Question

1. A Veterinarian investigates the number of viral infections cats contract as a function of the amount of psychological stress they experience during a one-year period. The Veterinarian wants to see if there are significant differences (at the significance level of 0.05) in the mean number of viral infections depending on the amount of stress. The doctor obtained the following data (N=20):

_____________________________________________________

    Negligible         Minimal          Moderate         Severe

        Stress             Stress              Stress              Stress

_____________________________________________________

            2                      4                      6                      5

            1                      3                      5                      7

            4                      2                      7                      8

            1                      3                      5                      4

            2                      2                      6                      8

_____________________________________________________

Please answer the following questions:

(a) What are the null and alternative hypotheses?

(b) What assumptions should be made? Provide 4 assumptions.

            

            1)

            2)

            3)

            4)

Answer 1

Let and denote the the mean number of viral infections for negligible, minimal, moderate and severe stress respectively.

To test null hypothesis against alternative hypothesis H₁ : at least one mean is different.

One should have a ANOVA test in this case.

b) The assumptions for ANOVA :

1. Each group sample is drawn from a normally distributed population.

2. All populations have a common variance.

3. All samples are drawn independently of each other

4. Within each sample, the observations are sampled randomly and independently of each other