1) The table below summarizes responses to the question "have you ever violated the honor code?" for 41 students who took our opening week survey. Violated Code Never Violated Code 14 27 a) Calculate a 94% confidence interval for the proportion of all Pacific students who have violated the honor code. Write a sentence interpreting the result. b) How large of a sample size is needed to estimate the population proportion of Pacific students who have violated the code to within 3% at a 94% confidence level?2) A sample of six defenses from my Clash of Clans log yielded a sample mean of 64.17 damage per defense with a sample standard deviation of 12.89. a) Calculate a 90% confidence interval for the mean damage done on all my defenses. Write a sentence interpreting the result. b) Suppose that I took a larger sample size of 10 defenses with a similar sample standard deviation. Briefly explain how this change would affect the width of the confidence interval from a). c) Assuming nothing else changes, would a 95% confidence interval for my mean defenses be wider or narrower than my interval from a)? Briefly explain.3) Use the information given in problem 2 to answer this question. Suppose we wish to perform a hypothesis test to determine if the mean damage per defense is significantly greater than 50. a) State the null and alternative hypotheses for this test b) Calculate the rejection region if we use a 0.01 significance level. c) State the appropriate decision for the test with justification.4) Use the data given in problem 1 to answer this question. According to a 1990s study, 64% of all US college students admitted to cheating. Suppose we wish to determine if the proportion of students who have violated the honor code at Pacific is significantly different from this nationwide rate using a 0.01 significance level a) State the null and alternative hypotheses for this test b) Calculate the test statistic and p-value for the sample data in Question 1. c) State appropriate decision for our test based off our sample data. Justify your conclusion.5) A nationwide survey found that about 44% of all college students reported having used marijuana in 2020. Suppose we wish to do a hypothesis test to determine if the usage rates at Pacific are significantly higher than this nationwide rate using a 0.1 significance level and a sample of 41 students. a) For what sample proportions will we reject the null hypothesis? b) A random sample of 41 students from our opening week survey yielded a sample proportion of 0.46. What would be the conclusion of our hypothesis test? c) Which error could we have made in part b? Briefly explain