Question: A statistician and an engineer flipped a coin to see who would buy lunch. The engineer lost and challenged the statistician to “prove” that the coin was fair. The engineer flipped the coin in question 1,000 times for Trial 1, 10,000 times for Trial 2 and 100,000 times for Trial 3. The following results were recorded:

Trial 1: 1,000 tosses gave 505 heads

Trial 2: 10,000 tosses gave 5,049 heads

Trial 3: 100,000 tosses gave 50,501 heads

Use a z-test for proportions to see whether the results from each trial would support the claim that the coin was a “fair” coin (A coin that comes up heads 50% of the time). Use a 5% level of significance. For each trial:

a. Construct a set of hypotheses (they will be the same for all 3 trials)

b. Calculate a point estimate for p and the appropriate test statistic and p-value for each trial.

c. Make a statistical decision regarding the hypotheses and show the numbers you used to make that decision for each trial.

d. Make a concluding summary statement about what you found for each trial.

e. What type of error is possible for each trial?

f. Was the coin used a “fair” coin? Should the engineer require a “different” coin for the next bet? Explain you reasoning.