Question 127710
Does lovastatin (a cholesterol-lowering drug) reduce the risk of heart attack? In a Texas study, researchers gave lovastatin to 2,325 people 
and an inactive substitute to 2,081 people (average age 58). 
After 5 years, 57 of the lovastatin group had suffered a heart attack, 
compared with 97 for the inactive pill.
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(a) State the appropriate hypotheses. 
Ho: p(inactive) - P(active) =0
Ha: p(inactive) - p(active) > 0
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p-hat(inactive) = 97/2081 = 0.0466
p-hat(active) = 57/2325= 0.0245
If you pool the data you get p-bar = (97+57)/(2081+2325) = 0.0350
and q-bar = 1-p-bar = 0.9650
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alpha = 1%; critical value = z = 2.326
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(b) Obtain a test statistic and p-value.
z(0.0466-0.0245) = (0.0221)/sqrt[(0.035*0.965/2081)+(0.035*0.965/2325)]
3.9849
p-value - 0.0000338
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Interpret the results at alpha = .01
Because the p-value is less than alpha, reject Ho; there is significant 
statistical evidende that the application of the medicine reduces the
incidence of death.
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(c) Is normality assured?
2081*0.035= 72.84 > 5 and 2081*0.965 >5
2325*0.035=70.86 > 5 and 2325*0.965 >5
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(d) Is the difference large enough to be important?
The p-value gives very strong evidence that for the truth of Ha.
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(e) What else would medical researchers need to know before prescribing this drug widely?
I'll leave that to you.
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Cheers,
Stan H.