Two popular drugs used for the treatment of depression are R

Two popular drugs used for the treatment of depression are Resithan and Exemor. A random sample of 586 depressed individuals is selected and treated with Resithan, and 180 find relief from their depression. A random sample of 516 depressed individuals is independently selected from the first sample and treated with Exemor, and 200 find relief from their depression. Can we conclude, at the 0.01 level of significance, that the proportion p1 of depressed individuals taking Resithan who find relief from depression is less than the proportion p2 of all depressed individuals taking Exemor who find relief from depression? Perform a one-tailed test. Then fill in the table below. Carry your intermediate computations to at least three decimal places and round your answers as specified in the table. (If necessary, consult a list of formulas.)

Solution

Formulating the hypotheses          

Ho: p1 - p2   >=   0   [ANSWER]

H1: p1 - p2   <   0   [ANSWER]

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We use Z STATISTIC here. [ANSWER]

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Here, we see that pdo =    0   , the hypothesized population proportion difference.  
          
Getting p1^ and p2^,          
          
p1^ = x1/n1 =    0.386100386      
p2^ = x2/n2 =    0.450643777      
          
Also, the standard error of the difference is          
          
sd = sqrt[ p1 (1 - p1) / n1 + p2 (1 - p2) / n2] =    0.031445731      
          
Thus,          
          
z = [p1 - p2 - pdo]/sd =    -2.052532699   [ANSWER, VALUE OF TEST STATISTIC]

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Also, the p value is, as this is one tailed,          
          
P =    0.02005896   [ANSWER, P VALUE]

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As P < 0.1, YES. [ANSWR, CAN WE CONCLUDE...]