Question

A random sample of 22 adult male wolves from the Canadian
Northwest Territories gave an average weight *x*_{1}
= 96.0 pounds with estimated sample standard deviation
*s*_{1} = 5.7 pounds. Another sample of 28 adult
male wolves from Alaska gave an average weight
*x*_{2} = 88.0 pounds with estimated sample standard
deviation *s*_{2} = 6.2 pounds.

(a) Categorize the problem below according to parameter being
estimated, proportion *p*, mean *μ*, difference of
means *μ*_{1} – *μ*_{2}, or
difference of proportions *p*_{1} –
*p*_{2}. Then solve the problem.

μ_{1} – μ_{2}

*p*

*p*_{1} – *p*_{2}

μ

(b) Let *μ*_{1} represent the population mean
weight of adult male wolves from the Northwest Territories, and let
*μ*_{2} represent the population mean weight of
adult male wolves from Alaska. Find a 95% confidence interval for
*μ*_{1} – *μ*_{2}. (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 95% 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

Part a)

μ_{1} – μ_{2}

Part b)

Confidence interval :-

t(α/2, DF) = t(0.05 /2, 46 ) = 2.013

DF = 46

Lower Limit =

Lower Limit = 4.6019 ≈ 4.6

Upper Limit =

Upper Limit = 11.3981 ≈ 11.4

**95% Confidence interval is ( 4.6 , 11.4 )**

Part c)

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

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