Question

2.

Some people use magnets as a treatment for back pain. A sample of 25 people treated with magnets had a mean reduction in pain of 0.73 and a standard deviation of 0.25. A sample of 27 people treated with placebo had a mean reduction in pain of 0.64 and a standard deviation of 0.34. Use a 5% significance level to test the claim that people treated with magnets for back pain have the same reduction in pain as those treated with a placebo (assume the variances are equal).

Group of answer choices

H0: μmag = μpla

Ha: μmag≠ μpla

Test statistic: t = 1.080 Critical values: 1.676
Do not reject the null hypothesis. At the 5% significance level, the data does not provide sufficient evidence to reject the claim.

H0: σmag = σpla

Ha: σmag≠ σpla

Test statistic: t = 1.850 Critical values: 2.552
Do not reject the null hypothesis. At the 5% significance level, the data does not provide sufficient evidence to support the claim.

H0: σmag = σpla

Ha: σmag ≠ σpla

Test statistic: t = 1.36 Critical values: 2.552
Do not reject the null hypothesis. At the 1% significance level, the data does not provide sufficient evidence to reject the claim .

H0: μmag = μpla

Ha: μmag ≠ μpla

Test statistic: t = 1.080 Critical values: 2.009
Do not reject the null hypothesis. At the 5% significance level, the data does not provide sufficient evidence to reject the claim.

H0: μmag = μpla

Ha: μmag ≠ μpla

Test statistic: t = 1.093 Critical values: 2.009
Do not reject the null hypothesis. At the 5% significance level, the data does not provide sufficient evidence to reject the claim.

None of these.

Answer 1

Solution:

Given:

Sample of people treated with magnets:

Sample size = n₁ = 25

Sample mean =

Sample standard deviation = s₁ = 0.25

Sample of people treated with Placebo:

Sample size = n₂ = 27

Sample mean =

Sample standard deviation = s₂ = 0.34

Claim: people treated with magnets for back pain have the same reduction in pain as those treated with a placebo

Level of significance = 0.05

Assumption: the variances are equal

Step 1) State H0 and Ha:

H₀: μ_mag = μ_pla Vs H_a: μ_mag ≠ μ_pla

Step 2) Test statistic:

where

thus

Step 3) t critical values:

df = n₁ + n₂ - 2 = 25 + 27 - 2 = 50

Two tail area = Level of significance = 0.05

thus

t critical value = 2.009

Step 4) Decision Rule:

Reject null hypothesis H0, if absolute t test statistic value > t critical value =2.009, otherwise we fail to reject H0

Since absolute t test statistic value =   < t critical value =2.009, we fail to reject H0.

Do not reject the null hypothesis.

At the 5% significance level, the data does not provide sufficient evidence to reject the claim.

Thus correct answer is:

H0: μmag = μpla

Ha: μmag ≠ μpla

Test statistic: t = 1.080 Critical values: 2.009
Do not reject the null hypothesis. At the 5% significance level, the data does not provide sufficient evidence to reject the claim.