Case Study Chapter 6

Elementary Statistics

(Information for this case study came from page 324 in Elementary Statistics: Picturing the World, 4^th edition)

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.

Answer the following questions based on this data.As always, you must show all work and formulas used in order to receive full credit.Round all decimals to three places unless otherwise noted.

1.In the sample of 68 bears, 40 were males.Construct an 80% confidence interval for the population proportion of bears that are males and statement interpreting the interval.(12 points)

Questions 2 and 3 refer to the following information regarding 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.

1. Use the female sample to make an interval estimate of the mean shoulder height of female bears.Construct the confidence interval estimate using a 95% confidence level and make a statement interpreting this interval.(12 points)

1. Using a 99% level of confidence, construct the confidence interval for the population standard deviation based on the female data and make a statement interpreting these intervals.(12 points)

For questions 4 and 5, assume the population is normally distributed and the population standard deviation of shoulder heights is 11.75 centimeters.

4.Of the random sample, 40 bears were male.For these male bears, it was found that the sample mean shoulder height is 79.725 centimeters.Construct a 90% confidence interval for the population mean and statement interpreting this interval.(12 points)

5.What is the minimum sample size required if you want to be 99% confident that the sample mean is within 2.5 centimeters of the population mean of shoulder heights?(12 points)