Answered: b. Construct a confidence interval…

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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Researchers conducted a study to determine whether magnets are effective in treating back pain. The results are shown in the table for the treatment (with magnets) group and the sham (or placebo) group. The results are a measure of reduction in back pain. Assume that the two samples are independent simple random samples selected from normally distributed populations, and do not assume that the population standard deviations are equal. Complete parts (a) and (b) below.			Treatment	Sham
μ	μ1	μ2
n	20	20
x	0.51	0.36
s	0.86	1.45

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.

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

The test statistic, t, is _____
(Round to two decimal places as needed.)

The P-value is _____
(Round to three decimal places as needed.)

State the conclusion for the test.

(Reject

Fail to reject)

the null hypothesis. There

(is

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.

Is it valid to argue that magnets might appear to be effective if the sample sizes are larger?

Since the

(sample mean

sample standard deviation)

for those treated with magnets is

(equal to

less than

greater than)

the sample mean for those given a sham treatment, it

(is not

is)

valid to argue that magnets might appear to be effective if the sample sizes are larger.

b. Construct a confidence interval suitable for testing the claim that those treated with magnets have a greater mean reduction in pain than those given a sham treatment.

_____<μ1−μ2<________

(Round to three decimal places as needed.)

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

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