ECON 180 - Statistics-Bus & Econ Extra Credit Assignment (6% of your grade) 5 Due: Wednesday, April 22nd to 2ndbeginning of the LECTURE the LECTURE December December 3rd to the beginning of the LECTURE Wednesday, 5th Thursday at the beginning of the Wednesday, December Instructions: Clearly print your name and Howard ID. No late homework will be accepted. All exercises have to be in order (starting from 1 to 20). All homeworks have to be stapled. Please staple your homework. If I can' decipher what you wrote, you will get no credit. t 1. An airline' data indicate that 50 percent of people who begin the online process of booking a s ight never complete the process and pay for the ight. To reduce this percentage, the airline is considering changing its website so that the entire booking process, including ight and seat selection and payment, can be done on two simple pages rather than current four pages. A random sample of 300 customers who begin the booking process are provided with the new system, and 117 of them do not complete the process. Formualte the null and the alternative hypotheses needed to attempt to provide evidence that the new system has reduced the noncompletion percentage. Test at 5% signi...cance level. Find the p-value of the test. 2. In a poll taken to estimate the Prime Minister' current popularity, a random sample of 1000 voters was s taken, and 59% of them responded that he is doing a good job. Construct a 95% con...dence interval for the population proportion who think that way. 3. The metropolitan airport commission is considering the establishment of limitations on noise pollution around a local airport. At the present time, the noise level per jet takeo ine one neighborhood near the airport is approximately normally distributed with a mean of 100 decibels and a standard deviation of 6 decibels. a. What is the probability that a randomly selected jet will generate a noise level greater than 108 decibels in this neighborhood? b. What is the probability that a randomly selected jet will generate a noise level of exactly 100 decibels? c. Suppose a regulation is passed that requires jet noise in this neighborhood to be lower than 105 decibels 95% of the time. Assuming the standard deviation of the noise distribution remains the same, how much will the mean level have to be lowered to comply with the regulation? 4. The time in minutes for which a student uses a computer terminal at the computer center of a major university follows an exponential probability distribution with a mean of 36 minutes. Assume a student arrives at the terminal just as another student is beginning to work on the terminal. a. What is the probability that wait for the second student will be 15 minutes or less? b. What is the probability that the wait for the second student will be between 15 minutes and 45 minutes? c. What is the probability that the second student will have to wait an hour or more? 5. Weights of men in one age group are normally distributed with a standard deviation ( ) of 9 lb. A researcher wishes to estimate the mean weight of all men in this age group. Find how large a sample must be drawn in order to be 90 percent con...dent that the sample mean will not dier from the population mean by more than 2.96 lb. 6. Suppose the mean salary for full professors in the United States is believed to be $61,650. A sample of 36 full professors revealed a mean salary of $69,800. Assuming the standard deviation is $5,000, can it be concluded that the average salary has increased using a 1% level of signi...cance? 1 7. Historically, evening long-distance calls from a particular city have averaged 15.2 minutes per call. In a random sample of 35 calls, the sample mean time was 14.3 minutes. Assume the standard deviation is known to be 5 minutes. Using a 5% level of signi...cance, is there su cient evidence to conclude that the average evening long-distance call has decreased? Find the p-value. 8. It is claimed that a new treatment is more eective than the standard treatment for prolonging the lives of terminal cancer patients. The standard treatment has been in use for a long time, and from records in medical journals the mean survival period has been 4.2 years with a standard deviation of 1.1 years. The new treatment is administered to 80 patients, and their average duration of survival is calculated to be 4.5 years. Is the claim supported by these results? 9. The speed of cars (mph or miles/hour) on CA-60 freeway follows a normal distribution. A highway safety researcher believes that cars on CA-60 travel at an average speed of 70 mph. From a sample of 11 vehicles driving on the highway, he ...nds the sample average speed to be 74.5 mph with a sample standard deviation of 9 mph. a. Use a t-test to verify his belief b. Suppose that the population standard deviation is known to be 15. Use a suitable test at 5% level of signi...cance to verify the hypothesis mentioned in part (a). 10. A weight loss center provided a loss for 72% of its participants. The center' leader decides to test a new s weight loss strategy on a random sample size of 140 and found 109 participants lost weight. Should the center continue its new strategy? Test an appropriate hypothesis using 1% signi...cance level and state your conclusion. Note: You need Normal Distribution and t table to solve the exercises. They are uploaded on Blackboard under "Distribution Tables". 2