11. Find the Maximum Likelihood Estimator for p from the Binomial Distribution: Px) = (3) p* (1 -pN 12. In a certain city, the departure times of the trains are known to be notoriously unreliable. Trains have been known to leave as late as 75 mins. The Manager of the Train Station wants an estimate of the mean departure time (in mins.). In other words, the Manager wants an estimate on how late the trains are leaving. The Manager orders a random independent sampling of 12 trains. The average of sample times was 66.3 mins., with a standard deviation of 8.4 mins. The Manager wants an error of 5%. What was the estimate? What assumption(s) did you make? 13. A company claims that its light bulbs are superior to those of a competitor based on a study which showed that a sample of 40 of its bulbs had an average lifetime of 522 hours, with a S.D. of 28 hours; while a sample of 30 bulbs made by the competitor, had an average lifetime of 513 hours, with a S.D. of 24 hours. Test the null hypothesis 13 p2 =0 against a suitable one-sided alternative to test whether this claim is justified. Use o = .05. 14. A car 1s advertised as having a gas mileage rating of at least 30 miles/gallon in highway driving. If the miles per gallon obtained in 10 independent experiments are: 26, 24, 20, 25, 27, 25, 28, 30, 26, 33 should you believe the advertisement