|μ 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. n X A. Ho: H₁ H₂ H₁ H₁ H₂ 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? C. Ho: H₁
|μ 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. n X A. Ho: H₁ H₂ H₁ H₁ H₂ 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? C. Ho: H₁
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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Transcribed Image Text: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 Iμ
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.
O A. Ho: H₁ = H2
H₁: H₁ H₂
C. Ho: M₁ <H₂
H₁: H₁2H₂
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?
State the conclusion for the test.
B. Ho: H₁ H2
H₁: H₁
H₂
The test statistic, t, is 0.15. (Round to two decimal places as needed.)
The P-value is 0.443. (Round to three decimal places as needed.)
D. Ho: H₁
H₁: H₁
S
H₂
H₂
<H1-H₂ <
(Round to three decimal places as needed.)
Treatment
H₁
13
0.48
0.51
Sham
H₂
13
0.42
1.39
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.
Is it valid to argue that magnets might appear to be effective if the sample sizes are larger?
Since the
sample mean
for those treated with magnets is greater than the sample mean for those given a
sham treatment, it 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.
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