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Name: In a study to determine if using low-intensity laser therapy reduces p
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Description: In a study to determine if using low-intensity laser therapy reduces pain for orthodontic patients who are fitted with new braces, patients were randomly assigned to either a control group (who did not receive laser treatment) or an experimental grou

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

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter10: Statistics

Section10.3: Measures Of Spread

Problem 1GP

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In a study to determine if using low-intensity laser therapy reduces pain for orthodontic patients who are fitted with new braces, patients were randomly assigned to either a control group (who did not receive laser treatment) or an experimental group who did receive laser treatment.† The researchers found that the mean pain rating was lower for those in the laser treatment group than for those in the control group both two days and six days after receiving braces. The researchers used these data to determine if there was evidence to support the claim that the mean pain rating is lower for patients who receive the laser treatment.

Answer the four key questions.

Q, Question Type: Estimation or hypothesis testing?

estimationhypothesis testing

S, Study Type: Sample data or experiment data?

sample dataexperiment data

T, Type of Data: One variable or two? Categorical or numerical?

one categorical variableone numerical variable two categorical variablestwo numerical variables

N, Number of Samples or Treatments: How many samples or treatments?

one sampleone treatment two samplestwo treatments

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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