In this study measurements were made of anterior compartment

In this study, measurements were made of anterior compartment pressure (in millimeters of mercury) for ten healthy runners and ten healthy cyclists. The data summary is repeated here for your convenience. Assume that the data is collected from two normally distributed populations and use alpha = 0.05. Is there sufficient evidence to support a claim that the variance of compartment pressure differs for runners and cyclists who are resting? Is there sufficient evidence to support a claim that the variance of compartment pressure differs for runners and cyclists at maximal O_2 consumption? Suppose we wish to test for differences in mean compartment pressure between runners and cyclists. Clearly explain what the results in a) and b) imply if we wish to perform such hypothesis tests. Is there sufficient evidence to justify that a difference exists in mean compartment pressures for runners and cyclists who are resting? Use alpha = 0.05. Bound or determine the associated p-value. Does sufficient evidence exist to permit us to identify a difference in mean compartment pressures for runners and cyclists at the 80% maximal O_2 consumption? Use alpha = 0.05. Bound or determine the associated p-value.

Solution

a) H0: s1^ 2 = s2^2

Ha: s1^2 not equal to s2^2

(Two tailed test for comparison of variances between runners and cyclists at rest.)

Alpha = 0.05

n1 = n2 =10

df = 9,9

Test statistic F = 3.98/3.92 (since larger variance is taken in the numerator)

= 1.01531

p value =0.4912

Since p >0.05, accept null hypothesis that the two variances are equal.

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b)

H0: s1^ 2 = s2^2

Ha: s1^2 not equal to s2^2

(Two tailed test for comparison of variances between runners and cyclists at rest.)

Alpha = 0.05

n1 = n2 =10

df = 9,9

Test statistic F = 4.95/3.49 (since larger variance is taken in the numerator)

= 1.418

p value =0.3056

Since p >0.05, accept null hypothesis that the two variances are equal.

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c) If we want to check mean difference between the two samples, by the above two tests it implies that we can assume equal variances for these two samples.

d) H0: mu1 = mu2 (where mu1 and mu2 are the means for runners and cyclists at rest)

Ha: mu1 not equal to mu2

Two tailed test

Group  Group One    Group Two

Mean 14.5000 11.1000

SD 3.9200 3.9800

SEM 1.2396 1.2586

N 10 10

t = 1.9247
  df = 18
  standard error of difference = 1.767

The two-tailed P value equals 0.0702

Since p >0.05 accept that the two means are equal.