Torsion during hip external rotation and extension may explain why acetabular labral tears occur in professional athletes. The article “Hip Rotational Velocities During the Full Golf Swing” (J. of Sports Science and Med., 2009: 296–299) reported on an investigation in which lead hip internal peak rotational velocity (x) and trailing hip peak external rotational velocity (y) were determined for a sample of 15 golfers. Data provided by the article’s authors was used to calculate the following summary quantities:
Separate normal probability plots showed very substantial linear patterns.
- a. Calculate a point estimate for the population
correlation coefficient . - b. Carry out a test at significance level .01 to decide whether there is a linear relationship between the two velocities in the sampled population.
- c. Would the conclusion of (b) have changed if you had tested appropriate hypotheses to decide whether there is a positive linear association in the population? What if a significance level of .05 rather than .01 had been used?
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Chapter 12 Solutions
Student Solutions Manual for Devore's Probability and Statistics for Engineering and the Sciences, 9th
- The article "Modeling of Urban Area Stop-and-Go Traffic Noise" (P. Pamanikabud and C. Tharasawatipipat, Journal of Transportation Engineering, 1999:152–159) presents measurements of traffic noise, in dBA, from 10 locations in Bangkok, Thailand. Measurements, presented in the following table, were made at each location, in both the acceleration and deceleration lanes. Location Acceleration Deceleration 78.1 78.6 78.1 80.0 3 79.6 79.3 4 81.0 79.1 78.7 78.2 78.1 78.0 78.6 78.6 78.5 78.8 78.4 78.0 10 79.6 78.4 Can you conclude that there is a difference in the mean noise levels between acceleration and deceleration lanes?arrow_forwardLow back pain (LBP) is a serious health problem in many industrial settings.The scientific article (Ergnomics, 1995: 2107-2117) reported the accompanying data on lateral rangeof motion (in degrees) for a sample of workers with no history of low back pain and another sample with a history of low back pain. a) Perform the hypothesis test to determine if the type of lateral movement in degrees is affected by the pre-existing condition with a 95% confidence level. b) Calculate a 90% confidence interval for the difference between the mean degree of lateral movement of the population for the two conditions.The interval suggests that the mean lateral movement differs in the two conditions?Does the interval suggest that the mean lateral movement differs in the two conditions? Is the message different if a 95% confidence interval is used? Note:The exercise in the image is the original, it is in Spanish, but it is easy to understand.arrow_forwardRefer to laserjeans.xlsx to answer the questions below. These real data come from Ondogan, Z., Pamuk, O., Ondogan, E. N., & Ozguney, A. (2005). Improving the appearance of all textile products from clothing to home textile using laser technology. Optics and Laser Technology, 37, 631-637. Researchers sought to test the differences in tensile strength of jeans designed by hand versus those designed with lasers. 1. What type of measurement scale do each of the five variables use? 2. Create histograms for those that are continuous (interval or ratio). How would you describe the shape of these distributions? 3. A textile researcher wants to simplify the strength data by turning this continuous variable into an ordinal variable with 10 equal interval widths. Given that the lowest force resulting in a rip was 860 N, and the greatest force resulting in a rip was 1,450 N, what should the interval widths (also called bins or breaks) be? Fill in the second column of the…arrow_forward
- During the spring of 1999, many fuel storage facilities in Serbia were destroyed by bombing. As a result, significant quantities of oil products were spilled and burned,resulting in soil pollution. The article “Mobility of Heavy Metals Originating from Bombing of Industrial Sites” (B. Škrbić, J. Novaković, and N. Miljević, Journal of Environmental Science and Health, 2002:7–16) reports measurements of heavy metal concentrations at several industrial sites in June 1999, just after the bombing, and again in March of 2000. At the Smederevo site, on the banks of the Danube River, eight soil specimens taken in 1999 had an average lead concentration (in mg/kg) of 10.7 with a standard deviation of 3.3. Four specimens taken in 2000 had an average lead concentration of 33.8 with a standard deviation of 0.50. Find a 95% confidence interval for the increase in lead concentration between June 1999 and March 2000.arrow_forwardThe decline of salmon fisheries along the Columbia River in Oregon has caused great concern among commercial and recreational fishermen. The paper 'Feeding of Predaceous Fishes on Out-Migrating Juvenile Salmonids in John Day Reservoir, Columbia River' (Trans. Amer. Fisheries Soc. (1991: 405-420) gave the accompanying data on 10 values for the data sets where y = maximum size of salmonids consumed by a northern squaw fish (the most abundant salmonid predator) and x = squawfish length, both in mm. Here is the computer software printout of the summary: Coefficients: Estimate Std. Error t value Pr(> |t|) (Intercept) −90.020 16.702 −5.390 0.000 Length 0.705 0.049 14.358 0.000 Using this information, compute a 95% confidence interval for the slope.arrow_forwardThe article “Arsenic and Mercury in Lake Whitefish and Burbot Near the Abandoned Giant Mine on Great Slave Lake” (P. Cott, B. Zajdlik, et al., Journal of Great Lakes Research, 2016:223–232) presents measurements of arsenic concentrations in fish found in Northern Canada. In a sample of 8 whitefish caught in Yellowknife Bay, the mean arsenic concentration in the liver was 0.32 mg/kg, with a standard deviation of 0.05 mg/kg. Can you conclude that the mean arsenic concentration in whitefish in Yellowknife Bay is greater than 0.3 mg/kg?arrow_forward
