"2004 a Bad Year for the Grizzly Bear" reported that "31 bears were killed illegally or had to be destroyed in a mountain habitat of 6 million acres that has Glacier National Park and federal wilderness areas at its core. That is the largest number of deaths caused by humans in the region since 1974, when the grizzly was listed as threatened under the Endangered Species Act. More worrisome is that 18 of the dead bears were females, which are more important than males to the reproductive health of the entire population."38 This exercise requires you to use software to test if a disproportionate number of killed bears were female, assuming that half of all grizzlies are female.
a. In choosing whether to formulate a onesided or two-sided alternative hypothesis, keep in mind that most of us are not familiar enough with grizzly bear behavior to have any expectations as to whether females would be more or less likely to be killed. State H0 and Ha mathematically.
b. Report the sample proportion .
c. Report the standardized sample proportion z.
d. Report the P-value.
e. Was a disproportionate number of killed bears female, or could the sample proportion have come about by chance?
f. Would your answer to part (e) be the same if you had formulated the alternative hypothesis as Ha : p 0.5? Explain.
g. Report a 95% confidence interval for population proportion of bears that are female, based on sample proportion of females in the killed bears.
h. Does your 95% confidence interval contain 0.5?