Question

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 58 wolves, there were only 32 females. One theory is that male wolves tend to return soon than females to their old territories where the predecessors were exterminated. Do these data indicate that the population proportion of female wolves is now less than 50% in the region? Use α = 0.01.5- State your null and alternate hypothesis. What is the level of significance? Will you use a left tail, right tail or two-tail test?6- What is the value of the test statistic 7.Find the P-value. Sketch the sampling distribution z = to show the area corresponding to the P-value.8- Based on 5-7, will you reject or fail to reject the null hypothesis? Are the data statistically significant at level α ? State your conclusion in the context of the application.

Answer 1

5. State the null and the alternate hypothesis.

`\begin{gathered} H_0\Rightarrow\text{the population of the female wolves is equal to 50\%, p=50\%} \\ H_a\Rightarrow\text{the population of the female wolves is less than 50\%, p<50\%} \end{gathered}`

Given an alpha of 0.01, the level of significance will

`\begin{gathered} \text{Significant level=100-}\alpha \\ =1-0.01=0.99 \\ \therefore\text{significant level = 99\%} \end{gathered}`

A left tailed test will be used, because we want to nullify that the population is less than 50%

`p<50\text{ \%}`

6. The z-test statistic and the P-value will be

`\begin{gathered} p-\text{value }\Rightarrow(\alpha)/(2) \\ p=(0.01)/(2)=0.005 \\ z-score\text{ value for 99\% confidence interval }\Rightarrow2.576 \end{gathered}`

8. Since the p-value is less than the alpha value, then, we will reject the null hypothesis in favour of the alternative hypothesis.

Yes, the data are statistically significant at the level of alpha

We conclude that the population of the female wolves is less than 50%