The article “Supervised Exercise Versus Non- Supervised Exercise for Reducing Weight in Obese Adults” (The J. of Sports Med. and Physical Fitness, 2009: 85–90) reported on an investigation in which participants were randomly assigned to either a supervised exercise program or a control group. Those in the control group were told only that they should take measures to lose weight. After 4 months, the sample
a. Calculate a 99% lower prediction bound for the weight loss of a single randomly selected individual subjected to the supervised exercise program. Can you be highly confident that such an individual will actually lose weight?
b. Does it appear that true average decrease in body fat is more than two kg larger for the experimental condition than for the control condition? Use the accompanying Minitab output to reach a conclusion at significance level of .01. [Note: Minitab accepts such summary data as well as individual observations. Also, because the test is upper-tailed, the software provides a lower confidence bound rather than a conventional CI.]
Sample | N | Mean | StDev | SE Mean |
Exptl. | 17 | 6.20 | 4.50 | 1.1 |
Control | 17 | 1.70 | 3 .10 | 0.75 |
Difference 5 mu (1) 2 mu (2)
Estimate for difference: 4.50
95% lower bound for difference: 2.25
T-Test of difference 5 2 (vs >):
T-Value 5 1.89
P-Value 5 0.035 DF 5 28
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Chapter 9 Solutions
Student Solutions Manual for Devore's Probability and Statistics for Engineering and the Sciences, 9th
- What is meant by the sample space of an experiment?arrow_forwardWhat is an experiment?arrow_forwardSleep apnea is a disorder in which there are pauses in breathing during sleep. People with this condition must wake up frequently to breathe. The article “Postoperative Complications in Patients With Obstructive Sleep Apnea Syndrome Undergoing Hip or Knee Replacement: A Case-Control Study” (R. Gupta, J. Parvizi, et al., Mayo Clinic Proceedings, 2001:897–905) reported that in a sample of 427 people 65 and over, 104 of them had sleep apnea. a) Find a 95% confidence interval for the proportion of those 65 and over who have sleep apnea. b) Find a 99% confidence interval for the proportion of those 65 and over who have sleep apnea. c) Find the sample size needed for a 95% confidence interval to specify the proportion to within ±0.03. d) Find the sample size needed for a 99% confidence interval to specify the proportion to within ±0.03.arrow_forward
- A case−control study was performed among 145 subjects with macular degeneration and 34 controls, all of whom were 70- to 79-year-old women. A genetic risk score was developed to help differentiate the cases from the controls. The risk score was categorized into six groups (1, 2, 3, 4, 5, 6), with 6 being the highest risk and 1 being the lowest risk.The data in Table 10.48 were obtained relating the risk score to case/control status. taBlE 10.48 risk score cases controls 1 3 11 2 7 3 3 6 6 4 10 8 5 11 2 6 108 4 total 145 34 10.139 What test can be performed to study the asso- ciation between case/control status and risk score? Spe- cifically, we are interested in testing whether cases tend to have consistently higher risk scores or consistently lower risk scores than controls.arrow_forwardAngioplasty is a medical procedure in which an obstructed blood vessel is widened. In some cases, a wire mesh tube, called a stent, is placed in the vessel to help it remain open. The article “Long-term Outcomes of Patients Receiving Drug-eluting Stents” (A. Philpott, D. Southern, et al., Canadian Medical Association Journal, 2009:167–174) presents the results of a study comparing the effectiveness of a bare metal stent with one that that has been coated with a drug designed to prevent reblocking of the vessel. A total of 5320 patients received bare metal stents, and of these, 841 needed treatment for reblocking within a year. A total of 1120 received drug coated stents, and 134 of them required treatment within a year. a) Find a 98% confidence interval for the differences between the proportions for drug coated stents and bare metal stents. b) Suppose that additional patients are to be treated in order to increase the precision of the confidence interval. Three