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 16 16 x 0.55 0.36 s 0.84 1.49 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? A. H0: μ1=μ2 H1: μ1≠μ2 B. H0: μ1=μ2 H1: μ1>μ2 C. H0: μ1<μ2 H1: μ1≥μ2 D. H0: μ1≠μ2 H1: μ1<μ2 The test statistic, t, is The P-value is State the conclusion for the test. Fail to reject Reject the null hypothesis. There is not is 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 greater than less than equal to 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<

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Description: 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 bac

MATLAB: An Introduction with Applications

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ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

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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	16	16
x	0.55	0.36
s	0.84	1.49

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

The P-value is

State the conclusion for the test.

Fail to reject

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.

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

greater than

less than

equal to

the sample mean for those given a sham treatment, it

is not

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<

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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