A physician wants to know whether ibuprofen or acetaminophen is more effective i

Question

A physician wants to know whether ibuprofen or acetaminophen is more effective in relieving minor post-operative pain after wisdom tooth removal. He gives 11 randomly selected patients ibuprofen and 11 randomly selected patients acetaminophen. Dosage times and amounts are equivalent. He gives each patient a rating sheet on which to rate the severity of pain one hour after taking the second post-operative dose. Here are the pain ratings. Higher scores indicate more pain. Is the research hypothesis in this study directional or nondirectional? State the research alternative hypothesis. Calculate t and compare it with the tabled critical t at the,05alpha level. Can you reject the null hypothesis?

Explanation / Answer

a)

It doesn't know which one is more effective, so it is NONDIRECTIONAL. [ANSWER]

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b)

Let

u1 = mean of ibuprofen
u2 = mean of acetaminophen

Hence,

Ha: u1 - u2 =/= 0 [ANSWER]

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c)

Formulating the null and alternative hypotheses,              
              
Ho:   u1 - u2   =   0  
Ha:   u1 - u2   =/   0  
At level of significance =    0.05          
As we can see, this is a    two   tailed test.      
Calculating the means of each group,              
              
X1 =    4.636363636          
X2 =    6.363636364          
              
Calculating the standard deviations of each group,              
              
s1 =    1.911686547          
s2 =    1.963299634          
              
Thus, the standard error of their difference is, by using sD = sqrt(s1^2/n1 + s2^2/n2):              
              
n1 = sample size of group 1 =    11          
n2 = sample size of group 2 =    11          
Thus, df = n1 + n2 - 2 =    20          
Also, sD =    0.82622311          
              
Thus, the t statistic will be              
              
t = [X1 - X2 - uD]/sD =    -2.090564529   [ANSWER, t]

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where uD = hypothesized difference =    0          
              
Now, the critical value for t is              
              
tcrit =    +/-   2.085963447   [ANSWER, CRITICAL T]

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As |t| > 2.086,   YES, WE REJECT THE NULL HYPOTHESIS.   [ANSWER]      
              

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Hi! If you use another method/formula in calculating the degrees of freedom in this t-test, please resubmit this question together with the formula/method you use in determining the degrees of freedom. That way we can continue helping you! Thanks!

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