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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 find a solution before the exam begins Please turn off your cell phone. You cannot have your phone out at all. No one wants to hear “Oops I did it again” 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. Cheating includes looking at another person’s test/study sheet. Our job is to protect the integrity of the class, which is why it feels like we are looming. If someone is suspected of cheating they will not be called out because that is disruptive, we will deal with the situation afterwards. Hats or hoods must be removed. The door on a Brown Bear Cage is manufactured to withstand 3000 Pascals. The company says that is the force an average brown bear can put on a door. Assume your job is to sit in the truck with a cage full of an angry bear. You are going to do a hypothesis test using 32 random brown bears to see if the average force is really 3000 Pascals. Your goal is to avoid an awful death. (1) (3 minutes) If you could not use 0.05 as your alpha, what value of alpha would you pick, and why? (2) (8 minutes) The average strength of 32 bears was 3124 Pascals with a standard deviation of 124 Pascals. Using the alpha you picked test whether the cage door is safe on average. Use a p-value and all 7 steps of a hypothesis. (3) (5 minutes) (4) (2 minutes) Which of the following scenarios will have the greatest power? A) n=100 s=40 α=0.15 B) n=100 s=20 α=0.10 C) n=1000 s=20 α=0.15 D) n=1000 s=40 α=0.05 E) n=10 s=20 α=0.15 F) n=10 s=40 α=0.05 (5) (5 minutes) The time it takes a Welding Robotic Engine Car Kit to complete a welding job on an automobile is N(5, 0.49) minutes. A new safety feature requires the machine to wait for clearance from the Safety Test And Block. This will only cause a delay in the beginning of the process. The quality control expert wants to find the new average time to complete a welding job. He randomly selects 5 times to test the machine. His average time was 8.4 minutes. Find a 99% confidence interval for the true average time. (6) (6 minutes) We know desktops live longer than laptops, so we don’t need a hypothesis test. Instead we want a 90% confidence interval for how much longer they live. Find the interval. Desktops: Sample size: 81 desktops Sample average: 8 years Sample standard deviation: 3.5 years Laptops: Sample size: 81 laptops Sample average: 5 years Sample standard deviation: 1.2 years The following output comes from regression using the actual HW9 scores and the Final test scores from an introductory class I taught three years ago. Sample size: 48 R (correlation coefficient) = 0.4961 R-sq = 0.24614276 Estimate of error standard deviation: 14.458866 Parameter estimates: Parameter Estimate Std. Err. Intercept 47.97618 5.5324807 46 Slope DF T-Stat P-Value 8.671731 <0.0001 0.3491367 0.090088144 46 3.8755014 0.0003 (7) (2 minutes) Before analyzing the data above, is there evidence that any assumptions for regression could be violated in this data set? Explain which assumptions and what tells you they might be a problem. (8) (4 minutes) Assume no assumptions are violated. Form a 90% Confidence interval for how much your final is supposed to increase for each problem done on homework 9. (9) (3 minutes) (10) (4 minutes) The NYTimes did a study on the proportion of football players that have sustained a head injury. Their 95% confidence interval based on 109 random NFL players was (0.571, 0.629). Check which of the following (if any) are true. There is a 95% probability that the proportion is between 0.571 and 0.629 95% of the time the true proportion will be between 0.571 and 0.629 This sample was not large enough to be able to use the normal distribution by the Central Limit Theorem 95% of all confidence intervals from 109 NFL players will correctly contain the true proportion The true proportion is between 0.571 and 0.629 with 95% confidence For a new CI there is a 95% probability of the sample proportion being between 0.571 and 0.629 (11) (7 minutes) (12) (1 minute) What’s a good date idea that is under 10 dollars (and PG-13 or below)?