7.30 A new steroidal treatment for a skin condition in dogs was under evaluation by a veterinary hospital. One of the possible side effects of the treatment is that a dog receiving the treatment may have an allergic reaction to the treatment. This type of allegeric reaction manifests itself through an elevation in the resting pulse rate of the dog after the dog has received the treatment for a period of time. A group of 80 dogs of the same breed and age, and all having the skin condition, is randomly assigned to either a placebo treatment or the steroidal treatment. Four days after receiving the treatment, either steroidal or placebo, resting pulse rate measurements are taken on all the dogs. These data are displayed here. Dogs of this age and breed have a fairly constant resting pulse rate of 100 beats a minute.The researchers are interested in testing whether there is a significant difference between the placebo and treatment dogs in terms of both the means and standard deviations of the resting pulse rates. Placebo Group Pulse Rates 105.1 103.3 102.1 102.3 101.5 100.6 104.5 103.2 101.8 102.1 108.1 103.2 104.0 103.9 105.3 103.6 102.3 103.9 103.0 107.0 102.3 103.5 111.7 101.4 103.0 101.1 103.7 102.3 106.2 100.8 102.1 104.3 104.0 102.2 103.1 104.7 102.3 110.1 103.1 103.4 Treatment Group Pulse Rates 107.6 107.8 110.4 106.6 108.2 113.4 113.5 108.7 108.2 106.0 105.3 107.1 110.3 108.7 107.4 111.1 105.9 106.9 106.4 111.5 106.8 107.8 106.1 106.7 105.0 110.4 105.9 106.4 106.0 106.0 106.9 107.6 107.0 105.8 108.6 105.9 108.5 106.9 107.0 109.2 a. Is there significant evidence of an increase in the mean pulse rates for those dogs receiving the treatment? b. Is there significant evidence of a difference in the levels of variability in pulse rate between the placebo and the treatment group of dogs? c. Provide a 95% confidence interval on the difference in mean pulse rates between the placebo and treatment groups. d. Do the necessary conditions hold for the statistical procedures you applied in parts (a)–(c)? Justify your answer.
7.30
A new steroidal treatment for a skin condition in dogs was under evaluation by a veterinary hospital. One of the possible side effects of the treatment is that a dog receiving the treatment may have an allergic reaction to the treatment. This type of allegeric reaction manifests itself through an elevation in the resting pulse rate of the dog after the dog has received the treatment for a period of time. A group of 80 dogs of the same breed and age, and all having the skin condition, is randomly assigned to either a placebo treatment or the steroidal treatment. Four days after receiving the treatment, either steroidal or placebo, resting pulse rate measurements are taken on all the dogs. These data are displayed here. Dogs of this age and breed have a fairly constant resting pulse rate of 100 beats a minute.The researchers are interested in testing whether there is a significant difference between the placebo and treatment dogs in terms of both the means and standard deviations of the resting pulse rates.
Placebo Group Pulse Rates
| 105.1 | 103.3 | 102.1 | 102.3 | 101.5 | 100.6 | 104.5 | 103.2 | 101.8 |
| 102.1 | 108.1 | 103.2 | 104.0 | 103.9 | 105.3 | 103.6 | 102.3 | 103.9 |
| 103.0 | 107.0 | 102.3 | 103.5 | 111.7 | 101.4 | 103.0 | 101.1 | 103.7 |
| 102.3 | 106.2 | 100.8 | 102.1 | 104.3 | 104.0 | 102.2 | 103.1 | 104.7 |
| 102.3 | 110.1 | 103.1 | 103.4 |
Treatment Group Pulse Rates
| 107.6 | 107.8 | 110.4 | 106.6 | 108.2 | 113.4 | 113.5 | 108.7 | 108.2 |
| 106.0 | 105.3 | 107.1 | 110.3 | 108.7 | 107.4 | 111.1 | 105.9 | 106.9 |
| 106.4 | 111.5 | 106.8 | 107.8 | 106.1 | 106.7 | 105.0 | 110.4 | 105.9 |
| 106.4 | 106.0 | 106.0 | 106.9 | 107.6 | 107.0 | 105.8 | 108.6 | 105.9 |
| 108.5 | 106.9 | 107.0 | 109.2 |
a. Is there significant evidence of an increase in the mean pulse rates for those dogs receiving the treatment?
b. Is there significant evidence of a difference in the levels of variability in pulse rate between the placebo and the treatment group of dogs?
c. Provide a 95% confidence interval on the difference in mean pulse rates between the placebo and treatment groups.
d. Do the necessary conditions hold for the statistical procedures you applied in parts (a)–(c)? Justify your answer.
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