Can someone do my prob and stats project ASAP ?

MTH 240: Project 2

Directions: Show all answers and work on separate paper. You must show ALL work and

steps to receive credit. This project is NOT intended to be group work. Ask only your in-

structor or the tutors in the Math Center for help with this project.

As a prisoner of war during World War II, the English mathematician John Kerrich (1903−1985) per-

formed simple experiments to demonstrate a number of fundamental laws of probability. One such exper-

iment was tossing a coin 10,000 times and recording whether it landed heads or tails on each toss. He

obtained 5,067 heads. So, the empirical probability of getting heads on a single toss for his experiment was

p̂ = 5, 067/10, 000 = 50.67%.

1. Toss a coin n = 50 times and record the number of times it comes up heads. From your data, compute

a point estimate, p̂, for the fraction of times it comes up heads. Let p be the probability of heads on

a single toss. Construct a 99% confidence interval to test whether your data is consistent with the

hypothesis that the coin is fair. (Clearly set-up the null and alternative hypotheses and interpret the

results of your confidence interval).

2. Repeat the procedure from #1, but now toss the coin n = 100 times. Is your data still consistent with

the hypothesis that the coin is fair? What has happened to the margin of error?

3. Say you want to be 99% confident with a margin of error of 1% that you will capture the true probability

of landing heads on a single toss.

(a) Using your point estimate from #2, how many times must you toss the coin to achieve this?

(b) How many times must you toss the coin if you do not want to rely on a prior estimate?