2. A statistics professor has asked thier students to flip coins over the years. They have kept track of how many flips land heads and how many land tails. Combining the results of their students over many years, they have formed a 95% confidence interval for the long-run population proportion of heads to be

(.501, .513).

• a. Explain what could have contributed to this interval being so narrow?
• b. Suppose they were to conduct a hypothesis test of whether the long-run population proportion of heads differs from one-half. Based on this interval (do not conduct the test), would they reject the null hypothesis at the .05 significance level? Explain briefly (no more than one sentence).
• c. Does the interval provide strong evidence that the long-run population proportion of heads is much different from one-half? Explain briefly.