Binomial Distributions and Confidence Intervals

• Dec 1st 2008, 07:29 PM
lostnumber
Binomial Distributions and Confidence Intervals
If I have a binomial distribution, can I work out the confidence interval simply by summing up the probabilities of each set of outcomes until I reach 95%?

e.g. n = 70, p(success) = 0.25. I know that 95% of the distribution falls between 11 and 24.

Can I take this range as the 95% confidence interval or do I need to approximate to a normal distribution and do a z-test? The interval I have selected is evenly distributed +/-6.5 of the mean.

The mean of the data is 17.5, SD is 3.62 using this site

Binomial Distribution Calculator

(and if you put "Between 11 and 24" you will see that the probability is 0.9480 ~= 95%)

Here is a sample of my data if you wish to do some rough calculations

0 0.0000
1 0.0000
2 0.0000
3 0.0000
4 0.0000
5 0.0001
6 0.0003
7 0.0010
8 0.0026
9 0.0059
10 0.0121
*11 0.0219
*12 0.0360
*13 0.0535
*14 0.0726
*15 0.0903
*16 0.1035
*17 0.1096
*18 0.1075
*19 0.0981
*20 0.0834
*21 0.0662
*22 0.0491
*23 0.0342
*24 0.0223
25 0.0137
26 0.0079
27 0.0043
28 0.0022
29 0.0011
30 0.0005
31 0.0002
32 0.0001
33 0.0000

The thing here is I'm using a discrete variable so I don't think it would be right to approximate this to a normal distribution and then do a z-test.

Thanks.

PS: I think I might have posted this in the wrong forum: this might be more college/university level. Feel free to move it over - moderators.
• Dec 2nd 2008, 02:01 AM
mr fantastic
Quote:

Originally Posted by lostnumber
If I have a binomial distribution, can I work out the confidence interval simply by summing up the probabilities of each set of outcomes until I reach 95%?

e.g. n = 70, p(success) = 0.25. I know that 95% of the distribution falls between 11 and 24.

Can I take this range as the 95% confidence interval or do I need to approximate to a normal distribution and do a z-test? The interval I have selected is evenly distributed +/-6.5 of the mean.

The mean of the data is 17.5, SD is 3.62 using this site

Binomial Distribution Calculator

(and if you put "Between 11 and 24" you will see that the probability is 0.9480 ~= 95%)

Here is a sample of my data if you wish to do some rough calculations

0 0.0000
1 0.0000
2 0.0000
3 0.0000
4 0.0000
5 0.0001
6 0.0003
7 0.0010
8 0.0026
9 0.0059
10 0.0121
*11 0.0219
*12 0.0360
*13 0.0535
*14 0.0726
*15 0.0903
*16 0.1035
*17 0.1096
*18 0.1075
*19 0.0981
*20 0.0834
*21 0.0662
*22 0.0491
*23 0.0342
*24 0.0223
25 0.0137
26 0.0079
27 0.0043
28 0.0022
29 0.0011
30 0.0005
31 0.0002
32 0.0001
33 0.0000

The thing here is I'm using a discrete variable so I don't think it would be right to approximate this to a normal distribution and then do a z-test.

Thanks.

PS: I think I might have posted this in the wrong forum: this might be more college/university level. Feel free to move it over - moderators.

Your calculation looks OK to me.

The normal approximation would be valid here (why?) - perhaps you should use it just to see what happens.