Historically, the population of wolves in Canada have been found to have an average adult weight of 38.9 kilograms. The Canadian Wildlife Service believes that due to climate change, this may have increased. A random sample of 12 wolves is captured and weighed and the following results are obtained. Assume that the weights are normally distributed:
44.8, 40.7, 42.6, 46.8, 48.7, 35.4, 38.9, 39.5, 38.3, 48.9, 48.4, 38.4.
At a 0.05 significance level, test the hypothesis that the average weight of a wolf is more than 38.9.
a) | Identify the null
hypothesis and alternative hypothesis.
|
b) State the critical value.
For full marks your answer should be accurate to at least three
decimal places.
Critical value: ____
c) Determine the value of the test
statistic.
For full marks your answer should be accurate to at least three
decimal places.
Test statistic:___
d) | Identify the correct
interpretation.
|
e) | What conclusion can be
drawn from the interpretation at 0.05 significance level?
|
Answer)
A)
Ho : u <= 38.9
Ha : u > 38.9
B)
As the population s.d is unknown here we will use t distribution to conduct the test
N = 12
Degrees of freedom is = n-1 = 11
For df 11 and alpha 0.05,critical t value from t table is = 1.796
Rejection region is if t > 1.796
Reject Ho
C)
First we need to find the sample mean and s.d for the given data
Sample mean = 42.6167
S.d = 4.7472
Test statistics = (sample mean - claimed mean)/(s.d/√n)
= (42.6167 - 38.9)/(4.7472/√12)
= 2.712
D)
Since test statistics is in the rejection region (as 2.712 > 1.796) reject Ho and accept H1
E)
There is significant evidence that the average weight is more than 38.9.
Historically, the population of wolves in Canada have been found to have an average adult weight...
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