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 α = .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. (Note: If your calculator cannot compute the probabilities involved, use the dbinom() function in R to calculate them.) For example if you wanted to find the probability that a binomial random variable with n = 100 and p = .59 would have 60 successes you could enter the following into R: > dbinom(x = 60, size = 100, prob = .59) [1] 0.07955339 (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?