Please do not waste my question if you cannot answer this and please write legib
ID: 3340104 • Letter: P
Question
Please do not waste my question if you cannot answer this and please write legibly. Thank you
1. A general practitioner chooses a random sample of 25 women from the patient registry of her general practice and finds that 3 of them have a history of suffering from asthma. If the county prevalence of asthma in women is 15%, then is the prevalence of asthma among women in the general practice (GP) significantly smaller than that of the county rate? Solve this question: (i) with a 5% significance test using the five steps covered in class (20 points): (ii) using a 95% CI (20 points):Explanation / Answer
Question 1
(i) Step I:
Null hypothesis : H0 : Proportion of women having asthma in general practice is equal to proportion of women having asthma as same as county rate. p= p0 = 0.15
Alternative Hypothesis : Ha : Proportion of women having asthma in general practice is significantly less than to proportion of women having asthma as same as county rate. p< p0
Step Two : significance level alpha = 0.05
Step Three:
sample proportion p^ = 3/25 = 0.12
standard error of the proportion se0 = sqrt(0.15 * 0.85/25) = 0.0714
Test statistic :
Z = (p^ - p0)/ se0 = (0.12 - 0.15)/ 0.0714 = - 0.42
Step : IV
P - value = Pr(Z < -0.42) = 0.3372 < 0.05 so it is insignificant here.
Step :V
Since the p-value of 0.3228 is greater than 0.05, the null hypothesis provides a very poor explanation of the data. We find good evidence that the population proportion of of women having asthma in general practice is equal to proportion of women having asthma as same as county rate.
(2) 95% CI = p^ +- Z95% sqrt [p^ (1-p^/N]
= 0.12 +- 1.96 * sqrt[0.12 * 0.88/25]
= 0.12 +- 0.1274
= (0, 0.2474)
(c) This GP prevalnce is not signuificantly smaller than the county rate, so now county will include this GP practice among its asthma prevention programs. County will focus on it as there is no reduction in General practice.