Question

• Please state the null and alternative hypotheses.
• Using an alpha level of .05, please test the null hypothesis (what is the appropriate test, what is the critical value?). Draw the rejection region.
• Calculate the test statistic
• State the conclusion you are entitled to draw as a result of this test.
• Calculate the effect size as appropriate for the hypothesis test used.

2. A recent study on the effects of Tamiflu looked into whether the antiviral medication can reduce the duration of the flu or not. To test this, researchers selected sample of 42 individuals recently diagnosed with the flu. Twentyone of these individuals were given a placebo, and their average flu durations was 12.6 days (SD = 1.88). The remaining 21 subjects were given Tamiflu, and their average flu duration was 11.4 days (SD = 1.58). Did Tamiflu make reduce the duration of the flu? What was the effect size for Tamiflu?

Answer 1

Ho :   µ1 - µ2 =   0                  
Ha :   µ1-µ2 >   0                  
                          
Level of Significance ,    α =    0.05                  
                          
Sample #1   ---->   sample 1                  
mean of sample 1,    x̅1=   12.60                  
standard deviation of sample 1,   s1 =    1.88                  
size of sample 1,    n1=   21                  
                          
Sample #2   ---->   sample 2                  
mean of sample 2,    x̅2=   11.40                  
standard deviation of sample 2,   s2 =    1.58                  
size of sample 2,    n2=   21                  
                          
difference in sample means =    x̅1-x̅2 =    12.6000   -   11.4   =   1.20  
                          
pooled std dev , Sp=   √([(n1 - 1)s1² + (n2 - 1)s2²]/(n1+n2-2)) =    1.7365                  
std error , SE =    Sp*√(1/n1+1/n2) =    0.5359                  
                          
t-statistic = ((x̅1-x̅2)-µd)/SE = (   1.2000   -   0   ) /    0.54   =   2.24
                          
Degree of freedom, DF=   n1+n2-2 =    40                  
t-critical value , t* =        1.6839   (excel function: =t.inv(α,df)              
Decision:   | t-stat | > | critical value |, so, Reject Ho                      


Tamiflu make reduce the duration of the flu

....

effect size,      
cohen's d =    |( x̅1-x̅2 )/Sp | =    0.691
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Please revert back in case of any doubt.

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