Regression, One way ANOVA, Hypothesis Testing

4.
Generations of athletes have been cautioned that cigarette smoking retards performance. One measure of the truth of that warning is the effect of smoking on heart rate. To examine this impact, six of each of non-smokers, light smokers, moderate smokers, and heavy smokers undertook sustained physical exercise. Their heart rates were measured after resting for three minutes. The results are shown in the table below. If 1, 2, 3, and 4 denote the true average heart rates for the four groups of smokers, are the differences among the Y bar i?'s statistically significant to reject Ho: 1 = 2 = 3 = 4?

NON-SMOKERS LIGHT SMOKERS MODERATE SMOKERS HEAVY SMOKERS
69 55 66 91
52 60 81 72
71 78 70 81
58 58 77 67
59 62 57 95
65 66 79 84

5.
One of the most famous experiments in the history of science was performed by G. Mendel, who classified n = 556 peas according to two traits: shape (round or wrinkled) and color (yellow or green). Each seed was put into one of k = 4 classes, where r, w, g, and y denote round, wrinkled, green and yellow, respectively. The results of Mendel's breeding experiment are shown below.

SEED TYPE OBSERVED FREQUENCY
ry 315
wy 101
rg 108
wg 32

Mendel's theory predicted that the frequency counts of the seed types produced from his experiment should occur in the ratio 9:3:3:1, i.e., p1 = p(ry) = 9/16, p2 = p(rg) = 3/16, p3 = p(wy) = 3/16, p4 = p(wg) = 1/16. Do Mendel's theoretical predictions provide a good fit to the data?

6.
An individual claims that the fuel consumption of his car does not depend on how fast the car is driven. To test his claim, the car was tested at various speeds between 45 and 75 miles per hour (mph). The miles per gallon (mpg) attained at each of these speeds was determined:

SPEED (mph) mpg SPEED (mph) mpg
45 24.2 65 21.5
50 25.0 70 20.6
55 23.3 75 19.8
60 22.0

Do these data refute the claim that mpg is unaffected by the speed at which the car is being drive? You need to develop the estimated regression line first before performing the hypothesis testing.