sampling plans are…arrow_forwardA pathological video game user (PVGU) is a video game user that averages 31 or more hours a week of gameplay. According to the article “Pathological Video Game Use among Youths: A Two-Year Longitudinal Study” (Pediatrics, Vol. 127, No. 2, pp. 319–329) by D. Gentile et al., in 2011, about 9% of children in grades 3–8 were PVGUs. Suppose that, today, five youths in grades 3–8 are randomly selected. Let X represent the number of youths who are PVGUs. n = p = 1 – p = Prepare the probability distribution for the random variable X. Complete the following table. Round your answers to 4 decimal places e.g. 0.XXXX or .XXXX. X = x P(X=x) 0 1 2 3 4 5 ∑=1.0000∑=1.0000 Calculate the probability that EXACTLY three youths are PVGUs. Round your answers to 4 decimal places e.g. 0.XXXX or .XXXX. P(X = 3) = Calculate the probability that AT LEAST two youths are PVGUs. Round your answers to 4 decimal places e.g. 0.XXXX or .XXXX. P(X ≥ 2) = Calculate the…arrow_forward
- A pathological video game user (PVGU) is a video game user that averages 31 or more hours a week of gameplay. According to the article “Pathological Video Game Use among Youths: A Two-Year Longitudinal Study” (Pediatrics, Vol. 127, No. 2, pp. 319–329) by D. Gentile et al., in 2011, about 9% of children in grades 3–8 were PVGUs. Suppose that, today, five youths in grades 3–8 are randomly selected. Let X represent the number of youths who are PVGUs. Calculate the probability that EXACTLY three youths are PVGUsarrow_forwardWorker Fatigue. A study by M. Chen et al. titled "Heat Stress Evaluation and Worker Fatigue in a Steel Plant" (American Industrial Hygiene Association, Vol. 64, pp. 352-359) assessed fatigue in steel- plant workers due to heat stress. A random sample of 29 casting work- ers had a mean post-work heart rate of 78.3 beats per minute (bpm). At the 5% significance level, do the data provide sufficient evidence to conclude that the mean post-work heart rate for casting workers ex- ceeds the normal resting heart rate of 72 bpm? Assume that the popu- lation standard deviation of post-work heart rates for casting workers is 11.2 bpm. Perform one mean Z procedure a. Hypothesis: (5 points) b. Test statistic: (5 points) C. Critical-value: (4 points) d. P Value (4 Points) e. Hypothesis test conclusion and interpretation: (2 points)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
- Calcium and Blood Pressure: Sample data were collected in a study of calcium supplements and their effects on blood pressure. A placebo group and a calcium group began the study with blood pressure measurements (based on data from “Blood Pressure and Metabolic Effects of Calcium Supplementation in Normotensive White and Black Men,” by Lyle et al., Journal of the American Medical Association, Vol. 257, No. 13). Sample values are listed below. At the 0.05 significance level, test the claim that the two sample groups come from population with the same standard deviation. Placebo: 124.6 104.8 96.5 116.3 106.1 128.8 107.2 123.1 118.1 108.5 120.4 122.5 113.6 Calcium: 129.1 123.4 102.7 118.1 114.7 120.9 104.4 116.3 109.6 127.7 108.0 124.3 106.6 121.4 113.2…arrow_forwardCalcium and Blood Pressure Does increasing the amount of calcium in our diet reduce blood pressure? Examination of a large sample of people revealed a relationship between calcium intake and blood pressure. Such observational studies do not establish causation. Researchers therefore designed a randomized comparative experiment. The subjects were 21 healthy men who volunteered to take part in the experiment. They were randomly assigned to two groups: 10 of the men received a calcium supplement for 12 weeks, while the control group of 11 men received a placebo pill that looked identical. The experiment was double-blind. The response variable is the decrease in systolic (top number) blood pressure for a subject after 12 weeks, in millimeters of mercury. An increase appears as a negative number. Do the data provide convincing evidence that a calcium supplement reduces blood pressure more than a placebo, on average, for subjects like the ones in this study? Group 1 (calcium) Group (placebo)…arrow_forward
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