Question

Pilates is a popular set of exercises for the treatment of individuals with lower back pain. The method has six basic principles: centering, concentration, control, precision, flow, and breathing. An article reported on an experiment involving 82 subjects with nonspecific low back pain. The participants were randomly divided into two groups of equal size. The first group received just educational materials, whereas the second group participated in 6 weeks of Pilates exercises. The sample mean level of pain (on a scale from 0 to 10) for the control group at a 6-week follow-up was 5.1 and the sample mean for the treatment group was 3.2; both sample standard deviations were 2.3.

(a)

Does it appear that true average pain level for the control condition exceeds that for the treatment condition? Carry out a test of hypotheses using a significance level of 0.01

H₀: μ_control − μ_treatment = 0
H_a: μ_control − μ_treatment > 0

H₀: μ_control − μ_treatment = 0
H_a: μ_control − μ_treatment < 0   

H₀: μ_control − μ_treatment = 0
H_a: μ_control − μ_treatment ≤ 0

H₀: μ_control − μ_treatment = 0
H_a: μ_control − μ_treatment ≠ 0

H₀: μ_control − μ_treatment = 0
H_a: μ_control − μ_treatment ≥0

(b)

Does it appear that true average pain level for the control condition exceeds that for the treatment condition by more than 1 at a significance level of 0.01? Carry out a test of appropriate hypotheses.

State the relevant hypotheses.

H₀: μ_control − μ_treatment = 1
H_a: μ_control − μ_treatment < 1

H₀: μ_control − μ_treatment = 1
H_a: μ_control − μ_treatment ≤ 1    

H₀: μ_control − μ_treatment = 1
H_a: μ_control − μ_treatment > 1

H₀: μ_control − μ_treatment = 1
H_a: μ_control − μ_treatment ≠ 1

H₀: μ_control − μ_treatment = 1
H_a: μ_control − μ_treatment ≥ 1

Calculate the test statistic and P-value. (Round your test statistic to two decimal places and your P-value to four decimal places.)

z=   P-value=

State the conclusion in the problem context.

Reject H₀. The data suggests that true average pain level for the control condition exceeds that for the treatment condition by more than 1.

Reject H₀. The data does not suggest that true average pain level for the control condition exceeds that for the treatment condition by more than 1.   

Fail to reject H₀. The data does not suggest that true average pain level for the control condition exceeds that for the treatment condition by more than 1.

Fail to reject H₀. The data suggests that true average pain level

Answer 1