show all work please, thanks! A Sports Medicine clinic was encouraging the use o
ID: 3375489 • Letter: S
Question
show all work please, thanks! A Sports Medicine clinic was encouraging the use of a Conservative (nonsurgical) protocol in the treatment of complete ruptures of the Achilles tendon. This protocol consists of a series of castings and TENS treatment followed by ultrasound and rigorous physical therapy. In a study performed by the Sports Medicine clinic, of the 1000 patients who received this treatment, 90 re-ruptured the tendon within two years of the original injury The Standard (surgical) protocol involves surgery to reattach the tendon followed by physical therapy. Of those who receive the Standard protocol, 13% re-rupture the tendon within two years of the original injury Test the hypothesis that the Conservative protocol reduces this proportion of patients who re rupture the tendon (0-5%) Show all procedures of Hypothesis Testing.Explanation / Answer
Solution:-
State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.
Null hypothesis: P > 0.13
Alternative hypothesis: P < 0.13
Note that these hypotheses constitute a one-tailed test.
Formulate an analysis plan. For this analysis, the significance level is 0.05. The test method, shown in the next section, is a one-sample z-test.
Analyze sample data. Using sample data, we calculate the standard deviation (S.D) and compute the z-score test statistic (z).
S.D = sqrt[ P * ( 1 - P ) / n ]
S.D = 0.01063
z = (p - P) / S.D
z = - 3.76
where P is the hypothesized value of population proportion in the null hypothesis, p is the sample proportion, and n is the sample size.
Since we have a one-tailed test, the P-value is the probability that the z-score is less than -3.76.
Thus, the P-value = less than 0.0001.
Interpret results. Since the P-value (almost 0) is less than the significance level (0.05), we cannot accept the null hypothesis.
From the above test we have sufficient evidence in the favor of the claim that conservative protocol reduces this proportion of patients who re-repture the tendon.
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