Chapter 9.3, Problem 13P

For Problems 7-21, please provide the following information.

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

(b) Check Requirements What sampling distribution will you use? Do you think the sample size is sufficiently large? Explain. Compute the value of the sample test statistic and corresponding z value.

(c) Find the P-value of the lest statistic. Sketch the sampling distribution and show the area corresponding to the P-value.

(d) Based on your answers in parts (a) to (c). will you reject or fail to reject the null hypothesis? Are the data statistically significant at level $\alpha$?

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

Wildlife: Wolves The following is based on information from The Wolf in the Southwest: The Making of an Endangered Species by David E. Brown (University of Arizona Press). Before 1918, the proportion of female wolves in the general population of all southwestern wolves was about $50\%$. However, after 1918, southwestern cattle ranchers began a widespread effort to destroy wolves.

In a recent sample of 34 wolves, there were only 10 females. One theory is that male wolves tend to return sooner than do females to their old territories where their predecessors were exterminated. Do these data indicate that the population proportion of female wolves is now less than $50\%$ in the region? Use $\alpha =0.01$.