5. [5 points] Suppose researchers wish to study the effectiveness of a new drug

Question

5. [5 points] Suppose researchers wish to study the effectiveness of a new drug to alleviate hives due to math anxiety. Seven hundred math students are randomly assigned to take either this drug or a placebo. Suppose 34 of the 350 students who took the drug break out in hives compared to 56 of the 350 students who took the placebo. (a) Compute a 95% confidence interval for the proportion of students taking the drug who break (b) Compute a 95% confidence interval for the proportion of students on the placebo who break out (c) Do the intervals overlap? What, if anything, can you conclude about the effectiveness of the out in hives. in hives. drug?

Explanation / Answer

a)

from abvoe 95% CI =0.066 ; 0.128

b)

95% Ci =0.122 ; 0.198

c) Yes these interval overlap ; and therefore we can not conclude that drug is effective cause we do not have evideence that proportion is different for those who take palcebo than those who take drug

                                                                                           x                    =   34 sample size n                    = 350 sample proportion     p x/n= 0.0971 std error       =Se            =(p*(1-p)/n) = 0.0158 for 95 % CI value of z= 1.9600 margin of error E=z*std error                            = 0.031 lower confidence bound=sample proportion-margin of error 0.066 Upper confidence bound=sample proportion+margin of error 0.128

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