Concept explainers
The degenerative disease osteoarthritis most frequently affects weight-bearing joints such as the knee. The article “Evidence of Mechanical Load Redistribution at the Knee Joint in the Elderly When Ascending Stairs and Ramps” (Annals of Biomed. Engr., 2008: 467–476) presented the following summary data on stance duration (ms) for samples of both older and younger adults.
Age | Sample Mean | Sample SD | |
Older | 28 | 801 | 117 |
Younger | 16 | 780 | 72 |
Assume that both stance duration distributions are normal.
a. Calculate and interpret a 99% CI for true average stance duration among elderly individuals.
b. Carry out a test of hypotheses at significance level .05 to decide whether true average stance duration is larger among elderly individuals than among younger individuals.
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Chapter 9 Solutions
Probability and Statistics for Engineering and the Sciences
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- Following are the protein contents measured in two types of species:Species 1: 0.72 1.12 0.81 0.89 0.72 0.81 1.01 0.75 0.83Species 2: 1.21 0.93 0.80 1.12 1.22 0.94 0.87 i) Assuming normality, test the hypothesis that the two species have the sameaverage protein contents by using 5-step hypothesis testing procedure at 5 %level of significance, and using the critical values approach.ii) Calculate the p-value of this test and make decision.iii) Write down the standard error of this test and calculate its numerical value ?arrow_forwardSuppose a researcher is interested inthe effectiveness in a new childhood exercise program implemented in a SRS of schools across a particular county. In order to test the hypothesis that the new program decreases BMI (Kg/m2), the researcher takes a SRS of children from schools where the program is employed and a SRS from schools that do not employ the program and compares the results. Assume the following table represents the SRSs of students and their BMIs. Student intervention group BMI (kg/m2) Student control group BMI (kg/m2) A 18.6 A 21.6 B 18.2 B 18.9 C 19.5 C 19.4 D 18.9 D 22.6 E 24.1 F 23.6 A) Assuming that all the necessary conditions are met (normality, independence, etc.) carry out the appropriate statistical test to determine if the new exercise program is effective. Use an alpha level of 0.05. Do not assume equal variances.B) Construct a 95% confidence interval about your estimate for the average difference in BMI between the groups.arrow_forwardThe article “Dynamics of Insulin Action in Hypertension: Assessment from Minimal ModelInterpretation of Intravenous Glucose Tolerance Test Data” (R. Burattini, M. Morettini, etal., Med Biol Eng Comput, 2011:831–841) compared levels of an insulin sensitivity index SIin patients with high blood pressure and patients with normal blood pressure. Ten patientswith high blood pressure had a mean value of 3.4 with a standard deviation of 0.6, and eightpatients with normal blood pressure had a mean value of 7.9 with a standard deviation of0.6. Units are 10−5 · min−1 · pmol−1. Find a 98% confidence interval for the difference inmean levels between those with high blood pressure and those with normal blood pressure.arrow_forward
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