Quantitative noninvasive techniques are needed for routinely assessing symptoms of peripheral neuropathies, such as carpal tunnel syndrome (CTS). The article “A Gap Detection Tactility Test for Sensory Deficits Associated with Carpal Tunnel Syndrome” (Ergonomics, 1995: 2588–2601) reported on a test that involved sensing a tiny gap in an otherwise smooth surface by probing with a finger; this
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Chapter 9 Solutions
Student Solutions Manual for Devore's Probability and Statistics for Engineering and the Sciences, 9th
- Quantitative noninvasive techniques are needed for routinely assessing symptoms of peripheral neuropathies, such as carpal tunnel syndrome (CTS). An article reported on a test that involved sensing a tiny gap in an otherwise smooth surface by probing with a finger; this functionally resembles many work-related tactile activities, such as detecting scratches or surface defects. When finger probing was not allowed, the sample average gap detection threshold for m - 8 normal subjects was 1.75 mm, and the sample standard deviation was 0.55; forn - 12 CTS subjects, the sample mean and sample standard deviation were 2.52 and 0.85, respectively. Does this data suggest that the true average gap detection threshold for CTS subjects exceeds that for normal subjects? State and test the relevant hypotheses using a significance level of 0.01. (Use y, for normal subjects and for CTS subjects.) lo Hoi Uy M20 Hg: H₂H₂O | Ho: M₁ M₂ = 0 H₂H-Hy 20 ⒸH₂²A₁-M₂ = 0 Hải phim thay D |0 No: 111-112-0 H₂H₁-H₂0…arrow_forwardMagnet Treatment of Pain Researchers conducted a study to determine whether magnets are effective in treating back pain, with results given below (based on data from “Bipolar Permanent Magnets for the Treatment of Chronic Lower Back Pain: A Pilot Study,” by Collacott, Zimmerman, White, and Rindone, Journal of the American Medical Association, Vol. 283, No. 10). The values represent measurements of pain using the visual analog scale. Use a 0.05 significance level to test the claim that those given a sham treatment (similar to a placebo) have pain reductions that vary more than the pain reductions for those treated with magnets.arrow_forwardA study of the relationship between age and various visual functions (such as acuity and depth perception) reported the following observations on the area of scleral lamina (mm2) from human optic nerve heads: 2.79 2.66 2.80 3.92 2.28 2.81 4.02 4.16 3.95 4.26 3.51 4.61 2.37 3.66 2.72 3.64 2.96 (a) Calculate Σxi and Σxi2. (Round Σxi2 to two decimal places.) Σxi = mm2 Σxi2 = mm4 (b) Use the values calculated in part (a) to compute the sample variance s2 and then the sample standard deviation s. (Round your answers to three decimal places.) s2 = mm4 s = mm2arrow_forward
- Quantitative noninvasive techniques are needed for routinely assessing symptoms of peripheral neuropathies, such as carpal tunnel syndrome (CTS). An article reported on a test that involved sensing a tiny gap in an otherwise smooth surface by probing with a finger; this functionally resembles many work-related tactile activities, such as detecting scratches or surface defects. When finger probing was not allowed, the sample average gap detection threshold for m = 5 normal subjects was 1.62 mm, and the sample standard deviation was 0.53; for n = 10 CTS subjects, the sample mean and sample standard deviation were 2.36 and 0.85, respectively. Does this data suggest that the true average gap detection threshold for CTS subjects exceeds that for normal subjects? USE SALT State and test the relevant hypotheses using a significance level of 0.01. (Use μ, for normal subjects and #₂ for CTS subjects.) о но н1-12=0 Hải Hy M220 о но: 1-12=0 Hai H₁ - H₂ #0 о но: 1-12=0 Ha Hy - My 30 ⒸH₁² H₁-H₂ = 0…arrow_forwardA study of the relationship between age and various visual functions (such as acuity and depth perception) reported the following observations on the area of scleral lamina (mm2) from human optic nerve heads: 2.71 2.56 2.64 3.91 2.24 2.84 4.00 4.20 3.80 4.35 3.40 4.50 2.49 3.73 2.83 3.55 2.91 LAUSE SALT (a) Calculate Ex, and Ex₁². mm² Σχιζ = | (b) Use the values calculated in part (a) to compute the sample variance s² and then the sample standard deviation s. (Round your answers to four decimal places.) s² = mm4 mm² S= 4 mmarrow_forwardAn article in Knee Surgery, Sports Traumatology, Arthroscopy (2005, Vol. 13, pp. 273-279), considered arthroscopic meniscal repair with an absorbable screw. Results showed that for tears greater than 25 millimeters, 15 of 17 repairs were successful while for shorter tears, 22 of 31 repairs were successful. (a) Is there evidence that the success rate is greater for longer tears? Use a = 0.05.What is the P-value? (b) Calculate a one-sided 95% confidence bound on the difference in proportions that can be used to answer the question in part (a). (a) There evidence that the success rate is greater for longer tears. The P-value is Round your answer to four decimal places (e.g. 98.7654). (b) The one-sided 95% confidence bound is SPi - P2. Round your answer to three decimal places (e.g. 98.765).arrow_forward
