Question

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 37 wolves, there were only 11 females. One theory is that male wolves tend to return sooner than 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 α = 0.01.

(a) What is the level of significance?


State the null and alternate hypotheses.

H₀: p = 0.5; H₁: p > 0.5H₀: p = 0.5; H₁: p < 0.5    H₀: p = 0.5; H₁: p ≠ 0.5H₀: p < 0.5; H₁: p = 0.5

(b) What sampling distribution will you use?

The Student's t, since np > 5 and nq > 5.The Student's t, since np < 5 and nq < 5.    The standard normal, since np > 5 and nq > 5.The standard normal, since np < 5 and nq < 5.

What is the value of the sample test statistic? (Round your answer to two decimal places.)


(c) Find the P-value of the test statistic. (Round your answer to four decimal places.)


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 α?

At the α = 0.01 level, we reject the null hypothesis and conclude the data are statistically significant.At the α = 0.01 level, we reject the null hypothesis and conclude the data are not statistically significant.    At the α = 0.01 level, we fail to reject the null hypothesis and conclude the data are statistically significant.At the α = 0.01 level, we fail to reject the null hypothesis and conclude the data are not statistically significant.

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

There is sufficient evidence at the 1% level to conclude that the true proportion of female wolves in the region is less than 0.5.There is insufficient evidence at the 1% level to conclude that the true proportion of female wolves in the region is less than 0.5.    

Answer 1

a. Level of significance 0.01

b.

H0 : P = 0.50

H1 : P < 0.50

Sampling distribution is the standard normal, since np > 5 and nq >5

d.

At the α = 0.01 level, we fail to reject the null hypothesis and conclude the data are not statistically significant.

e.

There is insufficient evidence at the 1% level to conclude that the true proportion of female wolves in the region is less than 0.5.   

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