Question

A clinical trial tests a method designed to increase the probability of conceiving a girl. In the study 512 babies were born, and 256 of them were girls. Use the sample data to construct a 99% confidence interval estimate of the percentage of girls born. Based on the result, does the method appear to be effective? ___

Answer 1

p = 312/624 = 0.500 best estimate

mean is p N = (0.500) 624 = 312 obvious

standard deviation is sqrt[Np(1-p)] = 12.5

If we approximate the binomial by a Normal

we would be using mu = 312, s.d = 12.5

and the 99% C.I. is mean +- 2.57 s.d

we convert the mean to p by dividing by 624

so corresponding C.I. for p would be 0.500+ - (2.57)(12.5)/624

or 0.500+- 0.051

Answer 2

what about plugging in the numbers 256/512...I cant figure out how you did the standard deviation

Answer 3

Formula for the standard deviation of a binomial distribution with N data and probability p is
sqrt(Npq), where q = 1-p

Answer 4

ok so what about the 99% part.....here is what I have so far....I got a different set of numbers because i got the first one wrong....so:

p = 256/512 = .500
n= (,500)512) = 256
\[\sqrt{(256)(.500)(.5)}\]
mean = 256 sd = .5

at this point I am stuck...whats the rest?

Answer 5

For a Normal distribution
the 99.5%tile is mean + 2.57 s.d and the
0.5%tile is mean - 2.57 s.d.,
so the 99% confidence interval (0.5% to 99.5%)
is the mean plus or minus 2.57 times the s.d.

Answer 6

OK....I come up with .500 < p < .0502
but I dont think that is right :-/

Answer 7

(mean - 2.57 s.d)/624 < p < (mean + 2.57 s.d)/624

I got 0.495 < p < 0.505

Answer 8

oh wait....try using these numbers....the 624 is not the right one

here is the problem again...

A clinical trial tests a method designed to increase the probability of conceiving a girl. In the study 512 babies were born, and 256 of them were girls. Use the sample data to construct a 99% confidence interval estimate of the percentage of girls born. Based on the result, does the method appear to be effective?

Answer 9

so that makes it .494 < p < .505...did you get that? I am doing something wrong I think

Answer 10

".494" vs. ".495" we seem to agree. Check for rounding, yours or mine!

Answer 11

The 512 and 256 values give the same p= 0.500 and almost the same s.d. when you work it out as we did for the 624 and 312 case. Just recalculate mean and s.d. and then divide by 512, not 624.

Answer 12

ok thats what I did...so lets see if that works...well......it says its not right :( I rounded it correctly...

Answer 13

ok so i think where i am going wrong is in the sqrt part.....I am calculating n=256 p= .500 q= .5 ...do you see where I am confused?

Answer 14

if I do the sqrt equation like this: \[\sqrt{(256)(.5)(.5)}\] then I come up with 8...but where do I plug that in?

Answer 15

Wrong square root, need sqrt(512 x 0.5 x 0.5) = s.d. =11.31

p limits are (mean +- 2.57 s.d)/512 as done above.
Good night.

Answer 16

Ok great!! Thank YOU!!