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UCLA STATS 10 - practicefinal2a

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Practice for Final - Stats 10/2, Winter 2008Ryan Rosario - Section 2AA Few Multiple Choice Questions1. Sometimes when using the normal approximation to the binomial, we add the value 0.5 tothe value of X before we subtract the mean. For example, instead of calculating Z =X−np√npqwe compute Z =X+0.5−np√npq. The value 0.5 is called a continuity correction. The effect thiscorrection on the corresponding probability P (Z > z) is that the probability ismore extreme less extreme2. The events IS MALE and IS FEMALE are (circle all that apply)independent disjoint mutually exclusive dependent3. A doctor tests a patient for a certain type of cancer. The doctor concludes that the patientdoes not have cancer. It is later discovered that the patient indeed did have cancer. Thedoctor made which type of error?No Error Type I Type II4. A polling organization wants to minimize the margin of error for its estimate of the proportionof Americans that prefer a particular presidential candidate. It can accomplish this by doingall of the following except(a) increasing the sample size(b) decreasing the confidence level for the resulting confidence interval(c) both (a) and (b) will produce a smaller margin of error15. Suppose Kaplan is interested in determining whether or not their preparation courses makesa difference in individual SAT scores. They claim that a student that participates in theirprogram will improve their score at least 200 points. Which statistical test should they use?(a) independent samples t-test(b) paired t-test(c) one sample z-test(d) one sample t-test(e) a confidence interval6. The plot below displays the autocorrelation function for a time series. A time series is justa series of data points that are indexed by time (like stock prices). Each line in the plotbelow indicates the size of the correlation (r) between the first observation (at the beginningof the study. t = 0) and time t (in the following plot 0 ≤ t ≤ 13). If a point is betweenthe two dashed lines, then a hypothesis test for the correlation coefficient is not statisticallysignificant (that is, we would conclude r = 0 there).0 2 4 6 8 10 12−0.4 0.0 0.2 0.4 0.6 0.8 1.0Difference from Time 0 (called a "Lag")Correlation CoefficientAutocorrelation FunctionWhat does the plot of the autocorrelation function suggest?(a) As time passes, the linear relationship between time and the measured variable increases.(b) As time passes, the linear relationship between time and the measured variable decreases.(c) As time passes, the linear relationship between time and the measured variable remainsabout the same.(d) There is no linear relationship between time and the measured variable.(e) There is not enough information to answer this question.27. According to a 2007 data mining project performed by your TA, 4900 UCLA Facebook profilesand friend lists were downloaded to a hard disk using a Python crawler. The crawler startsby choosing a random Facebook UCLA profile, downloads it to disk, and thenaccesses the list of that user’s UCLA Facebook friends. The crawler then visitsthe profiles for all of those friends and moves on to their friends etc.One aspect was to determine whether or not third party (non-Facebook developed) wallapplications would bias an analysis of standard Wall posts. The number of profiles containingan active third party Wall box are listed below.Application Name ProfilesAdvanced Wall 124SuperWall 559FunWall 206Advanced Wall and SuperWall 26Advanced Wall and FunWall 20SuperWall and FunWall 84FunWall and SuperWall and Advanced Wall 12(a) Draw an appropriate Venn diagram to represent this context. Label the diagram withprobabilities. Let A represent Advanced Wall, let F represent FunWall and let S repre-sent SuperWall.(b) Find the probability that a randomly selected UCLA Facebook profile in this sampledoes not use any of these third party wall applications.3(c) Suppose my ultimate goal was to determine the proportion of all Facebook users thatdo not have any of these wall applications active. Suppose I use a confidence interval.Provide two reasons why using a confidence interval for this analysis is not valid. Youdo not need to know anything about Facebook to answer this question. Hint: Rereadthis entire problem very carefully, and read the bolded statements.(d) Consider the following table that breaks down the number of UCLA Facebook users inthe sample that displayed their Wall and those that have their Walls hidden (hidden tothe crawler) by gender.Sex Wall Displayed Wall Hidden Row TotalMale 2164 188 2352Female 1835 713 2548Column Total 3999 901 4900i. Among those with hidden Walls, what is the probability that the user is female?ii. Are gender and Wall privacy independent? Why or why not? Use a probablisticargument!!4(e) Suppose the crawler flips a coin to determine whether or not to download the currentprofile to disk. If the coin shows heads then the profile is downloaded to disk, otherwisewe just skip over it without saving any of its data. If it downloads the profile to disk, itwill visit that profile’s friends with probability 0.75. If it does not download the profileto disk, it will visit that profile’s friends with probability 0.1.i. Suppose we know that the crawler will visit the current user’s friends. What is theprobability that the current user’s profile was downloaded to disk?ii. Draw the tree that corresponds with the situation described above. Annotate allevents and probabilities for each branch.iii. Find the probability that the crawler will visit the profiles of the current user’sfriends.5It’s that time of year (well, for grades 2-11!)! In 1998, Gray Davis approved the Stan-dardized Testing and Reporting Program which mandated the use of Stanford AchievementTest, Ninth Edition as the sole norm-referenced measure of educational outcomes in the state.In 2003, the California Department of Education approved replacing Stanford 9 with anothertest, California Achievement Tests, Sixth Edition but only required 3rd and 7th graders totake the test. Everybody else had to take a different battery of tests referred to as ContentStandards Test. In this problem, we will analyze a couple of facets of this decision using thematerial we have studied this quarter.8. During the research phase leading to this decision, a sample of school districts were selected(and paid) to administer both Stanford 9 and CAT/6 to all of its students. The table belowdisplays 10 pairs of scaled scores for the


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