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 parameters, conditions, calculations, and a conclusion in your answer.

We accept H₀  we agree with manufacturer´s claim

Step-by-step explanation:

We have a test of proportion

Hypothesis test:

We need to develop a one tail test (left) two determine if we get evidence that the effectiveness of the new medication is less than 65 %

1.-) Test Hypothesis

Null Hypothesis                      H₀             p  =  65 %

Alternative Hypothesis          Hₐ             p <  65 %

2.-

Confidence interval and z(c)

Confidence interval is 95 %  or  0,95 then   α  = 0,05

and from z tables we see that  z(c) =  - 1.64

3.-We compute z(p)

z(p) = p - p₀ / √ P₀*Q₀ /n    (1)

p = 115/180   =  63,89 %  = 0,6389

P₀ = 65 %     then  Q₀  =  35 %     and    n  = 180

Plugging these values  in equation (1) we get

z(p) = ( 0,6389 -  65 )/ √(0,65)*(0,35)/180

z(p) = - 0,0111/ √0,001264

z(p) = - 0,0111/0,0356

z(p) = - 0,3118

4.- We compare z(c) and z(p)  

z(c) 0 -1,64   and z(p)  = - 0,3118

We see z(p) > z(c)   then  z(p) is in the acceptance region we accept H₀ we don´t have evidence to say that the effectivness of the medication is lower than a claim of the manufacturer