# SMAM 314 Quiz 9 Problem Questions

August 14, 2017

1. Large passenger vans are thought to have a high propensity of rollover accidents whenfully loaded. Thirty accidents of these vans were examined, and 11 vans had rolled over. Testthe claim that the proportion of rollovers exceeds 0.25 with ? = 0.10. Conduct the test byboth the critical region method and by calculating a P-value.2. After a period of apprenticeship, an organization gives an exam that they hope is passedby at least 80% of those who take it. Suppose ten people take the exam and 5 pass. Are thecompany’s expectations being met with ? = 0.05?3. A manufacturer of insecticides finds that 325 of 500 ants placed in a controlledenvironment are exterminated when the company’s Type 1 spray is used; 400 of 600 antsplaced in the same environment are killed when the company’s Type 2 spray is used. Dothese results indicate that the Type 2 spray is more effective than the Type 1 spray? Use ? =0.05. Conduct the test by both the critical region method and by calculating a P-value.4. A call center is typically most busy during the lunch hour (noon-1:00pm). Data iscollected on the number of call attempts made, during this time period, before gettingthrough to someone at the call center. Let X represent the number of attempts before gettingthrough. The resulting data is listed below:xFrequency1992653354225106107887(a) Assuming that the probability of getting a call through during the busy time is 0.35, usethe chi-square goodness-of-fit to test whether the geometric distribution is a good fit forthis data. Use ? = 0.05. [Recall the geometric distribution is f(x) = pqx-1 for x = 1,2,…](b) Approximate a P-value for this test.5. The data below represents time between arrivals at an ATM on a Friday afternoon.0.130.771.612.754.850.400.881.732.944.990.431.251.743.105.010.601.351.883.475.130.601.382.393.865.230.641.412.674.295.390.761.562.724.437.99(a) Use the chi-square goodness-of-fit test to test whether this data is exponentiallydistributed using ? = 0.10.(b) Use the K-S goodness-of-fit test to test whether this data is exponentially distributedusing ? = 0.10.6. The data below reflects the strength of polished windows used on airplanes (in ksi = 1000psi):18.83020.80021.65723.03023.23024.05024.32125.50025.52025.80026.69026.77026.78027.05027.67029.90031.11033.20033.73033.76033.89034.76035.75035.91036.98037.08037.09039.58044.04545.290(a) Use the chi-square goodness-of-fit test to test whether this data is normally distributedusing ? = 0.05.(b) Use the K-S goodness-of-fit test to test whether this data is normally distributed using ? =0.05.