3. Find the margin of error for estimating the population mean for a sample of 101 individuals with a standard deviation of 75, using confidence levels of (a) 90% and (b) 99%. What is the effect of your choice of confidence level on the margin of error?

4. The average value of speeding tickets issued to drivers in Westville last year was $150. The police department decides to analyze whether speeding tickets issued to teenage drivers (between age 16-19) were different from the norm. Analysts take a random sample of 27 tickets issued to teenage drivers during this time period and calculate a 95% confidence interval of (138, 162). Explain what is wrong with each interpretation of this interval: (a) The department can infer that 95% of teenage drivers in Westerville will receive a ticket between $138 and $162. (b) The department can be 95% confident that x-bar is between $138 and $162. (c) If the department repeatedly took random samples of 27 teenage speeding ticket recipients and calculated confidence intervals for ticket amounts, then 95% of the time the population mean would be estimated to fall between $138 and $162.