Answered: The 99% confidence interval for 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 medical study is conducted to determine which migraine treatment, A or B, provides faster relief. The study uses 10 volunteers who claim to suffer from migraines. Half of the volunteers are randomly assigned to use treatment A when they experience their first migraine. The other half are assigned to use treatment B. Then, after no treatment for one month, the treatments are reversed. The volunteers each record the amount of time it takes, in minutes, to experience relief from their migraine under each treatment. The data are displayed in the table.

The conditions for inference are met. The 99% confidence interval for the mean difference (A – B) in the time it takes to experience relief is –8.37 minutes to 0.732 minutes. What is the correct interpretation of this interval?

The researchers can be 99% confident that the interval from –8.37 minutes to 0.732 minutes captures the true mean time it takes to experience relief.

The researchers can be 99% confident that the interval from –8.37 minutes to 0.732 minutes captures the true mean difference in the time it takes to experience relief.

The researchers can be 99% confident that the interval from –8.37 minutes to 0.732 minutes captures the true mean time it takes these volunteers to experience relief.

The researchers can be 99% confident that the interval from –8.37 minutes to 0.732 minutes captures the true mean difference in the time it takes these volunteers to experience relief.

Volunteer
Treatment A
Treatment B
1
2
10 13
19
18
3
13
19
4
5
6
7
9 13 12 14
15
20
16
16
8
10
16
9
10
8
7
13 17

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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