- The purpose of a study was to determine the effectiveness of segmental wire fixation in athletes with spondylolysis. Between 1993 and 2000, 20 athletes (6 women and 14 men) with lumbar spondylolysis were treated surgically with the technique. The following table gives the Japanese Orthopaedic Association (JOA) evaluation score for lower back pain syndrome for men and women prior to the surgery. The lower score indicates less pain. Assume that the two populations of pain scores are normally distributed with equal variances. Gender JOA scores Female 14, 13, 24, 21, 20, 21 Male 21, 26, 24, 24, 22, 23, 18, 24, 13, 22, 25, 23, 21, 25 What is the pooled variance? (Answer was calculated using 3 decimals places for intermediate steps.)arrow_forwardThe purpose of a study was to determine the effectiveness of segmental wire fixation in athletes with spondylolysis. Between 1993 and 2000, 20 athletes (6 women and 14 men) with lumbar spondylolysis were treated surgically with the technique. The following table gives the Japanese Orthopaedic Association (JOA) evaluation score for lower back pain syndrome for men and women prior to the surgery. The lower score indicates less pain. Assume that the two populations of pain scores are normally distributed with equal variances. Gender JOA scoresFemale 14, 13, 24, 21, 20, 21Male 21, 26, 24, 24, 22, 23, 18, 24, 13, 22, 25, 23, 21, 25 What is the upper AND lower bound of a 90% confidence interval for the difference in means? (Hint: Use Female – Male)arrow_forwardPrevious studies have shown that playing video games can increase visual perception abilities on tasks presented in the gaming zone of the screen (within 5 degrees of the center). A graduate student is interested in whether playing video games increases peripheral visual perception abilities or decreases attention to peripheral regions because of focus on the gaming zone. For her study, she selects a random sample of 64 adults. The subjects complete a difficult spatial perception task to determine baseline levels of their abilities. After playing an action video game (a first-person combat simulation) for 1 hour a day over 10 days, they complete the difficult perception task for a second time. Before playing the action video game, the mean score in their accuracy on the spatial task was 0.42. After playing the action video game, the mean score was -0.08. The mean of the differences between each person's pre- and postscores was 0.5, with a standard deviation of the differences equal to…arrow_forward
- Neurologists have found that the hippocampus, a structure located in the brain, plays an important role in short-term memory. Data was collected on 21 Vietnam veterans with combat related post-traumatic stress disorder. Magnetic resonance imaging was used to measure the volume of the right hippocampus (in cubic millimeters) of each subject, while the verbal memory retention of each subject was measured by the percent retention subscale of the Wechsler Memory Scale. The least squares line relating verbal memory (y) with right hippocampal volume (x) was found to be 4 + 3x. The slope of the regression line can be interpreted in the following way: ŷ = When right hippocampal volume decreases by one cubic millimeter, the verbal memory score increases by 3%. When right hippocampal volume decreases by one cubic millimeter, the verbal memory score increases by 4%. When right hippocampal volume increases by one cubic millime decreases by 3%. the verbal memory score When right hippocampal volume…arrow_forwardPrevious studies have shown that playing video games can increase visual perception abilities on tasks presented in the gaming zone of the screen (within 5 degrees of the center). A graduate student is interested in whether playing video games increases peripheral visual perception abilities or decreases attention to peripheral regions because of focus on the gaming zone. For her study, she selects a random sample of 64 adults. The subjects complete a difficult spatial perception task to determine baseline levels of their abilities. After playing an action video game (a first-person combat simulation) for 1 hour a day over 10 days, they complete the difficult perception task for a second time. Before playing the action video game, the mean Score in their accuracy on the spatial task was 0.42. After playing the action video game, the mean score was -0.08. The mean of the differences between each person's pre- and postscores was 0.5, with a standard deviation of the differences equal to…arrow_forwardPrevious studies have shown that playing video games can increase visual perception abilities on tasks presented in the gaming zone of the screen (within 5 degrees of the center). A graduate student is interested in whether playing video games increases peripheral visual perception abilities or decreases attention to peripheral regions because of focus on the gaming zone. For her study, she selects a random sample of 64 adults. The subjects complete a difficult spatial perception task to determine baseline levels of their abilities. After playing an action video game (a first-person combat simulation) for 1 hour a day over 10 days, they complete the difficult perception task for a second time. Before playing the action video game, the mean score in their accuracy on the spatial task was 0.42. After playing the action video game, the mean score was -0.08. The mean of the differences between each person's pre- and postscores was 0.5, with a standard deviation of the differences equal to…arrow_forward
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