Is injecting medical cement effective in reducing pain for people who have suffered fractured vertebrae? A paper describes an experiment to compare patients who underwent vertebroplasty (the injection of cement) to patients in a placebo group who underwent a fake procedure in which no cement was actually injected. Because the placebo procedure was similar to the vertebroplasty procedure except for the actual injection of cement, patients participating in the experiment were not aware of which treatment they received. All patients were asked to rate their pain at three different times—3 days, 14 days, and 1 month after the procedure. Summary statistics are given in the accompanying table. Pain Intensity Vertebroplasty Group Placebo Group n = 76 n = 62 mean sd mean sd 3 days 4.2 2.8 3.9 2.9 14 days 4.3 2.9 4.5 2.8 1 month 3.9 2.9 4.6 3.0 Construct and interpret a 95% confidence interval for the difference in mean pain intensity 3 days after treatment for the vertebroplasty treatment and the fake treatment. (Use μVertebroplasty − μPlacebo. Round your answers to two decimal places.) ___ to Construct and interpret 95% confidence intervals for the difference in mean pain intensity at 14 days after treatment. (Use μVertebroplasty − μPlacebo. Round your answers to two decimal places.) _ to ___ Construct and interpret 95% confidence intervals for the difference in mean pain intensity at 1 month after treatment. (Use μVertebroplasty − μPlacebo. Round your answers to two decimal places.) _ to ______

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Description: Is injecting medical cement effective in reducing pain for people who have suffered fractured vertebrae? A paper describes an experiment to compare patients who underwent vertebroplasty (the injection of cement) to patients in a placebo group who und

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

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Is injecting medical cement effective in reducing pain for people who have suffered fractured vertebrae? A paper describes an experiment to compare patients who underwent vertebroplasty (the injection of cement) to patients in a placebo group who underwent a fake procedure in which no cement was actually injected. Because the placebo procedure was similar to the vertebroplasty procedure except for the actual injection of cement, patients participating in the experiment were not aware of which treatment they received.

All patients were asked to rate their pain at three different times—3 days, 14 days, and 1 month after the procedure. Summary statistics are given in the accompanying table.

	Pain Intensity
	Vertebroplasty Group	Placebo Group
	n = 76	n = 62
	mean	sd	mean	sd
3 days	4.2	2.8	3.9	2.9
14 days	4.3	2.9	4.5	2.8
1 month	3.9	2.9	4.6	3.0

Construct and interpret a 95% confidence interval for the difference in mean pain intensity 3 days after treatment for the vertebroplasty treatment and the fake treatment. (Use μ_{Vertebroplasty} − μ_Placebo. Round your answers to two decimal places.)

_________ to __________

Construct and interpret 95% confidence intervals for the difference in mean pain intensity at 14 days after treatment. (Use μ_{Vertebroplasty} − μ_Placebo. Round your answers to two decimal places.)

_________ to ___________

Construct and interpret 95% confidence intervals for the difference in mean pain intensity at 1 month after treatment. (Use μ_{Vertebroplasty} − μ_Placebo. Round your answers to two decimal places.)

_________ to __________

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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