Question

The health of the bear population in Yellowstone National Park is monitored by periodic measurements taken from anesthetized bears. A sample of 36 bears has a mean weight of 188.5 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 8.1 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?

Different from other questions bc sigma known so use z score? Test Stat: 1.11 was correct Critical -1.645 was INcorrect Pvalue .8665 was INcorrect

Answer 1

The sample mean is 188,5 lb and the popuation mean is 187 lb.

The standard deviation is 81 lb and th enumber of bears in the sample is 36.

We can formulate the following hypothesis:

H0: The mean weight of the bears is 187 lb, mu = lb

H1: The mean weight of the bears is different from 187 lb.

The test statistic under the null hypothesis is:

The value of th etest statistic is:

z = 1.11

The critical value at 5% level of significance is 1.96

The p-value of the test statistic is 0.13326

Since, the p-value of the test statistic is much greater than 0.05, we may accept the null hypothesis at 5% level of significance and conclude that the mean weight of th ebears may be equal to 187 lb.