The U.S. mint reports that some of the coins in circulation are in fact not fair, but others are fair. You flip a coin 100 times and it lands on heads 65 times.

(a). Perform a hypothesis test by doing the following steps

• State the null and alternative hypotheses. Specify if it is a one-sided or two-sided test.
• Find the z-statistic AND the p-value.
• Decide whether to reject or fail to reject the null hypothesis based on a significance level of = .05.

(b). The mint specifies that 99.9% of all coins are fair, and .1% of coins are weighted. The weighted coins all have a 65% probability of landing on heads. Use Bayes' Theorem to estimate the probability that the coin is weighted.

(c)Compare your conclusions under the hypothesis test and using Bayes' theorem. Are they similar or different? Why do the two approaches give you similar/different conclusions?