STAT303: Sections 510Fall 2003Exam #2Form AName:Section and Lab Number:1. Please write any questions or explanations on this exam. I will read them before assigningyour grade.2. There are 20 multiple-choice questions on this exam, each worth 5 points. There is partial credit. Pleasemark your answers clearly on the exam. Multiple marks will be counted wrong.3. You will have 60 minutes to finish this exam.4. If you are caught cheating or helping someone to cheat on this exam, you both will receive a gradeof zero on the exam. You must work alone AND you must not talk to anyone about this exam untilFriday.5. This exam is worth 100 points and the equilavent weight of a regular exam.6. Good luck!1STAT303: Sec 510 Exam #2, Form A Fall 20031. A biased sample is one that:A. is too small.B. will always lead to a wrong conclusion.C. has certain groups from the populationoverrepresented or underrepresented.D. is always nonrepresentative.E. never used if valid results are desired.2. The weight of a package of mints is believed tobe normally distributed with mean 21.37 gramsand standard deviation 0.4, X ∼ N(21.37, 0.42).What is the chance that a sample of 4 packagesof mints has an average weight, X4, between 21and 22 grams?A. 0.0314B. 0.9032C. 0.9426D. 0.9670E. 0.99383. Using the rules for shift and scale changes, ifX ∼ N(3, 52) and Y = 7 − 5X, what is thedistribution of Y ?A. N(−8, 11.22)B. N(−8, −52)C. N(−8, 252)D. N(8, 52)E. N(−8, 52)4. Suppose the IQ of children with Fetal Alco-hol Syndrome is normally distributed with truemean µ = 70 and true standard deviation σ =12. What does P(X < 50), where X is the IQ’sof these children, actually mean?A. how likely an average child with FAS wouldhave an IQ of 50 or lessB. how likely any child with FAS would havean IQ of 50 or lessC. how likely a sample of children with FASwould have an average of 50 or lessD. how likely one child out of a sample of chil-dren with FAS would have an IQ of 50 orlessE. how likely the true mean IQ of children withFAS is 50 or less5. What affects the sampling distribution of thesample mean, X?A. whether the sample is random or notB. the size of the sample, nC. the parent population distribution (thepopulation being sampled)D. All of the above affect the sampling distri-bution of X.E. Exactly two of the above affect the sam-pling distribution of X.6. There exists at least 100 years of weather data,but suppose we only took a sample of years andcalculated a 95% confidence interval for the trueyearly average total rainfall of (16.5,22) inches(obviously this isn’t for Texas A&M!). Which ofthe following is best interpretation of this inter-val?A. There is a 95% probability that the trueyearly average total rainfall is between 16.5and 22 inches.B. If we sampled many years, 95% of the yearlytotals would be between 16.5 and 22 inches.C. As long as we sampled enough years (atleast 30), we will be 95% confident that thetrue yearly average total rainfall between1.65 and 22 inches.D. If we took many different samples of years,about 95% of the confidence intervals cre-ated from these samples would contain thetrue yearly average total rainfall.E. If we took many different samples of years,about 95% of the yearly average totalswould equal the true yearly average totalrainfall.7. Referring to the confidence interval in the lastproblem, (16.5,22), which of the following state-ments are plausible for this data (with 95% con-fidence)?A. The true yearly average total rainfall couldbe 20 inches.B. The true yearly average total rainfall couldbe 16 inches.C. The true yearly average total rainfall couldNOT be 22 inches.D. All of the above are plausible.E. Only two of the above are plausible.2STAT303: Sec 510 Exam #2, Form A Fall 20038. We want to know the percentage of former stu-dents that use Statistics after graduation. Whatis the“best” sampling scheme to apply?A. We ask the Association of Former Studentsfor a list of graduates. We chose the first1000 names on the list to interview.B. We put an advertisement in the 3 majornewspapers in U.S. asking former studentsto contact us regarding a survey.C. We ask the Association of Former Studentsfor a list of graduates. We took a simplerandom sample of 1000 persons fron the listto interview them.D. We send 3 students to different gates inKyle Field before the A&M-UT game.They ask the people at the gates if they areformer students and if they answer yes, weask the question of interest. The studentsstop after 200 answers have been recorded.E. None of the above would give us the propersample.9. Suppose you have 3 confidence intervals for πfrom the same data: 90% - (0.45,0.55), 95% -(0.4,0.6) and 99% - (0.2,0.8). If I wanted toknow whether the true proportion was 60% ornot, what could I conclude?A. Since 60% is only in the 99%, I would reject60% as a plausible value for π at the 1%level.B. Since 60% is in the 95%, I would reject 60%as a plausible value for π at the 5 and 10%levels.C. Since 60% is in the 95%, I would reject 60%as a plausible value for π at the 10% levelonly.D. 60% is plausible since we can’t guaranteethe true proportion will fall in any interval.E. You can’t make conclusions with confidenceintervals, only hypothesis tests.10. The sample proportion of red M&M’s, in bagswith a total of 50, is pred∼ N(0.2, (0.0572). Howlikely are you to get only 2 reds (so pred= 2/50 =0.04)? What is P (pred≤ 0.04)?A. −2.81B. 0.0025C. 0.025D. 0.0218E. −2.01711. Assuming that my samples are always random,what could I do to reduce the standard deviationof my sample means, σXby a factor of 4, i.e.,make it one fourth as large?A. use 2 times as much dataB. use one fourth as much dataC. use 4 times as much dataD. use 8 times as much dataE. use 16 times as much data12. Ok, I just made these up, but suppose that thedistribution of quiz grades is the following:X | 0 | 10 | 20 | 30 | 40 | 50-----|------|------|------|------|------|------p(X)| 0.10 | 0.20 | 0.25 | 0.20 | 0.15 | 0.10What is the true mean score of the quiz grades?A. We can only estimate the true mean.B. 25C. 24D. 24.5E. 2013. What are the z critical values, the zα/2, for a91% confidence interval?A. ±0.48B. ±1.695C. ±0.82D. ±1.34E. ±0.6714. Suppose we have a biased coin so the true proba-bility of getting a head is actually 90%, π = 0.90.How many times must we toss it for the samplingproportion, p, to be approximately normally dis-tributed?A. A sample size, n ≥ 30 is always necessary.B. Categorical
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