Question

We need to find a 95% Confidence Interval. Alpha = .05, n=10, b = 4. Using the binomial table, the answer for the confidence interval is (.1216,.7376). I need to know how to use the binomial table in order to get that answer.

How do you use the binomial table to get the confidence interval (.1216,.7376).

Answer 1

For finding exact confidence interval for population proportion using binomial distribution, we need to use beta distribution

Because CDF of binomial distribution follows beta distribution.

Using excel:

Lower limit of p :

The general command is "=1-BETAINV((1-/2 ,n - k + 1, k)

Here k = number of success = 4

n = 10

Therefore, lower limit of p is = "=1-BETAINV(0.975,7,4)" = 0.121552 = 0.1216 (After rounding it up to fore decimal)

Upper limit of p :

The general command is "=1-BETAINV((/2 ,n - k, k+1)

Therefore, lower limit of p is = "=1-BETAINV(0.025,6,5)" = 0.121552 = 0.0.737622 = 0.7376 (After rounding it up to fore decimal)

Note that, we can not directly use Binomial table to find the exact confidence interval of population proportion p.