The degenerative disease most frequency affect weight-bearing joints such as the

Question

The degenerative disease most frequency affect weight-bearing joints such as the knee. An article presented the following summary data on stance duration (ms) for samples of both older Assume that both stance duration distributions are normal. Calculate a 99% for true average stance duration among elderly individuals. With 99% confidence, we can say that true average stance duration among elderly individual falls above the upper bound with 99% confidence, we can say that true average stance duration among elderly individual falls between this values. With 99% confidence, we can say that true average stance duration among elderly individual falls below the lower bound. With 99% confidence, we can say that true average stance duration among elderly individual falls outside these values. Carry out a test of hypotheses at significance level 0.05 to decide whether true average stance duration is larger among elderly individuals than among younger individuals. (Use for elder individuals.) State the relevant hypotheses. H_0: mu_1 - mu_2 = 0 H_a: mu_1 - mu_2 > 0 H_0: mu_1 - mu_2 = 0 H_a: mu_1 - mu_2

Explanation / Answer

(a)
for 99% CI, z-value = 2.578

lower limit = 807 - 2.578*116/sqrt(26) = 748.352
upper limit = 807 + 2.578*116/sqrt(26) = 865.648

99% CI = (748.352, 865.648)

(b)
For given hypothesis test,
SE = sqrt(s1^2/n1 + s2^2/n2) = 2.9184

t = (x1 - x2)/SE = 5.8251

degrees of freedom = 41

p-value = 0.00001

As p-value < significance level of 0.05, we reject null hypothesis

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