STAT303 Sec 508-510Fall 2008Exam #2Form AInstructor: Julie Hagen CarrollName:1. Don’t even open this until you are told to do so.2. All graphs are on the last page which you may remove.3. There are 20 multiple-choice questions on this exam, each worth 5 points. There is partial credit. Please mark youranswers clearly. Multiple marks will be c ounted wrong.4. You will have 60 minutes to finish this exam.5. If you have questions, please write out what you are thinking on the back of the page so that we can discuss it afterI return it to you.6. If you are c aught cheating or helping someone to cheat on this exam, you both will receive a grade of zero on theexam. You must work alone.7. This exam is worth the 15% of your course grade.8. When you are finished please make sure you have marked your CORRECT section (Tuesday 12:45 is 508, 2:20 is 509,and 3:55 is 510) and FORM and 20 answers, then turn in JUST your scantron to the correct pile for your section.9. Good luck!1STAT303 sec 508-510 Exam #2, Form A Fall 20081. Which of the following is (are) appropriate statementsabout randomness and/or probability?A. A phenomenon is called random if individual out-comes are uncertain but in a large number of repe-titions there is a regular distribution of outc omes.B. The word random in statistics is a description ofa kind of order that emerges in the long run.C. Probability describes only what happe ns in thelong run.D. In a small or moderate number of repetitions, theobserved proportion of an outcome can be far fromthe probability of the outcome.E. All of the above are appropriate state ments.2. Suppose we want to test H0: µ = 30 vs. HA: µ 6= 30but all we have is a 95% confidence interval for t he truemean, µ, (27.8,31.2). Which of the following is true?A. We would re j e ct the null since t he sample mean is29.5 not 30.B. We would f ail to reject the null at the 5 and 1%levels.C. We would reject the null at the 5 and 1% levels.D. We would reject the null at 10% level.E. Two of the above are true.3. Suppose a simple random sample is selected from a pop-ulation with mean, µ and variance, σ2. The centrallimit theorem tells us thatA. the sample mean,x, gets closer to the populationmean, µ, as the sample size increases.B. if the sample size n is sufficiently large, the samplewill be approximately normal.C. the mean of X will be µ if the sample size n issufficiently large.D. if t he sample size is sufficiently large, the distribu-tion ofX will be approximately normal with meanµ and standard deviation,σ√n.E. the distributionX of will be normal only if thepopulation from which the sample is selected isalso normal.4. What are the z critical values, the zα/2, for a 39% con-fidence interval?A. ±0.28B. ±0.51C. ±0.65D. ±0.61E. ±0.735. In the fall of 2003, a magazine article reported thatabout 87% of adults drink milk. A lo c al dairy farm-ers’ association is planning a new marketing c ampaignfor the tri-county area they represent. They randomlypolled 800 people in the area. In this sample, 654 peo-ple said that they drink milk. If 87% is the correctpercentage of adults who drink milk, what is the sam-pling distribution of the sample proportion, p800?A. We c an’t tell if the shape is normal since we don’thave a plot of the data.B. N(0.87, 0.000142)C. N(0.87, 0.011892)D. N(0.00109, 0.000142)E. N(0.87, 0.001092)6. I want to test H0: µ = 100 vs. HA: µ > 100. I take asample of 15 from a normal population with standarddeviation, σ = 4.2 and get a sample meanx = 102.3.What is my test statistic value and the correct p-value?A. 0.55 and 0.7088B. 0.55 and 0.2912C. 2.12 and 0.035D. 2.12 and 0.983E. 2.12 and 0.0177. Which of the following would be a Type II error for theset of hypotheses above?A. failing to prove the true mean is not 100B. failing to prove the t rue mean is not 100 when it’sactually more than 100C. failing to prove the true mean is 100 when it’sactually more than 100D. failing to prove the true mean is more than 100when it’s actually not 100E. failing to prove the true mean is more than 100when it’s actually more than 1008. The American Veterinary Association claims that theannual cost of medical care for dogs averages $100 witha standard deviation of $30. The cost for cats averages$120 with a standard deviation of $35. So the averageof the difference in the cost of medical care for dogsand cats is then $100 - $120 = - $20. The standarddeviation of that same difference equals $46. If thedifference in costs follows a normal distribution, whatis the probability that the cost for someone’s dog ishigher than for the cat?A. 0.2843B. 0.7157C. 0.3336D. 0.6664E. 02STAT303 sec 508-510 Exam #2, Form A Fall 20089. Suppose a simple random sample of 100 observations isto be selected from a population that is highly skewedwith mean µ = 4 and variance σ2= 8. Which of thefollowing statements about the sampling distribution ofX is FAL SE?A. The distribution ofX w ill have mean µ = 4.B. The distribution will be approximately normal.C. Because the distribution is highly skewed, theshape of the distribution of X will also show skew-ness.D. Even though the distribution of the populationvariable is skewed, the distribution ofX will beapproximately symmetric around µ = 4.E. The standard deviation of the distribution ofXwill be σ = 0.283.10. Which of the following is NOT a question you need toask when reviewing a test of hypothesis conclusion?A. Who paid for the study?B. What sample size did they use?C. What population does the sample represent?D. All of the above are important questions t o ask.E. Two of the three questions ab ove do not need tobe asked.11. What is the missing probability and then the mean ofthe distribution below?X | -1 | 0 | 2 | 4 |-----------------------------------------prob | 0.4 | ??? | 0.3 | 0.1 |A. 0 and µ = 0.6B. 0.2 andX = 0.6C. 0.2 and µ = 0.6D. 0 and µ = 1.4E. 0.2 and µ = 1.412. Using the previous distribution, how likely are you todraw a 2 and a 4?A. 0.03B. 0.4C. 0.3D. 0.2E. 0.513. If the population variable is known to be normally dis-tributed with mean µ50 and variance σ2= 225 and thesample size used is to be n = 16, what is the probabilitythat the sample mean will b e between 48.35 and 55.74,i.e., P (48.35 < ¯x < 55.74)?A. 0.393B. 0.607C. 0.937D. 0.330E. Not within ± 0.010 of any of the above.14. Suppose I use computer software to do the following.I generate ten random numbers from a N(500, 102)distribution. From these ten numbers I
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