1. The US. mint reports that some of the coins in circulation are in fact not fair, but others are fair. You ip a coin 100 times and it lands on heads 65 times. (a) Perform a hypothesis test by doing the following steps o State the null and alternative hypotheses. Specify if it is a one-sided or two-sided test. 0 Find the z-statistic AND the pvalue. o Decide whether to reject or fail to reject the null hypothesis based on a signicance level of o: = .05. (b) The mint species that 99.9% of all coins are fair1 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 involved1 use the dbinornO func- tion in R to calculate them.) For example if you wanted to nd 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] 0.0795533?! (c) Compare your conclusions under the hypothesis test and using Bayes\" theo- rem. Are they similar or different? "Why do the two approaches give you simi- lar/different conclusions