Question

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 | |

m | m1 | m2 |

n | 29 | 29 |

x | .54 | .43 |

s | .85 | 1.08 |

**a.** Use a 0.05 significance level, and test the
claim that those treated with magnets have a greater mean reduction
in pain than those given a sham treatment.

1. What are the null and alternative hypotheses?

2. The test statistic,is ______

(Round to two decimal places as needed.)

3. The P-value is ______

(Round to three decimal places as needed.)

4. State the conclusion for the test.

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

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

Since the ___________ for those treated with magnets is _________ the sample mean for those given a sham treatment, it ___________ 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.)

Answer #1

A study was conducted to determine whether magnets were
effective in treating pain. The values represent measurements of
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independent simple random samples from populations having normal
distributions. Use a 0.05 significance level to test the claim that
those given a sham treatment have pain reductions that vary more
than the pain reductions for those treated with magnets.
n x s
Sham 20 0.42 1.38
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A study was conducted to determine whether magnets were
effective in treating pain. The values represent measurements of
pain using the visual analog scale. Assume that both samples are
independent simple random samples from populations having normal
distributions. Use a 0.05 significance level to test the claim that
those given a sham treatment have pain reductions that vary more
than the pain reductions for those treated with magnets. n x s Sham
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in the table for the treatment (with magnets) group and the sham
(or placebo) group. The results are a measure of reduction in back
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samples selected from normally distributed populations, and do not
assume that the population standard deviations are equal. Complete
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A study was done using a treatment group and a placebo group. The
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Use a
0.10
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