Flip a coin 60 times Record the outcome of each of the 60 fl

Flip a coin 60 times. Record the outcome of each of the 60 flips in order from 1 to 60, using the Tally Sheet accompanying the Final Exam. Tally the number of heads and the number of tails and calculate the proportion of heads in your sample.

Based on your sample result, calculate a 95% Confidence Interval for the true population value. Calculate a 95% Confidence Interval for the proportion of heads.

Solution

Say you flipped a coin 60 times and recorded heads 36 times and tails 24 times.
The proportion of heads in your sample,phat = 36/60 = 0.60

standard error, SE = sqrt(phat(1-phat)/n)
SE = sqrt(0.6(1-0.6) / 60) = 0.06325

alpha,a = 1-0.95 = 0.05
Za/2 = Z0.025= 1.96

95% Confidence Interval for the true population proportion of heads
phat +/- [Za/2 * SE]
0.60 +/- [1.96 * 0.06325]
0.60 +/- 0.124
( 0.476 , 0.724 )

0.476 <P< 0.724

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Say if we are testing the hypothesis that the coin is not biased so there is equal chance of expecting heads and tails.

H0: p = 0.50
H1: p is not equal to 0.50

Since 0.50 lies in the confidence interval hence H0 can not be rejected.
So, we conclude that the coin is not biased.