A statistics practitioner working for a for a Majo League Ba

A statistics practitioner working for a for a Majo League Baseball wants to supply radio and television commentators with interesting statistics. He observed serveral hundred games and counted the number of times a runner on first base attempted to steal second base. He found there were 373 such events, of which 259 were successful. Estimate with 95% confidence the proportion of all attempted thefts of second base that are successful.

Please show formula and how the answer is derived.

Solution

CI = p ± Z a/2 Sqrt(p*(1-p)/n)))
x = Mean
n = Sample Size
a = 1 - (Confidence Level/100)
Za/2 = Z-table value
CI = Confidence Interval
Mean(x)=259
Sample Size(n)=373
Sample proportion = x/n =0.694
Confidence Interval = [ 0.694 ±Z a/2 ( Sqrt ( 0.694*0.306) /373)]
= [ 0.694 - 1.96* Sqrt(0.001) , 0.694 + 1.96* Sqrt(0.001) ]
= [ 0.647,0.741]