The height of a patient is useful for a variety of medical purposes, such as estimating tidal volume of someone in an intensive care who requires artificial ventilation. However, it can be difficult to make an accurate measurement if the patient is confused, unconscious, or sedated. And measurement of height while an individual is lying down is also not straightforward. In contrast, ulna length measurements are generally quick and easy to obtain, even in chair- or bed-bound patients. The accompanying data on x = ulna length (cm) and y = height (cm) for males older than 65 was read from a graph in the article “Ulna Length to Predict Height in English and Portuguese Patient Populations” (European J. of Clinical Nutr., 2012: 209–215).
x | 22.5 | 22.8 | 22.8 | 23.3 | 23.3 | 24.4 | 25.0 |
y | 158 | 155 | 156 | 160 | 161 | 162 | 164 |
x | 25.0 | 25.0 | 25.0 | 26.0 | 26.0 | 26.8 | 28.2 |
y | 166 | 167 | 170 | 166 | 173 | 178 | 174 |
Summary quantities include Σxi = 346.1, Σyi = 2310,
Sxx = 36.463571, Sxy = 137.60, Syy = 626.00.
- a. Obtain the equation of the estimated regression line and interpret its slope.
- b. Calculate and interpret the coefficient of determination.
- c. Carry out a test of model utility.
- d. Calculate prediction intervals for the heights of two individuals whose ulna lengths are 23 and 25, respectively; use a prediction level of 95% for each interval.
- e. Based on the predictions of (d), would you agree with the statement in the cited article that “height can be predicted from ulna length with precision”?
Trending nowThis is a popular solution!
Chapter 12 Solutions
Probability and Statistics for Engineering and the Sciences
- Is it true that z values have no units of measurements?arrow_forwardThe sides of a rectangle measure 5 ± 1 (cm) and 8 ± 2 (cm). How much is your area worth?Consider the statistical hypothesis to calculate the propagation of errorsarrow_forwardThe department of zoology at the Virginia Polytechnic Institute and State University carried out a study to determine if there is a significant difference in the density of organisms in two different stations located in Cedar Run, a secondary river that is located in the river basin. Roanoke. Drainage from a sewage treatment plant and overflow from the Federal Mogul Corporation sedimentation pond enter the flow near the source of the river. The following data give the density measurements, in numbers of organisms per square meter, at the two different collecting stations. Number of organisms per square meter Station 1 Station 2 5030 2800 13700 4670 10730 6890 11400 7720 860 7030 2200 7330 4250 2810 15040 1330 4980 3320 11910 1230 8130 2130 26850 2190 17660 22800 1130 1690 With a significance level of 0.05, can we conclude that the densities are the same in the two…arrow_forward
- what is z observed?arrow_forwardDo the data in the accompanying table support Kepler’s third law? Give reasons for your answer.arrow_forwardThe average weight of a Coastal male Grizzly Bear is approximately normal with E(x); =795 pounds and SD * (x) = 80 pounds. 8. How likely is it to randomly select 64 Coastal male Grizzly Bears with a sample average weight of 810 pounds or more? Which density curve is the best model for this problem?arrow_forward
- The determination of the shear strength of spot welds is relatively difficult, whereas measuring the weld diameter of spot welds is relatively simple. As a result, it would be advantageous if shear strength could be predicted from a measurement of weld diameter. The data are as follows: Shear strength (psi) Weld diameter (0.0001 in) 370 400 780 800 1210 1250 1560 1600 1980 2000 2450 2500 3070 3100 3550 3600 3940 4000 3950 4000 a) Test the hypothesis that the slope of the regression line is equal to 1 at the 0.05 level of significance.arrow_forwardIf we went ahead and used parametric statistics, even though our usual assumptions were NOT met, what would be the result?arrow_forwardAlso find the third quartile.arrow_forward
- For normally distributed data, what is the area greater than z = 0.34?arrow_forwardIn the 2015 AFC Championship game, there was a charge that the New England Patriots underinflated their footballs for an advantage. The Patriots' opponents during the championship game were the Indianapolis Colts. Measurements of the Colts' footballs were taken. The balls should be inflated to between 12.5 and 13.5 pounds per square inch (psi). The accompanying data consists of six of the eight measurements on the Colts' footballs. Complete parts (a) and (b) below. 12.75, 12.50, 12.15, 12.35, 12.55, 12.30 The test statistic is = (Round to two decimal places as needed.) The p-value is = (Round to three decimal places as needed.) b. Use the data to construct a 95% confidence interval for the mean psi for the Colts' footballs. How does this confidence interval support your conclusion in part (a)? The 95% confidence interval is ___ psi to ___ psi. (Round to two decimal places as needed. Use ascending order.)arrow_forwardAn ecologist hypothesizes that birds with longer wing spans use wider tree branches. The ecologist captured male birds, measured their wing span and other characteristics in millimeters, and then marked and released them. During the ensuing winter, the ecologist repeatedly observed the marked birds as they foraged for food on tree branches. He noted the branch diameter on each occasion, and calculated the average branch diameter for each bird in centimeters. The measurement data are below. What can the ecologist conclude with an α of 0.05 wing span branch diameter 79.380.180.781.579.580.781.180.580.7 1.561.531.391.041.391.021.211.311.21 A) What is the appropriate statistic? Then Compute the statistic B) Compute the appropriate test statistic(s) for H1: ρ > 0 critical value = test statistic= C) Effect Sizearrow_forward
- MATLAB: An Introduction with ApplicationsStatisticsISBN:9781119256830Author:Amos GilatPublisher:John Wiley & Sons IncProbability and Statistics for Engineering and th...StatisticsISBN:9781305251809Author:Jay L. DevorePublisher:Cengage LearningStatistics for The Behavioral Sciences (MindTap C...StatisticsISBN:9781305504912Author:Frederick J Gravetter, Larry B. WallnauPublisher:Cengage Learning
- Elementary Statistics: Picturing the World (7th E...StatisticsISBN:9780134683416Author:Ron Larson, Betsy FarberPublisher:PEARSONThe Basic Practice of StatisticsStatisticsISBN:9781319042578Author:David S. Moore, William I. Notz, Michael A. FlignerPublisher:W. H. FreemanIntroduction to the Practice of StatisticsStatisticsISBN:9781319013387Author:David S. Moore, George P. McCabe, Bruce A. CraigPublisher:W. H. Freeman