Question

The Appalachian Bear Center (ABC) is a not-for-profit organization located near the Great Smoky Mountains National Park. ABC’s programs include the rehabilitation of orphaned and injured black bears, as well as research and education about Appalachian black bears. ABC provides the most natural environment possible for rehabilitating black bears before their release back into the wild. Katie Settlage performed a study to learn more about the Appalachian black bear population in the Great Smoky Mountains National Park. She and a team of researchers used a sample of 68 black bears in the park and took measurements such as paw size, weight, and shoulder height.

Questions 2 and 3 refer to the following information regarding the shoulder height of the 28 female bears from the study. For these 28 female bears, the sample mean is 75.679 cm and the sample standard deviation is 7.592 cm. Assume the data is normally distributed and the sample is randomly selected.

3. Using an 80% level of confidence, construct the confidence interval for the population standard deviation of the shoulder heights based on the female data and make a statement interpreting these intervals. (12 points)

Answer 1

n=28, s=7.592, s²=57.638

(1-alpha)*100 confidence interval for ?={ sqrt((n-1)s²/chi-sq( alpha/2 ,n-1)),sqrt((n-1)s²/chi-sq(1- alpha/2 ,n-1)) }

80% confidence interval for ?={ sqrt((28-1)57.638/chi-sq(0.2/2 ,28-1)),sqrt((28-1)*57.638/chi-sq(1-0.2/2 ,28-1)) }

={ sqrt((28-1)*57.638/36.74),sqrt((28-1)*57.638/18.11)) =(6.508,9.269)

chi-sq(1-0.2/2,27)=18.11,                   chi-sq(0.2/2,16)=36.74