A drug claims to cure patients in 80% of all cases. A sample of 10 patients was taken, 5 got cured,

Trystan Yates

Trystan Yates

Answered question

2022-06-04

A drug claims to cure patients in 80% of all cases. A sample of 10 patients was taken, 5 got cured, 5 not. I need to decide if the manufacturer should change their claim. Assume 5% to be the significance level.
- H 0 : p = 0.8
- H A : p < 0.8
So, my approach:
1. sample size = 10, p = 0.5, std dev = 0.25
2. calculate the z-value for the sample:
z = ( m e a n s a m p l e   m e a n ) s t d   e r r o r
3. here, I am not sure how to calculate s t d   e r r o r. I am considering two formulas:
- s t d   e r r o r 1 = e x p e c t e d   s t d   d e v = 0.8 × 0.2 = 1.6 = 1.264
- s t d   e r r o r 2 = a c t u a l   s t d   d e v = p × ( 1 p ) s a m p l e   s i z e = 0.5 × ( 1 0.5 ) 10 = 2.5 = 1.58
4. check the z-value to be less than 1.65, if so, reject H 0
Is it makes sense?

Answer & Explanation

Xavier Vargas

Xavier Vargas

Beginner2022-06-05Added 4 answers

Your approach of testing proportions makes sense. However since you already have P values you don't need to use estimate and should find variance directly using P = .8 not .5

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