Question

A manufacturer of a new medication on the market for Alzheimer's disease makes a claim that the medication is effective in 65% of people who have the disease. One hundred eighty individuals with Alzheimer's disease are given the medication, and 115 of them note the medication was effective. Does this finding provide statistical evidence at the 0.05 level that the effectiveness is less than the 65% claim the company made? Make sure to include parameter, conditions, calculations, and a conclusion in your answer. (10 points)

Answer 1

The null and alternative hypothesis

0.65

< 0.65

where p is the population proportion of Alzheimer's patient for whom the medicine is effective .

We can use z test as n =180 is large , both np=180*0.65 =117 and n(1-p)=63 is greater than 10

Test statistic

where

   =115/180 = 0.64 ( sample proportion of Alzheimer's patient for whom the medicine is effective)

thus ,

= -0.28

P value = P ( z < -0.28 ) = 0.3897   (from z table)

Since P value > 0.05

Fail to reject H0

There is not sufficient evidence at 0.05 to conclude that the medication is less effective than the 65% claim the company made.