Reference no: EM13580751
Q1. Hallux abducto valgus (call it HAV)is a deformation of the big toe that often requires surgery. Doctors used X-rays to measure the angle (in degrees) of deformity in 38 patients under the age of 21 who came to a medical center for surgery to correct HAV. The angle is a measure of the seriousness of the deformity. Here are the data:
28 32 25 34 38 26 25 18 30 26 28 13 20
21 17 16 21 23 14 32 25 21 22 20 18 26
16 30 30 20 50 26 28 31 38 38 21
It is reasonable to regard these patients as a random sample of young patients who require HAV surgery.
(a) Construct a 95% confidence interval for the mean HAV angle in the population of all such patients.
(b) Construct a histogram and assess the shape, center, and spread. Remove the patient(s) that who are outliers.
(c) Construct a 95% confidence interval for the population mean based on the remaining patients after you drop the outlier(s).
(d) Compare your interval in (a) with your interval in (c). What is the most important effect of removing the outlier(s)?
Q2. How much oil wells in a given field will ultimately produce is key information in deciding whether to drill more wells. Following are the estimated total amounts of oil recovered from 64 wells in the Devonian Richmond Dolomite area of the Michigan basin, in thousands of barrels.
Take these wells to be a Simple Random Sample of wells in this area.
21.71 53.2 46.4 42.7 50.4 97.7 103.1 51.9
43.4 69.5 156.5 34.6 37.9 12.9 2.5 31.4
79.5 26.9 18.5 14.7 32.9 196 24.9 118.2
82.2 35.1 47.6 54.2 63.1 69.8 57.4 65.6
56.4 49.4 44.9 34.6 92.2 37.0 58.8 21.3
36.6 64.9 14.8 17.6 29.1 61.4 38.6 32.5
12.0 28.3 204.9 44.5 10.3 37.7 33.7 81.1
12.1 20.1 30.5 7.1 10.1 18.0 3.0 2.0
Construct a 95% confidence interval for the mean amount of oil recovered from all wells in this area using t procedures.
Make a histogram of the data and discuss the shape, center, and spread. A computer-intensive method that gives accurate confidence intervals without assuming any specific shape of the distribution gives a 95% confidence interval of 40.28 to 60.32. How does the t interval that you constructed compare with this interval? Should the t procedures be used with this data?