A random sample of 17 wolf litters in Ontario, Canada, gave an average of 1 = 4.9 wolf pups per litter with estimated sample standard deviation s1 = 1.0. Another random sample of 6 wolf litters in Finland gave an average of 2 = 2.8 wolf pups per litter with sample standard deviation s2 = 1.2.
(a) Find an 85% confidence interval for μ1 - μ2, the difference in population mean litter size between Ontario and Finland.
(b) 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 85% level of confidence, does it appear that the average litter size of wolf pups in Ontario is greater than the average litter size in Finland?
(c) Test the claim that the average litter size of wolf pups in Ontario is greater than the average litter size of wolf pups in Finland. Use α = 0.01.
For each hypothesis test, please provide the following information:
(i) What is the level of significance? State the null and alternate hypotheses.
(ii) What sampling distribution will you use? What assumptions are you making? What is the value of the sample test statistic?
(iii) Find (or estimate) the P-value. Sketch the sampling distribution and show the area corresponding to the P-value.
(iv) 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 α?
(v) Interpret your conclusion in the context of the application.