Getting 28 heads in 50 coin flips corresponds to a proportion of . In the simulation, this result had a relative frequency between_ and_ .

Question

You flip a coin 6 times and do not get tails. The probability of this happening is, so you suspect this coin favors heads. You simulate flipping the coin 50 times by repeatedly drawing 200 random samples of size 50 from a population of 50% ones and 50% zeros. You let the population of ones represent the event of flipping the coin and getting heads. The histogram of the distribution of the sample proportions is shown below. What should you conclude when you flip the actual coin 50 times and get 28 heads?

Answer 1

The population percent in question is p=44%

The standard deviation is

sqrt( p * (1-p)/ n)

sqrt ( 44% * 56% / 6)

= 1.2158947322856530905334995364832‬

The test statistic is to divide the difference of the proportions by the standard deviation:

(0.5 - 0.44)/stndDev

0.06/1.2158947322856530905334995364832‬

= 0.049346....

The experimental results support that the coin is NOT biased.