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TAMU STAT 303 - ex1asp10

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STAT303 Sec 508-510Spring 2010Exam #1Form AInstructor: Julie Hagen CarrollName:1. Don’t even open this until you are told to do so.2. 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 counted wrong.3. You will have 60 minutes to finish this exam.4. 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.5. If you are caught cheating or helping someone to cheat on this exam, you both will receive a grade of zero on theexam. You must work alone.6. 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.7. Good luck!1STAT303 sec 508-510 Exam #1, Form A Spring 20101. Looking at the standard normal distribution, what isthe proportion of values between z = −1.56 and z =−2.05?A. 0.9204B. 0.0392C. 0.0796D. 0.0594E. 0.02022. Which of the following is/are true?A. An unbiased estimator has the same shape as theoriginal (parent) population.B. Increasing the sample size, increases the chance ofhaving an unbiased estimator.C. An unbiased estimator has the same spread as theoriginal (parent) population.D. All of the above are true.E. None of the above are true.3. Which of the following is true about the boxplotsabove? Label the topmost 1, then down to 5. Eachdistribution has 50 observations.A. The distributions for 3 and 4 are the same.B. Since 3 and 4 don’t have outliers, they are uni-formly distributed.C. 2 has a smaller standard deviation than 3 and 4.D. Two of the above are true.E. None of the above are true.4. What is the 5 Number Summary for the histogram andwhich boxplot does it match?A. 0, 1, 2, 3, 6; boxplot 3 or 4B. 0, 2, 3, 3, 6; none of the boxplotsC. 0, 1, 2, 3, 7; boxplot 1D. 0, 2, 2.5, 3, 6; boxplot 2E. 1, 2, 2.5, 3, 4; boxplot 25. If X ∼ N(15, 42), what is P (X > 20)?A. 0.1056B. 0.8944C. 0.9938D. 0.0062E. 0.02026. What do we mean when we talk about the samplingdistribution of Xnfor estimating µ?A. The distribution of the different values of the sam-ple mean for all samples of any size.B. The distribution of the different values of the pop-ulation mean.C. The distribution of the samples themselves, wherewe look at samples of the same size.D. The distribution of the samples themselves, wherewe look at all samples of any size.E. The distribution of the different values of the sam-ple mean for all samples of the same size.7. Suppose the grades on an exam are X ∼ N (55, 102).I want to raise the mean by 20 points plus reduce thestandard deviation by 5, so I convert the grades usingY = X/5 + 20. What is the new distribution of thegrades? Note: this is just a shift and scale change, butit may not give me the distribution I wanted.A. Y ∼ N (75, 52)B. Y ∼ N (75, 22)C. Y ∼ N (15, 52)D. Y ∼ N (31, 22)E. Y ∼ N (31, 222)8. Which of the following would be true if we multiplyeach data point in a distribution by 3?A. The z-scores would not change.B. The standard deviation would change but not theIQR.C. The mean would change but not the median.D. All of the above are true.E. Two of the above are true.9. Let X4∼ N(13, 52), sample means based on samplesof size 4. What is P (7 < X4< 20)?A. 0.0343B. 0.9892C. 0.8041D. 0.5793E. 0.00562STAT303 sec 508-510 Exam #1, Form A Spring 201010. Jack and Jill are in different sections of 303. Jack madea 82 on the first test and his class average was a 75 witha standard deviation of 6. Jill made an 80 and her classaverage was a 72 with a standard deviation of 8. Whohas the better class standing?A. Jack since he has a higher score.B. Jill since she is 8 points over the mean and Jackis only 7 points over.C. Their standing is the same since they both madeabove the mean.D. JackE. We can’t compare since we don’t know if the dis-tributions are normal.11. I hope the distribution of the exam scores is skewed leftbecauseA. that would mean the average was high, in the up-per half, not centered.B. that would mean more than half the class had pos-itive z-scores.C. that would mean more than half the class passed.D. Two of the above are good reasons.E. None are correct. I should want the distributionto be normal.12. If X ∼ N (5, 82) and Y ∼ N(9, 162), what is the dis-tribution of X − Y ? NOTE: I rounded to the nearestwhole number.A. N (14, 82)B. N (14, 182)C. N (−4, −82)D. N (−4, 82)E. N (−4, 182)13. Which of the following indicate that the data must beat least approximately normally distributed?A. The mean is approximately equal to the median.B. The normal quantile plot shows the data pointsfollowing the line on the plot.C. The boxplot is symmetric.D. All of the above indicate that the data is normallydistributed.E. Exactly two of the above indicate that the data isnormally distributed (excluding D.).14. If X is a continuous random variable, like a normal,then P (a < X < b) = ?A. 1 − P (X ≤ a) − P (X < b)B. 1 − P (X ≥ a) − P (X > b)C. P (X < b) + P (X > a)D. P (X > b) − P (X < a)E. None of the above are correct.15. Suppose we have a distribution, X, with mean, µ = 25,and standard deviation, σ = 9. The sampling distribu-tion of the sample mean from a sample of size 16, X16,wouldA. be N(µ = 25, (σ = 3/4)2)B. be N(µ = 25, (σ = 9/4)2)C. be N(µ = 25, (σ = 9/16)2)D. have µ = 25, (σ = 3/4)2but unknown shapeE. have (µ = 25, (σ = 9/4)2but unknown shape16. Say we have a random sample. If we took another oneof the same size from the same population, the new oneA. could have the same values as the first one.B. could have completely different values than thefirst one.C. would have the same distribution for the samplemean.D. All of the above are true.E. Only two of the above are true.17. If X is distributed normally with a mean of 4 and astandard deviation of 3, find x so that the proportionof values greater that x is 0.20.A. 1.48B. -0.84C. 0.84D. 7E. 6.5218. If the five number summary for a distributionis (−18.72, −16.06, −13.98, −11.08, 18.95), outside ofwhat two numbers will the outliers fall?A. −18.72 and 18.95B. −16.06 and −11.08C. −23.53 and −3.61D. −8.59 and −18.55E. −6.10 and −21.0419. Which of the following is true?A. Every statistic has a sampling distribution.B. Every statistic’s distribution can be approximatedby the normal distribution.C. Every statistic is unbiased.D. All


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