Problem 3 (Hypothesis tests) I want to figure out if a coin is fair, so I flip it 100 times, and the coin comes up heads 38 times. (If the coin is fair, then p = P(heads) = 0.5). (a) What hypotheses (Ho and HA) should be used to test if the coin is fair or not? (b) Conduct the hypothesis test at the a = 0.05 significance level. State the value of the test statistic, the p-value, and your conclusion. (c) What is the probability of Type I error?Problem 5 (Hypothesis tests and confidence intervals) Referring to the coin in Problem 3, construct a 95% confidence interval for p (the true prob- ability that the coin comes up heads). Does this interval support your findings in Problem 3