Give an example of two Sample Proportions the difference of

Give an example of two Sample Proportions the difference of which a Health Professional would like to use to make a Statistical Inference. Your answer MUST include the target Populations of your Statistical Inference activities along with what sample characteristic the sample proportions are measuring.

Solution

suppose, a medicine Company has developed a new medicine. The company claims that the new medicine will cure more quickly than the old medicine.

so, now we have to test which of them is showing effects quicker!Right?

Old medicine compnay applied their medicine to 30 people and New company applied med. to 25 different people.

Person\'s having the Old med,had an average time of 78 hrs to feel good,with a standard deviation of 10; and Person\'s having New med. had an average time of 85 hrs to feel right,with a standard deviation of 15.

we have to test:

Null hypothesis: mu1 - mu2 = 0
Alternative hypothesis: mu1 - mu2 >0

Target popltn= person\'s having some type of disease for which the medicines will be given!
Actually being measured= the difference in time the 2 medicines are taking to cure a person!

The inference should be the tested result which is \" which Medicine is doing the work quickly\" and thus people should get an idea about the medicines.similarly, the qualities of such medicines, side effects all can be measured by testing!

SE = sqrt[(s₁²/n₁) + (s₂²/n₂)]
SE = sqrt[(10²/30) + (15²/25] = sqrt(3.33 + 9) = sqrt(12.33) = 3.51

DF = (s₁²/n₁ + s₂²/n₂)² / { [ (s₁² / n₁)² / (n₁ - 1) ] + [ (s₂² / n₂)² / (n₂ - 1) ] }
DF = (10²/30 + 15²/25)² / { [ (10² / 30)² / (29) ] + [ (15² / 25)² / (24) ] }
DF = (3.33 + 9)² / { [ (3.33)² / (29) ] + [ (9)² / (24) ] } = 152.03 / (0.382 + 3.375) = 152.03/3.757 = 40.47

t = [ (x₁ - x₂) - d ] / SE = [ (78 - 85) - 0 ] / 3.51 = -7/3.51 = -1.99

where s₁ is the standard deviation of sample 1, s₂ is the standard deviation of sample 2, n₁ is the size of sample 1, n₂ is the size of sample 2, x₁ is the mean of sample 1, x₂ is the mean of sample 2, d is the hypothesized difference between the population means, and SE is the standard error.

t-score = -1.99

Thus, the P-value = 0.027..

Since the P-value (0.027) is less than the significance level (0.10), we cannot accept the null hypothesis.

so, we the new medicine is showing effects quicker than the old one!