7.30A 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 Rates105.1103.3102.1102.3101.5100.6104.5103.2101.8102.1108.1103.2104.0103.9105.3103.6102.3103.9103.0107.0102.3103.5111.7101.4103.0101.1103.7102.3106.2100.8102.1104.3104.0102.2103.1104.7102.3110.1103.1103.4                                       Treatment Group Pulse Rates107.6107.8110.4106.6108.2113.4113.5108.7108.2106.0105.3107.1110.3108.7107.4111.1105.9106.9106.4111.5106.8107.8106.1106.7105.0110.4105.9106.4106.0106.0106.9107.6107.0105.8108.6105.9108.5106.9107.0109.2     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.

Question
Asked Mar 1, 2019

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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Expert Answer

Step 1

Given information:

It is given that; a group of 80 dogs of same breed and age are randomly assigned either to a placebo treatment or a steroidal treatment to test the effectiveness of steroidal treatment in reducing the allergic reaction of skin condition of dogs.

Here, 40 dogs are randomly assigned to treatment groups and 40 dogs are randomly assigned to placebo group. After 4 days of receiving treatment resting pulse rate measurements are taken on both dogs.

The data represents the resting pulse rate measurements of 40 dogs under placebo group and 40 dogs under steroidal treatment group.

Step 2

a.

Test whether there is enough evidence to conclude that the mean pulse rate of treatment group is greater than the mean pulse rate of placebo group:

Let μ1 be the mean pulse rate of treatment group and μ2 be the mean pulse rate of placebo group.

State the appropriate hypothesis.

The hypotheses are given below:

Null hypothesis:

H0 : μ1 = μ2

That is, there is no significant difference between the mean pulse rate of treatment group and mean pulse rate of placebo group.

Alternative hypothesis:

H1 : μ1 > μ2

That is, the mean pulse rate of treatment group is greater than the mean pulse rate of placebo group.

Step 3

Obtain the test statistic value.

Here, MINITAB software is used to find the test statistic.

Software procedure:

Step by step procedure to obtain the test statistic using the MINITAB software:

  • Choose Stat > Basic Statistics > 2 sample t.
  • Choose Each sample in its own column.
  • In Sample1 enter Treatment group and in sample2 enter Placebo group.
  • Select Options. In Confidence interval enter 95%.
  • In Hypothesized difference, enter
  • Under Alternative...
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