Statistics 4220 Test 2 Version A NAME: _________________________________________ Instructions: Read these instructions Do not turn the page until the test begins You have 50 minutes This test is printed on both sides, so don’t miss a page. For this test you may use a page of notes, a calculator, z-tables, and t-tables If you need any of these please tell me – we can find a solution preferably before the exam begins Please turn off your cell phone. You cannot have your phone out at all. No one wants to hear “Yellow Submarine” in the middle of the test If you have a question during the test please come forward quietly so that you are not disruptive. If you leave early please do so quietly. Note that I cannot give answers that are part of the test, only clarify the English being used. You must show your work. Answers which are correct but do not show any work may not get full credit. I might assume you either guessed, cheated, or used some fancy calculator. Cheating is not tolerated. If someone is suspected of cheating I will deal with the situation afterwards. Hats or hoods must be removed. 1) (9 minutes) The distribution of radiowaves has an assumed standard deviation of 0.7 MhZ. In 1960 the average was 2 MhZ. A research group is doing a test where they randomly sample 40 radiowaves. Their p-value is shown in the picture below. Do all seven steps of their hypothesis. Pick your alpha. You should be able to get reasonable estimates from the picture. 2) (3 minutes) A research group is testing the average number of daily emails sent by UW students using the alternative Ha: μ ≠ 35. Their x = 21. The p-value from their test is 0.074. Then they decide to change to the alternative Ha: μ > 35. What will their new p-value be? 3) (6 minutes) Standard String Theory states that the Higgs boson should have mass of 126.0 (measured in GeV/c2) on average. New String Theory states the mass should be 125.3 on average. Both theories state the static mass should have a standard deviation of 1.5 (the error is mostly due to measurement error of the accelerator). Scientists at CERN are assuming the Standard String Theory is correct, and they are going to test if the mass is less than 126.0 using 33 measurements and α = 0.05. For proponents of the New String Theory, how powerful is the test at CERN expected to be? 4) (5 minutes) 5) (4 minutes) Suppose you have just been hired to check the quality of the Repaid Ytrid infant car seat. Your boss has issued a statement that the seats can withstand a 30 mile an hour car crash. You will randomly select 100 car seats, and simulate crashes at increasing speeds until each car seat fails. If the car seat is unsafe you will have to issue a press conference to expose the scandal. If it is safe your name will be put on the company claim. You had α=0.05, but then you were told to change it. What would you change it to and why? 6) (4 minutes) A research firm knows the average lifetime for a lightbulb has a population standard deviation of 144 hours. They would like to know the average lifetime, so they randomly sample 12 lightbulbs and get an average of 1000 hours. What is the 95% confidence interval for the average? 7) (9 minutes) In Fort Knox the US government has $168 billion dollars in gold bars. Each gold bar must be 1000 grams on average so that the US can know how much it has. A random sample of 15 gold bars from Fort Knox found an average of 999.5 grams with a standard deviation of 1 gram. Assuming the weight is normally distributed test whether the bars are being made accurately. 8) (5 minutes) A canvas tent could be stretched from the wind. To find out how far it can stretch before tearing a random sample of 48 tents were stretched. The average was 2.33 feet with a standard deviation of 1.645 feet. Find the 90% confidence interval for the average stretching distance. 9) (4 minutes) The amount of time students take on this exam is random, but a 95% confidence interval on the true average amount of time is (42, 55) minutes. How can you explain the use of 95%? a. 95% of the averages for time on this test are between 42 and 55 minutes b. The probability that μ is between 42 and 55 minutes is 95% c. The true average time spent on this test is between 42 and 55 95% of the time d. Of all possible 95% confidence intervals 95% of them would capture the true mean e. 95% of all students finish this test in 42 to 55 minutes 10) (1 minute) If you were to pick a theme song for this class, what would you pick?