Question 1. The table below summarize responses to the question "have you ever violated the honor code?" for 41 student who took our opening week surveys.

Violated Code	Never Violated Code
17	24

a) Calculate a 92% confidence interval for the proportion of all pacific student

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 student who have violated the code to within 2% at a 92% Confidence level?

Question 2. A Sample of 10 attacks from my clash of clan's log yielded a sample mean of 62.5 damage per attack with a sample of standard deviation of 12.24.

a)Calculate a 95% confidence interval for the mean damage of all my attacks. Write a sentence interpreting the result.

b)Suppose that I took a smaller sample size of six attacks with a similar sample standard deviation. Briefly explain how this change would affect the width of the confidence internal from a).

c)Assuming nothing else changes would a 90% confidence interval for my mean attacks be wider or narrower than my interval from a) briefly explain.

Question 3. Use the information given in problem 2 to answer this question. Suppose we wish to perform a hypothesis test to determine if my mean damage per attack is significantly greater than 50.

a) State the null and alternative hypotheses for this test

b)Calculate the rejection region if we use a 0.05 significance level.

c)State the appropriate decision for the test with rustication.

Question 4. Use the date given in problem 1 to answer this question. According to a 2014 study, 35% of all US college student admitted to violating the honor code at their schools. Suppose we wish to determine if the proportion of student who have violated the honor code at pacific is significantly different from the nationwide rate using a 0.1 significance level

a)State the null and alternative hypotheses for this test.

b)Calculate the rest statistic and P-value for the sample data in Question1.

c)State appropriate decision for our test based off our sample data. Justify your conclusion.

Question 5. A nationwide survey found that about 44% of all college students reported having used of marijuana in 2020. Suppose we wish to do a hypothesis test to determine if the usage rates at pacific are significantly lower than this nationwide rate4 using a 0.05 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 out opening week survey yielded a sample of proportion of 0.34. what would be the conclusion of our hypothesis test?

c)Which error could we have made in part b? briefly explain.