Chronic anterior compartment syndrome is a condition characterized by exercise-induced pain in the lower leg. Swelling and impaired nerve and muscle function also accompany this pain, which is relieved by rest. Researchers conducted an experiment involving 10 healthy runners and 10 healthy cyclists to determine whether there are significant differences in pressure measurements within the anterior muscle compartment for runners and cyclists. In addition to the compartment pressures, the level of creatine phosphokinase (CPK) in blood samples, a measure of muscle damage, was determined for each of

n₁ = 10

runners and

n₂ = 10

cyclists before and after exercise. The data summaryCPK values in units/literis as follows.

		Runners		Cyclists
Condition	Mean	Standard Deviation	Mean	Standard Deviation
Before Exercise	251.67	115.42	173.5	60.66
After Exercise	284.71	132.64	175.6	64.57
Difference	33.04	21.05	2.1	6.75

(a) Test for a significant difference in mean CPK values for runners and cyclists before exercise under the assumption that

₁² ₂²;

use

= 0.05.

State the null and alternative hypotheses.

H₀: (_{1 2}) = 0 versus H_a: (_{1 2}) 0H₀: (_{1 2}) 0 versus H_a: (_{1 2}) = 0 H₀: (_{1 2}) = 0 versus H_a: (_{1 2}) > 0H₀: (_{1 2}) < 0 versus H_a: (_{1 2}) 0H₀: (_{1 2}) = 0 versus H_a: (_{1 2}) < 0

State the test statistic. (Round your answer to three decimal places.) t = State the rejection region. (If the test is one-tailed, enter NONE for the unused region. Round your answers to three decimal places.)

t >

t <

State the conclusion.

H₀ is rejected. There is insufficient evidence to indicate a difference in mean CPK values for runners and cyclists before exercise.H₀ is not rejected. There is sufficient evidence to indicate a difference in mean CPK values for runners and cyclists before exercise. H₀ is not rejected. There is insufficient evidence to indicate a difference in mean CPK values for runners and cyclists before exercise.H₀ is rejected. There is sufficient evidence to indicate a difference in mean CPK values for runners and cyclists before exercise.

Find a 95% confidence interval estimate (in units/L) for the corresponding difference in means. (Round your answers to three decimal places.) units/L to units/L (b) Test for a significant difference in mean CPK values for runners and cyclists after exercise under the assumption that

₁² ₂²;

use

= 0.05.

State the null and alternative hypotheses.

H₀: (_{1 2}) = 0 versus H_a: (_{1 2}) < 0H₀: (_{1 2}) 0 versus H_a: (_{1 2}) = 0 H₀: (_{1 2}) = 0 versus H_a: (_{1 2}) > 0H₀: (_{1 2}) = 0 versus H_a: (_{1 2}) 0H₀: (_{1 2}) < 0 versus H_a: (_{1 2}) 0

State the test statistic. (Round your answer to three decimal places.) t = State the rejection region. (If the test is one-tailed, enter NONE for the unused region. Round your answers to three decimal places.)

t >

t <

State the conclusion.

H₀ is rejected. There is insufficient evidence to indicate a difference in mean CPK values for runners and cyclists after exercise.H₀ is not rejected. There is sufficient evidence to indicate a difference in mean CPK values for runners and cyclists after exercise. H₀ is not rejected. There is insufficient evidence to indicate a difference in mean CPK values for runners and cyclists after exercise.H₀ is rejected. There is sufficient evidence to indicate a difference in mean CPK values for runners and cyclists after exercise.

Find a 95% confidence interval estimate (in units/L) for the corresponding difference in means. (Round your answers to three decimal places.) units/L to units/L (c) Test for a significant difference in mean CPK values for runners before and after exercise. (Use ₁ for after exercise and ₂ for before exercise.) State the null and alternative hypotheses.

H₀: (_{1 2}) = 0 versus H_a: (_{1 2}) 0H₀: (_{1 2}) < 0 versus H_a: (_{1 2}) 0 H₀: (_{1 2}) 0 versus H_a: (_{1 2}) = 0H₀: (_{1 2}) = 0 versus H_a: (_{1 2}) > 0H₀: (_{1 2}) = 0 versus H_a: (_{1 2}) < 0

State the test statistic. (Round your answer to three decimal places.) t = State the rejection region. (If the test is one-tailed, enter NONE for the unused region. Round your answers to three decimal places.)

t >

t <

State the conclusion.

H₀ is not rejected. There is sufficient evidence to indicate a difference in mean CPK values for runners before and after exercise.H₀ is rejected. There is sufficient evidence to indicate a difference in mean CPK values for runners before and after exercise. H₀ is not rejected. There is insufficient evidence to indicate a difference in mean CPK values for runners before and after exercise.H₀ is rejected. There is insufficient evidence to indicate a difference in mean CPK values for runners before and after exercise.

(d) Find a 95% confidence interval estimate for the difference in mean CPK values (in units/L) for cyclists before and after exercise. (Use _{1 2}, with ₁ for after exercise and ₂ for before exercise. Round your answers to three decimal places.) units/L to units/L Does your estimate indicate that there is no significant difference in mean CPK levels for cyclists before and after exercise?

Since the interval contains the value (_{1 2}) = 0, we cannot conclude that there is a significant difference between the means.Since the interval contains the value (_{1 2}) = 0, we can conclude that there is a significant difference between the means. Since the interval does not contain the value (_{1 2}) = 0, we cannot conclude that there is a significant difference between the means.Since the interval does not contain the value (_{1 2}) = 0, we can conclude that there is a significant difference between the means.