For each question, define random variable and justify its distribution. 1. A random sample of 18 airline passengers at the Ottawa International Airport gave a mean time spent waiting in line to check in at the ticket counters 28 minutes with a standard deviation of 6 minutes. Construct a 99% confidence interval to estimate the average time spent waiting in line by all passengers at this airport. Interpret the result. 2. An insurance company selected a random sample of 60 auto claims filed with it and investigated those claims carefully. The company found that 8 of those claims were fraudulent. (a) What is the point estimate of the percentage of all auto claims filed with this company that are fraudulent? (b) Construct a 95% confidence interval to estimate the true percentage of all auto claims filed with this company that are fraudulent. Interpret the result. 3. A provincial wildlife service wants to estimate the average number of days licensed hunters spend hunting during a given season. They want the estimate to be within 2 days of the true mean with probability 0.95. Previous studies showed that the standard deviation is approximately 10 hunting days. Approximately how many hunters must be included in the survey? 4. A sample of 14 children from Ontario showed that the mean time they spend watching television is 28.5 hours per week with a standard deviation of 4 hours. Another sample of 10 children from Nova Scotia showed that the mean time spent by them watching television is 23.25 hours per week with a standard deviation of 5 hours. (a) Should you assume the populations standard deviations are equal or unequal? Explain. (b) Find a 95% confidence interval for the difference in the mean times spent by watching television by children from the 2 provinces. Interpret the result.