Question

The health of the bear population in Yellowstone National Park is monitored by periodic measurements taken from anesthetized bears. A sample of 38 bears has a mean weight of 189.6 lb. At α = .05, can it be concluded that the average weight of a bear in Yellowstone National Park is different from 187 lb? Note that the standard deviation of the weight of a bear is known to be 8.2 lb. (a) Find the value of the test statistic for the above hypothesis. (b) Find the critical value. (c) Find the p-value. (d) What is the correct way to draw a conclusion regarding the above hypothesis test? (A) If the answer in (b) is greater than the answer in (c) then we cannot conclude at the 5% significance level that the average weight of a bear in Yellowstone National Park is different from 187 lb. (B) If the answer in (b) is greater than the answer in (c) then we conclude at the 5% significance level that the average weight of a bear in Yellowstone National Park is different from 187 lb. (C) If the answer in (a) is greater than the answer in (b) then we conclude at the 5% significance level that the average weight of a bear in Yellowstone National Park is different from 187 lb. (D) If the answer in (a) is greater than the answer in (c) then we conclude at the 5% significance level that the average weight of a bear in Yellowstone National Park is different from 187 lb. (E) If the answer in (c) is less than 0.05 then we cannot conclude at the 5% significance level that the average weight of a bear in Yellowstone National Park is different from 187 lb. (F) If the answer in (c) is greater than 0.05 then we conclude at the 5% significance level that the average weight of a bear in Yellowstone National Park is different from 187 lb. (G) If the answer in (a) is greater than the answer in (b) then we cannot conclude at the 5% significance level that the average weight of a bear in Yellowstone National Park is different from 187 lb. (H) If the answer in (a) is greater than the answer in (c) then we cannot conclude at the 5% significance level that the average weight of a bear in Yellowstone National Park is different from 187 lb.

Answer 1

To Test :-

H₀ :-  

H₁ :-  

Test Statistic :-

Part b)

Critical value is  

Part c) P value

looking for the t = 1.9546 in t table across 37 degree of freedom we get values

t = 1.9546 lies between the values 1.684 and 2.021 with the P value 0.10 and 0.05

Using excel to calculate the exact P value is 0.05822

Part d)

Decision based on P value

Reject null hypothesis if P value < level fo significance

0.05822 > 0.05, hence we fail to reject null hypothesis

Conclusion :- Accept Null Hypothesis

Decision based on critical value

Reject null hypothesis if

Result :- Fail to reject null hypothesis

Conclusion :- Accept Null hypothesis

There is no evidence to support the claim that average weight of bear in yellowstone national park is different from 17 lbs.