2. A drug company has introduced a new treatment for sun burn. The current leadi

Question

2. A drug company has introduced a new treatment for sun burn. The current leading brand’s treatment cures sun burn in 70% of patients. In a random sample of 150 people, the new treatment cured warts in 114 people.

a. Find the 99% confidence interval for the true proportion of warts cured for the new treatment.

b. Interpret the confidence interval in the words of the problem.

c. Find the margin of error.

d. Does this data and analysis provide evidence so that the company can claim its new treatment is superior to the leading brand? Justify!

Explanation / Answer

here phat=114/150=0.76

a)for n=150 ; std error =(phat*(1-phat)/n)1/2 =0.0349

for 99% CI ; z=2.5758

hence 99% confidence interval for the true proportion =phat -/+ z*std error =0.6702 ; 0.8498

b) above interval gives 99% confidence interval to contain  true proportion of warts cured for the new treatment

c) margin of error =z*std error =0.0898

d) as our confidence interval contains 0.70 (70%) as probable value of true proportion this  data and analysis does not provide sufficient evidence that its new treatment is superior to the leading brand

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