Chapter 10, Problem 5CR

For each hypothesis test in Problems 3-10, please provide the following information:

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

Check Requirements What sampling distribution will you use? What assumptions are you making? What is the value of the sample test statistic?

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

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 $\alpha$ ?

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 cases, this choice will increase the P-value by a small amount or increase the length of a confidence interval, thereby making the answer slightly more “conservative." Answers may vary due to rounding.

Wildlife: Wolves A random sample of 18 adult male wolves from the Canadian Northwest Territories gave an average weight ${\bar{x}}_1=98$ lb with estimated sample standard deviation $s_1=6.5$ lb. Another sample of 24 adult male wolves from Alaska gave an average weight ${\bar{x}}_2=90$ lb with estimated sample standard deviation $s_2=7.3$ lb (Source: The Wolf, by L. D. Mech, University of Minnesota Press).

Let ${\mu }_1$ represent the population mean weight of adult male wolves from the Northwest Territories, and let ${\mu }_2$ represent the population mean weight of adult male wolves from Alaska. Find a 75% confidence interval

for ${\mu }_1-{\mu }_2$.

Examine the confidence interval and explain what it means in the context of this problem. Does the interval consist of numbers that are all positive? All negative? Of different signs? At the 75% level of confidence, does it appear that the average weight of adult male wolves from the Northwest Territories is greater than that of the Alaska wolves?

Test the claim that the average weight of adult male wolves from the Northwest Territories is different from that of Alaska wolves. Use $\alpha$ = 0.01.