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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.

| Sham | |

μ | μ1 | μ2 |

n | 25 | 25 |

x | 0.52 | 0.41 |

s | 0.97 | 1.03 |

**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?

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

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 < ______

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