Question

A random sample of 15 adult male wolves from the Canadian Northwest Territories gave an average weight x₁ = 96.0 pounds with estimated sample standard deviation s₁ = 7.5 pounds. Another sample of 27 adult male wolves from Alaska gave an average weight x₂ = 89.0 pounds with estimated sample standard deviation s₂ = 7.5 pounds. (a) Categorize the problem below according to parameter being estimated, proportion p, mean μ, difference of means μ₁ – μ₂, or difference of proportions p₁ – p₂. Then solve the problem.

1 μ₁ – μ₂

2p

3    μ

4 p₁ – p₂

(b) Let μ₁ represent the population mean weight of adult male wolves from the Northwest Territories, and let μ₂ represent the population mean weight of adult male wolves from Alaska. Find a 90% confidence interval for μ₁ – μ₂. (Use 1 decimal place.)

lower limit

upper limit

(c) 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 90% 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?

Because the interval contains only positive numbers, we can say that Canadian wolves weigh more than Alaskan wolves.

Because the interval contains both positive and negative numbers, we can not say that Canadian wolves weigh more than Alaskan wolves.

We can not make any conclusions using this confidence interval.

Because the interval contains only negative numbers, we can say that Alaskan wolves weigh more than Canadian wolves.

Answer 1

(A) we are find the mean difference for Alaskan wolve and Canadian wolves.

so, point estimate =

(B) Using TI 84 calculator

press stat then tests then 2-sampTInt

enter the data  

Pooled: yes

C-level = 0.90

press ENTER

lower limit = 2.9

upper limit = 11.1

(C) Since the confidence interval is calculated for mean of Canadian wolves minus the mean of Alaska wolves and we get positive limits for the confidence interval

this means that the mean for canadian wolves is greater than mean for Alaska wolves

Because the interval contains only positive numbers, we can say that Canadian wolves weigh more than Alaskan wolves.