Shoulder Height of Appalachian Black Bears Appalachian Bear Rescue (ABR) is a no
ID: 3021092 • Letter: S
Question
Shoulder Height of Appalachian Black Bears Appalachian Bear Rescue (ABR) is a not-for-profit organization located near the Great Smoky Mountains National Park. ABR's programs include the rehabilitation of orphaned and injured black bears, as well as research and education about Appalachian black bears, ABR provides the most natural environment possible for rehabilitating black bears before their release back into the wild. Recently, 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 found 68 black bears in the park and took measurement such as paw size, weight, and shoulder height. The stem-and-leaf plots below show the shoulder heights (in centimeters) of the 40 male and 28 female bears from the study. Shoulder Heights (in cm) of Male Bears Shoulder Heights (in cm) of Female Bears Exercise Use the sample to find a point estimate for the mean shoulder height of male bears female bears. Find the standard deviation of the sample of shoulder heights for the male bears female bears Use the sample to construct a 95% confidence interval for the mean shoulder height of male bears female bears. Use the sample to construct a 95% confidence interval for the mean shoulder height of all bears is the study. How do your results differ from those in Exercise 3? Explain. A research wants to estimate the mean shoulder heights for both male and female bears within 0.5 centimeter. Determine the minimum sample size required to construct a 99% confidence interval for the population mean shoulder height of male bears, Assume the population standard deviation is 7.8 centimeters.Explanation / Answer
3)For confidence intervals first we find mean and std dev of the sample
Male Bears Females Bears 49 57 50 68 67 69 68 71 71 71 72 72 73 72 73 72 73 72 73 72 73 73 74 73 74 73 75 74 75 74 75 75 75 75 75 76 75 76 76 77 79 78 81 78 82 84 82 82 83 83 83 84 84 84 85 85 93 86 Mean 75.67857 86 Std dev 7.59168 87 n 28 89 Std error 1.434693 90 90 93 96 97 99 102 114 Males Females 79.95122 Mean 75.679 40 n 28 11.99781 Std dev 7.5917 1.897021 std error 5.291503 Males Confidence interval 76.7813 83.12114 1.671 t0.05 1.701 3.169922 Mar of error 9.000846 Females conf interval 66.67815 84.67985