Please help with question and please show work Thanks A pers

Please help with question and please show work. Thanks!

A person claims to be able to predict the outcome of flipping a coin. This person is correct 16/25 times. Compute the 95% confidence interval on the proportion of times this person can predict coin flips correctly. What conclusion can you draw about this test of his ability to predict the future?

Solution

p=16/25 =0.64

Given a=1-0.95=0.05, Z(0.025) = 1.96 (from standard normal table)

So the lower bound is

p - Z*sqrt(p*(1-p)/n) =0.64-1.96*sqrt(0.64*(1-0.64)/25) =0.45184

So the upper bound is

p + Z*sqrt(p*(1-p)/n) =0.64+1.96*sqrt(0.64*(1-0.64)/25) =0.82816

We have 95% confident that the population proportion will be within this interval.