Question

The health of the bear population in Yellowstone National Park is monitored by periodic measurements taken from anesthetized bears. A sample of 37 bears has a mean weight of 189.1 lb.

At α = .02, 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?

Answer 1

a)

H0: = 187

Ha: 187

This is two tailed test.

Test statistics

z = ( - ) / ( / sqrt(n) )

= ( 189.1 - 187) / ( 8.2 / sqrt ( 37) )

= 1.56

b)

From Z table,

Critical value at 0.02 significance level = 2.326

c)

p-value = 2 * P(Z > z)

= 2 * P(Z > 1.56)

= 2 * 0.0594

= 0.1188

Decision = Since p-value > 0.02 level, We fail to reject H0.

d)

Conclusion - We conclude at 0.02 level that we fail to support the claim that the average weight of a

bear in Yellowstone National Park is different from 187 lb