carlosleblanc26
15.04.2020 •
Mathematics
A pharmaceutical company proposes a new drug treatment for alleviating symptoms of PMS (premenstrual syndrome). In the first stages of a clinical trial, it was successful for 7 out of the 14 women. What is the 95% confidence interval for p, the true proportion of all women who will find success with this new treatment?
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Ответ:
95% confidence interval for p, the true proportion of all women who will find success with this new treatment is [0.238 , 0.762].
Step-by-step explanation:
We are given that a pharmaceutical company proposes a new drug treatment for alleviating symptoms of PMS (premenstrual syndrome).
In the first stages of a clinical trial, it was successful for 7 out of the 14 women.
Firstly, the pivotal quantity for 95% confidence interval for the true proportion is given by;
P.Q. = ~ N(0,1)
where, = sample proportion of women who find success with this new treatment = = 0.50
n = sample of women = 14
Here for constructing 95% confidence interval we have used One-sample z proportion statistics.
So, 95% confidence interval for the true proportion, p is ;
P(-1.96 < N(0,1) < 1.96) = 0.95 {As the critical value of z at 2.5%
level of significance are -1.96 & 1.96}
P(-1.96 < < 1.96) = 0.95
P( < < ) = 0.95
P( < p < ) = 0.95
95% confidence interval for p = [ , ]
= [ , ]
= [0.238 , 0.762]
Therefore, 95% confidence interval for p, the true proportion of all women who will find success with this new treatment is [0.238 , 0.762].
Ответ: