Karl Pearson once tossed a coin 24,000 times and recorded 12,012 heads.

a. Calculate the point estimate for p  P(head)

based on Pearson’s results.

b. Determine the standard error of proportion.

c. Determine the 95% confidence interval estimate for p  P(head).

d. It must have taken Mr. Pearson many hours to toss a coin 24,000 times. You can simulate 24,000 coin tosses using the computer and calculator commands that follow. (Note: A Bernoulli experiment is like a “single” trial binomial experiment. That is, one toss of a coin is one Bernoulli experiment with p  0.5; and 24,000 tosses of a coin either is a binomial experiment with n  24,000 or is 24,000 Bernoulli experiments. Code: 0  tail, 1 

head. The sum of the 1s will be the number of heads in the 24,000 tosses.)

MINITAB Choose Calc  Random Data  Bernoulli, entering 24000 for generate, C1 for Store in column(s) and 0.5 for Probability of success. Sum the data and divide by 24,000.

Excel Choose Tools  Data Analysis  Random Number Generation

 Bernoulli, entering 1 for Number of Variables, 24000 for Number of Random Numbers and 0.5 for p Value. Sum the data and divide by 24,000.

TI-83/84 PLUS Choose MATH  PRB  5:randInt, then enter 0, 1, number of trials. The maximum number of elements (trials) in a list is 999. (slow process for large n’s) Sum the data and divide by n.

e. How do your simulated results compare with Pearson’s?

f. Use the commands (part

d) and generate another set of 24,000 coin tosses. Compare these results to those obtained by Pearson. Also, compare the two simulated samples to each other. Explain what you can conclude from these results.