Question

An experimenter flips a coin 100 times and gets 42 heads. Find the 90% confidence interval for the probability of flipping a head with this coin.

Answer 1

Solution :

Given that,

n = 100

x = 42

Point estimate = sample proportion = = x / n = 42/100=0.42

1 - = 1-0.42=0.58

At 90% confidence level

= 1 - 90%  

= 1 - 0.90 =0.10

/2 = 0.05

Z/2 = Z0.05 = 1.645 ( Using z table )

Margin of error = E = Z / 2 * (( * (1 - )) / n)

= 1.645 (((0.42*0.58) / 100)

= 0.08

A 90% confidence interval is ,

- E < p < + E

0.42-0.08 < p < 0.42+0.08

(0.34 ,0.50)