Answered: A study was conducted to measure the…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Question

A study was conducted to measure the effectiveness of hypnotism in reducing pain. The measurements are centimeters on a pain scale before and after hypnosis. Assume that the paired sample data are simple random samples and that the differences have a distribution that is approximately normal. Construct a 95% confidence interval for the mean of the "beforeminus after" differences. Does hypnotism appear to be effective in reducing pain?

a. Construct a 95% confidence interval for the mean of the "beforeminusafter" differences.

less than mu Subscript dless than

(Round to two decimal places as needed.)

b. Does hypnotism appear to be effective in reducing pain?

**Data Comparison: Before and After**

The table illustrates a comparison of numerical values before and after a specific event or intervention.

- **Before:**
- 10.4, 6.8, 6.3, 10.2, 11.3, 7.7, 2.0, 1.7

- **After:**
- 6.7, 2.6, 7.8, 8.9, 8.2, 6.9, 3.7, 2.2

These values may reflect measurements in a study, such as test scores, substance levels, or other quantifiable data, showing changes after applying certain conditions or treatments. By analyzing these values, one can draw conclusions on the effectiveness or impact of the intervention.

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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