Chapter 10.2, Problem 19P

Please provide the following information for Problems 11-22. part (a):

(i) What is the level of significance? State the null and alternate hypotheses.

(ii)Check Requirements What sampling distribution will you use? What assumptions are you making? What is the value of the sample test statistic? Compute the corresponding z or t value as appropriate.

(iii)Find (or estimate) the P-value. Sketch the sampling distribution and show the area corresponding to the P-value.

(iv)Based on your answers in parts (i)—(iii), will you reject or fail to reject the null hypothesis? Are the data statistically significant at level a?

(v)Interpret your conclusion in the context of the application.

Note: For degrees of freedom d.f. not in the Student's t table, use the closest d.f. that is smaller. In some situations, this choice of d.f. may increase the P-value a small amount, and therefore produce a slightly more “conservative” answer. Answers may vary due to rounding.

Wildlife: Fox Rabies A study of fox rabies in southern Germany gave information about different regions and the occurrence of rabies in each region (Reference: B. Sayers et al., “A Pattern Analysis Study of a Wildlife Rabies Epizootic" Medical Informatics 2:11-34). Based on information from this article, a random sample of $n_1=16$ locations in region I gave the following information about the number of cases of fox rabies near that location:

x₁: Region I data

1	8	8	8	7	8	8	1
3	3	3	2	5	1	4	6

A second random sample of $n_2=15$ locations in region II gave the following information about the number of cases of fox rabies near that location:

x₂: Region II data

1	1	3	1	4	8	5	4
4	4	2	2	5	6	9

Use a calculator with sample mean and sample standard deviation keys to verify that ${\bar{x}}_1=4.75\text{ with }{s}_1\approx 2.82$ in region I and ${\bar{x}}_2=3.93\text{ with }{s}_2\approx 2.43$ in region II.

(a) Does this information indicate that there is a difference (either way) in the mean number of cases of fox rabies between the two regions? Use a 5% level of significance. (Assume the distribution of rabies cases in both regions is mound-shaped and approximately normal.)

(b) Find a 95% confidence interval for ${\mu }_1-{\mu }_2$. Explain the meaning of the confidence interval in the context of the problem.