The Appalachian Bear Center (ABC) is a not-for-profitorganization located near the Great Smoky Mountains National Park.ABC’s programs include the rehabilitation of orphaned and injuredblack bears, as well as research and education about Appalachianblack bears. ABC provides the most natural environment possible forrehabilitating black bears before their release back into the wild.Katie Settlage performed a study to learn more about theAppalachian black bear population in the Great Smoky MountainsNational Park. She and a team of researchers used a sample of 68black 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 fullcredit. Round all decimals to three places unless otherwisenoted.

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

Questions 2 and 3 refer to the following information regardingthe 28 female bears from the study. For these 28 female bears, thesample mean is 75.679 cm and the sample standard deviation is 7.592cm. Assume the data is normally distributed and the sample israndomly selected.

2. Use the female sample to make an interval estimate of themean shoulder height of female bears. Construct the confidenceinterval estimate using a 95% confidence level and make a statementinterpreting this interval.

3. Using a 99% level of confidence, construct the confidenceinterval for the population standard deviation based on the femaledata and make a statement interpreting these intervals.