Question

homework
question 6, 9.2.11-t
part 4 of 7
hw score: 56.74%, 6.81 of 12 points
points: 0.63 of 1
researchers conducted a study to determine whether magnets are effective in treating back pain. pain was measured using the visual analog scale, and the results shown below are among the results obtained in the study. higher scores correspond to greater pain levels. 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) to (c) below.
reduction in pain level after magnet treatment (μ₁) n = 20, x̄ = 0.42, s = 1.01
reduction in pain level after sham treatment (μ₂) n = 20, x̄ = 0.35, s = 1.56

a. use a 0.01 significance level to test the claim that those treated with magnets have a greater mean reduction in pain than those given a sham treatment (similar to a placebo).
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 0.17. (round to two decimal places as needed.)
the p - value is 0.433. (round to three decimal places as needed.)
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.

Explanation:

Step1: Identify Hypotheses

The claim is that magnet - treated (\(\mu_1\)) have greater mean pain reduction than sham - treated (\(\mu_2\)). So, the null hypothesis \(H_0\) is the equality of means (\(H_0:\mu_1 = \mu_2\)), and the alternative hypothesis \(H_1\) is \(\mu_1>\mu_2\) (since we are testing if magnet - treated has greater mean). So option B (\(H_0:\mu_1=\mu_2\), \(H_1:\mu_1 > \mu_2\)) is correct.

Step2: Test Statistic and P - value Interpretation

The test statistic \(t = 0.17\) and \(P - value=0.433\). For a significance level \(\alpha = 0.01\), since \(P - value=0.433>\alpha = 0.01\), we fail to reject the null hypothesis.

Step3: Conclusion

Since we fail to reject \(H_0\), there is not sufficient evidence to support the claim that magnet - treated have a greater mean pain reduction than sham - treated.

Answer:

a. The correct option is B. \(H_0:\mu_1=\mu_2\), \(H_1:\mu_1 > \mu_2\)
b. The test statistic \(t = 0.17\)
c. The \(P - value=0.433\)
d. We fail to reject the null hypothesis. There is not sufficient evidence to support the claim.