Answered: Researchers conducted a study to…

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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Part 1

a. Use a

0.05

significance level to test the claim that those treated with magnets have a greater mean reduction in pain than those given a sham treatment (similar to a placebo).

What are the null and alternative hypotheses?

H0:

μ1<μ2

H1:

μ1≥μ2

H0:

μ1≠μ2

H1:

μ1<μ2

H0:

μ1=μ2

H1:

μ1>μ2

H0:

μ1=μ2

H1:

μ1≠μ2

Part 2

The test statistic, t, is

enter your response here.

(Round to two decimal places as needed.)

Part 3

The P-value is

enter your response here.

(Round to three decimal places as needed.)

Part 4

State the conclusion for the test.

▼

Reject

Fail to reject

the null hypothesis. There

▼

is not

sufficient evidence to support the claim that those treated with magnets have a greater mean reduction in pain than those given a sham treatment.

Part 5

b. Construct a confidence interval appropriate for the hypothesis test in part (a).

enter your response here<μ1−μ2<enter your response here

(Round to two decimal places as needed.)

Part 6

c. Does it appear that magnets are effective in treating back pain? Is it valid to argue that magnets might appear to be effective if the sample sizes are larger? Choose the correct answer below.

It appears that magnets

are

effective in treating back pain, because the confidence interval contains only positive values.

It appears that magnets

are not

effective in treating back pain, because the P-value is

less

than the significance level.

It appears that magnets

are not

effective in treating back pain, because 0

in the confidence interval.

It appears that magnets

are

effective in treating back pain, because the P-value is

greater

than the significance level.

Part 7

Is it valid to argue that magnets might appear to be effective if the sample sizes are larger? Choose the correct answer below.

No, because the magnets already appear to be effective.

No, because increasing the sample size will increase the P-value.

Yes, because increasing the sample size will decrease the P-value.

Yes, because increasing the sample size will increase the effectiveness.

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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