1. Construct a 95% confidence interval for the average yearly tuition for all In-state New Jersey colleges/universItles. Interpret this interval in the context of the problem

2. What would happen to the width of the Interval in the first problem if you decided to a 99% confidence interval instead? What would happen to the center of the Interval? Which interval would have a higher chance of being accurate? Which interval would be more precise?

3. What would happen to the 95% confidence interval in the first problem if you decided to go and sample an additional 10 colleges In New Jersey to add to your data?

4. while doing your research on college tuition, you see a quote from a local politician. This politician is quoted as saying "College tuition in this state is completely ridiculous) The average yearly tuition for instate New Jersey residents is $27,000!" You suspect this Politician is being a bit dramatic (in other words, you suspect that the average yearly tuition for in-state New Jersey residents is lower.) Perform a hypothesis test at the α = 0.10 level. Be sure to include the following in your hypothesis test null and alternate stated, test statistic and p-value reported, conclusion in the context of the problem stated.