- Foot ulcers are a common problem for people with diabetes. Higher skin temperatures on the foot indicate an increased risk of ulcers. The article "An Intelligent Insole for Diabetic Patients with the Loss of Protective Sensation" (Kimberly Anderson, M.S. Thesis, Colorado School of Mines), reports measurements of temperatures, in °F, of both feet for 181 diabetic patients. The results are presented in the following table. Left Foot Right Foot 80 80 85 85 75 80 88 86 89 87 87 82 78 78 88 89 89 90 76 81 89 86 87 82 78 78 80 81 87 82 86 85 76 80 88 89 Construct a scatterplot of the right foot temperature (y) versus the left foot temperature (x). Verify that a linear model is appropriate. b. Compute the least-squares line for predicting the right foot temperature from the left foot temperature. If the left foot temperatures of two patients differ by 2 degrees, by how much would you predict their right foot temperatures to differ? Predict the right foot temperature for a patient whose left…arrow_forwardThe depth of wetting of a soil is the depth to which water content will increase owing to extemal factors. The article "Discussion of Method for Evaluation of Depth of Wetting in Residential Areas" (J. Nelson, K. Chao, and D. Overton, Journal of Geotechnical and Geoenvironmental Engineering, 2011:293-296) discusses the relationship between depth of wetting beneath a structure and the age of the structure. The article presents measurements of depth of wetting, in meters, and the ages, in years, of 21 houses, as shown in the following table. Age Depth 7.6 4 4.6 6.1 9.1 3 4.3 7.3 5.2 10.4 15.5 5.8 10.7 4 5.5 6.1 10.7 10.4 4.6 7.0 6.1 14 16.8 10 9.1 8.8 Compute the least-squares line for predicting depth of wetting (y) from age (x). b. Identify a point with an unusually large x-value. Compute the least-squares line that results from deletion of this point. Identify another point which can be classified as an outlier. Compute the least-squares line that results from deletion of the outlier,…arrow_forwardwidely used as dielectrics and coolants in electrical systems in the past. They were found to be a major environmental contaminant in the 1960s. In a study, the mean PCB content at each of thirteen sites was reported for the years 1982 and 1996 (from “The ratio of DDE to PCB concentrations in Great Lakes herring gull eggs and its use in interpreting contaminants data”, Journal of Great Lakes Research 24 (1): 12-31, 1998). The data are below.Site:12345678910111213198261.4864.4745.5059.7058.8175.9671.5738.0630.5139.7029.7866.8963.93199613.9918.2611.2810.0221.0017.3628.207.3012.809.4112.6316.8322.74(a) Which test would be more appropriate in this case: a t-test for the difference between two population means, or a paired t-test? Why?(b) Do the data provide sufficient evidence to support the claim that the mean PCB level has decreased in the region? Be sure to check all assumptions, write the null and alternative hypotheses, calculate the appropriate test statistic, calculate the p-value,…arrow_forward
- The article "Refinement of Gravimetric Geoid Using GPS and Leveling Data" (W. Thurston, Journal of Surveying Engineering, 2000:27-56) presents a method for measuring orthometric heights above sea level. For a sample of 1225 baselines, 926 gave results that were within the class C spirit leveling tolerance limits. Can we conclude that this method produces results within the tolerance limits more than 75% of the time? Test on a 5% significance level. The P-value is 0.32, we cannot conclude that the method produces good results more than 75% of the time. The P-value is 0.01, we can conclude that the method produces good results more than 75% of the time. The P-value is 0.03, we can conclude that the method produces good results more than 75% of the time. The P-value is 0.27, we cannot conclude that the method produces good results more than 75% of the time.arrow_forwardAortic stenosis refers to a narrowing of the aortic valvein the heart. The article “Correlation Analysis ofStenotic Aortic Valve Flow Patterns Using PhaseContrast MRI” (Annals of Biomed. Engr., 2005:878–887) gave the following data on aortic root diameter(cm) and gender for a sample of patients having variousdegrees of aortic stenosis:M: 3.7 3.4 3.7 4.0 3.9 3.8 3.4 3.6 3.1 4.0 3.4 3.8 3.5F: 3.8 2.6 3.2 3.0 4.3 3.5 3.1 3.1 3.2 3.0a. Compare and contrast the diameter observations forthe two genders.b. Calculate a 10% trimmed mean for each of the twosamples, and compare to other measures of center(for the male sample, the interpolation method mentionedin Section 1.3 must be used).arrow_forwardThe authors of the paper "Statistical Methods for Assessing Agreement Between Two Methods of Clinical Measurement"† compared two different instruments for measuring a person's ability to breathe out air. (This measurement is helpful in diagnosing various lung disorders.) The two instruments considered were a Wright peak flow meter and a mini-Wright peak flow meter. Seventeen people participated in the study, and for each person air flow was measured once using the Wright meter and once using the mini-Wright meter. Subject Mini-WrightMeter WrightMeter Subject Mini-WrightMeter WrightMeter 1 512 494 10 445 433 2 430 395 11 432 417 3 520 516 12 626 656 4 428 434 13 260 267 5 500 476 14 477 478 6 600 557 15 259 178 7 364 413 16 350 423 8 380 442 17 451 427 9 658 650 (a) Suppose that the Wright meter is considered to provide a better measure of air flow, but the mini-Wright meter is easier to transport and to use. If the two types of meters produce different…arrow_forward
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