d. what are the df? what is the critical values? e. what decision can you make and what does that mean? f. calculate and evaluate r^2 • A researcher would like to evaluate whether a pain-relief patch designed forlower back pain is effective at lowering pain. Prior to testing the patch, eachof n = 8 patients rates the current level of back pain on a scale from 1 to 10(lower values indicate lower pain). After wearing the patch for 90 minutes, asecond pain rating is recorded. The data are as follows:BeforeAfter78.47448.8.73.1.2.2.3.6

Given data: Number of patients included in the sample, n = 8. The researcher would like to evaluate…

Answered: • A researcher would like to evaluate…

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter10: Statistics

Section10.1: Measures Of Center

Problem 4GP

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d. what are the df? what is the critical values?

e. what decision can you make and what does that mean?

f. calculate and evaluate r^2

• A researcher would like to evaluate whether a pain-relief patch designed for
lower back pain is effective at lowering pain. Prior to testing the patch, each
of n = 8 patients rates the current level of back pain on a scale from 1 to 10
(lower values indicate lower pain). After wearing the patch for 90 minutes, a
second pain rating is recorded. The data are as follows:
Before
After
7
8.
4
7
4
4
8.
8.
7
3.
1.
2.
2.
3.
6

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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