You flip a fair coin thirty-six times and record the proportion of heads you obt

Question

You flip a fair coin thirty-six times and record the proportion of heads you obtain. You then repeat this process of flipping the coin thirty-six times and recording the proportion of heads obtained for many, many such trials. When done, you make a histogram of your results.

a) About where do you expect the center of your histogram to be? Use appropriate notation to describe this fact.

b) What is the standard deviation of the sampling distribution of the proportion p ˆ of heads obtained?

c) Describe the shape of the sampling distribution of p ˆ . Justify your answer.

d) What is the probability that the sample proportion would be more than 0.6333? Would this make the assumption of a fair coin doubtful?

Explanation / Answer

a) we expect center to be 0.5

as the coin is fair sample proportion should be 0.5

b)

sd of p^ = sqrt*pq/n) = sqrt(0.5 * 0.5/36) = 0.5/6= 1/12

c)

(p^ - p)/sqrt(pq/n) follow normal distribution

Z = (p^ - 0.5)/(1/12)

d) P(p^ > 0.6333)

= P(Z > (0.6333 - 0.5)/(1/12))

= P(Z > 1.5996)

=

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