Problem #4: The health of the bear population in Yellowstone National Park is mo

Question

Problem #4: The health of the bear population in Yellowstone National Park is monitored by periodic measurements taken from anesthetized bears. A sample of 43 bears has a mean weight of 189.9 lb with standard deviation 8.4 lb. 05, can it be concluded that the average weight of a bear in Yellowstone National Park is different from 187 At lb? (a) Find the value of the test statistic for the above hypothesis. (b) Find the critical value Find the p-value. (d) What is the correct way to drawa regarding the above hypothesis test? Problem #4(a): 12.26 Problem #4(b): 12.42 Problem #4(c): 10.1180 test statistic (correct to 2 decimals) critical value (correct to 2 decimals) p-value (correct to 4 decimals)

Explanation / Answer

as the sample is greater than 40 , hence we should go for z test

Z = (xbar-mu)/(sd/sqrt(n))

so
given the values
xbar = 189.9
mu = 187
n = 43
sd = 8.4

so the z value is

Z = (189.9-187)/(8.4/sqrt(43))
= 2.26

now we check the critical value from the z table
from alpha =0.05 as
-1.6449

also , from the z table the p value is 0.9880

Hence we fail to reject the null hypothesis and conclude that avergae weight is not different from 187 lb

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