Statistical Inference: A Short Course

Exercises

1. For the given v and α values, find the implied quantiles of the chi-square distribution:

a. α = 0.05, v = 12

b. α = 0.01, v = 5

c. α = 0.01, v = 20

d. α = 0.05, v = 8

2. Ten years ago the non-athlete versus athlete graduation ratio at a local liberal arts college was known to be 8 to 1 in favor of non-athletes (there were eight non-athletes graduating for every athlete who graduated). Suppose that in a recent survey conducted by the Registrar's Office it was found that in a random sample of 450 degree applicants, 68 were athletes. Has the ratio changed significantly? Use α = 0.05.

3. If four variants of a certain plant species are believed to be present in a South American rain forest in the 9:3:3:1 ratio, what are the null and alternative hypotheses if this belief is to be tested?

4. Billings Motors surveyed 250 of its customers regarding their preferred time for servicing their vehicles: morning (M), afternoon (A), or evening (E). The results were M = 101, A = 60, and E = 89. The service department thinks that the proportions for the three groups should be , respectively. Is there any evidence that these proportions differ from 2:1:1? Use α = 0.01.

5. SMART Publications has four salesmen (denoted 1, 2, 3, and 4) in its advertising department. These salesmen have similar territories. Sales calls for last month were:

For α = 0.05, is the number of sales calls ...