Pain Management: Laser Therapy “Effect of Helium-Neon Laser Auriculotherapy on Experimental Pain Threshold” is the title of an article in the journal Physical Therapy (Vol. 70, No. 1, pp. 24–30). In this article, laser therapy was discussed as a useful alternative to drugs in pain management of chronically ill patients. To measure pain threshold, a machine was used that delivered low-voltage direct current to different parts of the body (wrist, neck, and back). The machine measured current in milliamperes (mA). The pretreatment experimental group in the study had an average threshold of pain (pain was first detectable) at μ 5 3.15mA with standard deviation σ = 1.45mA. Assume that the distribution of threshold pain, measured in milliamperes, is symmetric and more or less mound-shaped. Use the
- (a) estimate a
range of milliamperes centered about the mean in which about 68% of the experimental group had a threshold of pain. - (b) estimate a range of milliamperes centered about the mean in which about 95% of the experimental group had a threshold of pain.
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Understandable Statistics: Concepts and Methods
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- Wild irises are beautiful flowers found throughout the United States, Canada, and northern Europe. This problem concerns the length of the sepal (leaf-like part covering the flower) of different species of wild iris. Data are based on information taken from an article by R. A. Fisher in Annals of Eugenics (Vol. 7, part 2, pp. 179 -188). Measurements of sepal length in centimeters from random samples of Iris setosa (I), Iris versicolor (II), and Iris virginica (III) are as follows below. I II III 5.6 5.5 6.9 4.5 6.6 5.5 5.4 6.5 4.3 5.4 4.6 7.9 4.7 5.6 5.8 5.9 6.6 6.3 5.6 5.6 6.9 Shall we reject or not reject the claim that there are no differences among the population means of sepal length for the different species of iris? (b) Find SSTOT, SSBET, and SSW and check that SSTOT = SSBET + SSW. (Use 3 decimal places.) SSTOT = SSBET = SSW = Find d.f.BET, d.f.W, MSBET, and MSW. (Use 4 decimal places for MSBET, and MSW.) dfBET = dfW =…arrow_forwardWild irises are beautiful flowers found throughout the United States, Canada, and northern Europe. This problem concerns the length of the sepal (leaf-like part covering the flower) of different species of wild iris. Data are based on information taken from an article by R. A. Fisher in Annals of Eugenics (Vol. 7, part 2, pp. 179 -188). Measurements of sepal length in centimeters from random samples of Iris setosa (I), Iris versicolor (II), and Iris virginica (III) are as follows below. I II III 5.5 5.2 6.7 4.4 6.5 5.7 5.2 6.9 4.1 5.9 4.4 7.8 4.3 5.5 5.7 5.3 6.4 6.1 5.8 5.5 6.9 Shall we reject or not reject the claim that there are no differences among the population means of sepal length for the different species of iris? Use a 10% level of significance. (a) What is the level of significance? (b) Find SSTOT, SSBET, and SSW and check that SSTOT = SSBET + SSW. (Use 3 decimal places.) SSTOT = ? SSBET = ? SSW = ? Find d.f.BET, d.f.W, MSBET, and…arrow_forwardThe Great White Shark. In an article titled “Great White, Deep Trouble” (National Geographic, Vol. 197(4), pp. 2–29), Peter Benchley—the author of JAWS—discussed various aspects of the Great White Shark (Carcharodon carcharias). Data on the number of pups borne in a lifetime by each of 80 Great White Shark females are provided on the WeissStats site. Use the technology of your choice to a. obtain frequency and relative-frequency distributions, using single-value grouping. b. construct and interpret either a frequency histogram or a relativefrequency histogram.arrow_forward
- Estriol Level and Birth Weight. J. Greene and J. Touchstone conducted a study on the relationship between the estriol levels of pregnant women and the birth weights of their children. Their findings, “Urinary Tract Estriol: An Index of Placental Function,” were published in the American Journal of Obstetrics and Gynecology (Vol. 85(1), pp. 1–9). The data from the study are provided on the WeissStats site, where estriol levels are in mg/24 hr and birth weights are in hectograms. a. Decide whether finding a regression line for the data is reasonable. If so, then also do parts (b)–(d). b. Obtain the coefficient of determination. c. Determine the percentage of variation in the observed values of the response variable explained by the regression, and interpret your answer. d. State how useful the regression equation appears to be for making predictions.arrow_forwardThe Norwegian government wants to know whether restricting the opening hours of liquor stores reduces alcohol consumption. Holger, an employee of Statistics Norway, is asked to investigate this research question. He uses panel data for n = 60 municipalities observed in T = 10 time periods. The data set contains information on per capita alcohol consumption (in liters per year) in municipality i in year t (alcoholit) and on the number of hours that liquor stores were open during year t in municipality i (hoursit). Holger estimates by OLS and obtains the following estimation results. regress alcohol Inhours, robust Linear regression alcohol alcoholit Bo + ßiln(hoursit) + Uit B Inhours cons Coef. 5.288235 2.768777 Robust Std. Err. .7486464 5.686286 t 0.49 P>|t| Number of obs = 0.626 R-squared Root MSE alcoholit = Bo+piln(hoursit) + ai + Uit [95% Conf. Interval] -8.398742 0.0745 .9568 a) Test the null hypothesis that B₁ = 0 at a 1% significance level. b) Use the above estimation results to…arrow_forwardThe amt of pollution in waterways…arrow_forward
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