1. What is the P-Value? (3 points) 2. You are interested in studying the extent to which people convicted of burglary committed several acts of theft before being arrested You thus decide to measure the number of times a typical person convicted of burglary has committed theft prior to his/ her arrest. You draw a random sample of 75 people and find an average of 4.5 times and a standard deviation of 3. (8 points) a) Please construct and interpret a 99% confidence interval. b) If you were to increase the confidence level, what would happen to the margin of error? 3. Conventional wisdom holds that among Canadians who engage in tax evasion, the average amount unduly kept from the government per year is $400. You want to test whether this conventional wisdom does in fact represent the true parameter value by running a two-tailed hypothesis test. You randomly sample 80 Canadian "tax cheats" and find a mean of $430, with a standard deviation of $100. (12 points) a) Detail the steps of the hypothesis test you would run at a 90% confidence level, including the conclusion and its interpretation. b) Demonstrate how the answer arrived at in (a) is validated by running a 90% confidence interval