|
Tar (mg), x
|
Nicotine (mg), y
|
|
Barclay 100
|
5
|
0.4
|
|
Benson and Hedges King
|
16
|
1.1
|
|
Camel Regular
|
24
|
1.7
|
|
Chesterfield King
|
24
|
1.4
|
|
Doral
|
8
|
0.5
|
|
Kent Golden Lights
|
9
|
0.8
|
|
Kool Menthol
|
9
|
0.8
|
|
Lucky Strike
|
24
|
1.5
|
|
Marlboro Gold
|
15
|
1.2
|
|
Newport Menthol
|
18
|
1.3
|
|
Salem Menthol
|
17
|
1.3
|
|
Virginia Slims Ultra Light
|
5
|
0.5
|
|
Winston Light
|
10
|
0.8
|
(a) Treating the amount of tar as the explanatory variable, x, determine the estimates of ß0 and ß1.
(b) Compute the standard error of the estimate.
(c) Determine whether the residuals are normally distributed.
(d) If the residuals are normally distributed, determine sb1.
(e) If the residuals are normally distributed, test whether a linear relation exists between the amount of tar, x, and the amount of nicotine, y, at the a = 0.1 level of significance.
(f) If the residuals are normally distributed, construct a 90% confidence interval for the slope of the true least-squares regression line.
(g) What is the mean amount of nicotine in a cigarette that has 12 milligrams of tar?