There is a wenn known medicine on the market called \"Espron\" with a suc- cess
ID: 3066136 • Letter: T
Question
There is a wenn known medicine on the market called "Espron" with a suc- cess probability for cure of p -0.45. The competition sells since a few weeks a new medicine called " Raton" and clai heir medicine is more than 0.45 To advertise with this claim they start a study with 100 patients giving the new medicine to them. With help of all collected data they want to prove their claim with a level of 0.05 ms that the cure probability of t a) Formulate the null hypothesis and the alternative hypothesis. Formu- late also a proper test procedure. Find the critical value and the effective signincance. b) Find the type 1 error, if the real cure probability is p 0.40 c) Find the type 2 error with usage of normal approximation with continuity correction, if the real cure probability if p - 0.5 d) Which decision will be made, if 40, 50 or 60 Patience will be cured by the original medicine " Espron"Explanation / Answer
Inference problem:
H0: Null hypothesis (hypothesis of no difference generally)
H1: Alternate hypothesis
P = probability of success of ‘Raton’ (new drug)
Probability of success of existing drug ‘Espron’ = 0.45
We will consider the above probability as proportion (since the sample size is 100)
(Alpha) = 0.05
For out sample size 100, we will consider Z statistic.
A.In the given case,
Ho: P = 0.45
H1: P > 0.45
The critical value is z score from z table at ) = 0.05
We have critical table value = 1.645
B.The statistic we will use is:
Z = (P0 – P)/sqrt((P*(1-P))/n)
Where, P0 is observed probability, sqrt is short form of square root
Now the observed proportion is given to us as P0 = 0.40
To compute the type 1 error for P0 = 0.40, we will compute p-value of Z statistic.
Using the above Z statistic formula, replacing P0 = 0,40 and P = 0.45, n = 100, we get,
P value = 0.8171 (computed using software)
Hence type 1 error = 0.8171
C.To take decision, we will use p value criteria
Decision Rule:
If p-value < alpha give (0.05) then reject H0(null hypothesis)
Otherwise, we fail to reject H0.
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