AP Statistics: Midterm Review 2014 Name Directions: This assignment is due at the beginning of class on Friday, January 9th This homework is intended to help you prepare for the midterm exam. The questions are of roughly the same level of difficulty as those that will appear on the exam, and solving them will require you to review key concepts that are likely to be tested. If you need additional work space, use notebook paper and attach it to this packet. This assignment is a measure of your ability to apply your knowledge. It is to be completed individually using only your class notes, textbook, calculator, and handouts. Any questions regarding the assignment should be directed to Mrs. Becker afterschool or glorybeth_becker@hcpss.org. I will be checking my email during the break and will be available afterschool (to be announced) during the first week of January. Please read and sign the statement below. I affirm that I completed this assignment by myself using only my notes, handouts, calculator, and textbook. Furthermore, I affirm that I discussed this assignment with no one any questions I had regarding this assignment were directed to Mrs. Becker Signature: Date: MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 1) School administrators collect data on students attending the school. Which of the following variables is quantitative? A) whether the student has taken the SAT B) grade point average C) whether the student is in AP* classes D) class (freshman, soph., junior, senior) E) none of these 1) 2) Which of the following variables would most likely follow a Normal model? 2) A) heights of singers in a co-ed choir B) family income C) scores on an easy test D) all of these E) weights of adult male elephants 3) A professor has kept records on grades that students have earned in his class. If he wants to examine the percentage of students earning the grades A, B, C, D, and F during the most recent term, which kind of plot could he make? A) dotplot B) timeplot C) pie chart D) boxplot E) histogram 3) 1
4) Which is true of the data shown in the histogram? 4) I. The distribution is approximately symmetric. II. The mean and median are approximately equal. III. The median and IQR summarize the data better than the mean and standard deviation. A) I only B) III only C) I and III D) I, II, and III E) I and II 5) Two sections of a class took the same quiz. Section A had 15 students who had a mean score of 80, and Section B had 20 students who had a mean score of 90. Overall, what was the approximate mean score for all of the students on the quiz? A) 85.0 B) 84.3 C) none of these D) 85.7 E) It cannot be determined. 5) 6) Your Stats teacher tells you your test score was the 3rd quartile for the class. Which is true? I. You got 75% on the test. II. You can't really tell what this means without knowing the standard deviation. III. You can't really tell what this means unless the class distribution is nearly Normal. A) II and III B) none of these C) II only D) I only E) III only 7) Suppose that a Normal model described student scores in a history class. Parker has a standardized score (z-score) of +2.5. This means that Parker A) is 2.5 standard deviations above average for the class. B) has a standard deviation of 2.5. C) has a score that is 2.5 times the average for the class. D) none of these E) is 2.5 points above average for the class. 6) 7) 2
8) The advantage of making a stem-and-leaf display instead of a dotplot is that a stem-and-leaf display A) satisfies the area principle. B) none of these C) shows the shape of the distribution better than a dotplot. D) A stem-and-leaf display is for quantitative data, while a dotplot shows categorical data. E) preserves the individual data values. 9) The five-number summary of credit hours for 24 students in a statistics class is: 8) 9) From this information we know that A) there is at least one high outlier in the data. B) there are both low and high outliers in the data. C) none of these D) there is at least one low outlier in the data. E) there are no outliers in the data. 10) Which of the following data summaries are changed by adding a constant to each data value? I. the mean II. the median III. the standard deviation A) III only B) I, II, and III C) I and III D) I only E) I and II 10) 11) All but one of these statements contain a mistake. Which could be true? 11) A) There is a high correlation (1.09) between height of a corn stalk and its age in weeks. B) The correlation between a car's length and its fuel efficiency is 0.71 miles per gallon. C) The correlation between the amount of fertilizer used and the yield of beans is 0.42. D) The correlation between a football player's weight and the position he plays is 0.54. E) There is a correlation of 0.63 between gender and political party. 12) Residuals are... 12) A) data collected from individuals that is not consistent with the rest of the group. B) possible models not explored by the researcher. C) variation in the data that is explained by the model. D) the difference between observed responses and values predicted by the model. E) none of these 3
13) Which statement about influential points is true? I. Removal of an influential point changes the regression line. II. Data points that are outliers in the horizontal direction are more likely to be influential than points that are outliers in the vertical direction. III. Influential points have large residuals. A) I and III B) I only C) I and II D) I, II, and III E) II and III 14) Which is true? I. Random scatter in the residuals indicates a model with high predictive power. II. If two variables are very strongly associated, then the correlation between them will be near +1.0 or -1.0. III. The higher the correlation between two variables the more likely the association is based in cause and effect. A) I only B) none C) I and II only D) II only E) I, II, and III 13) 14) 15) A company's sales increase by the same amount each year. This growth is... 15) A) exponential B) power C) linear D) quadratic E) logarithmic 16) Another company's sales increase by the same percent each year. This growth is... 16) A) logarithmic B) power C) exponential D) linear E) quadratic 17) A scatterplot of 1 vs. x shows a strong positive linear pattern. It is probably true that 17) y A) large values of X are associated with large values of Y. B) the correlation between X and Y is near +1.0. C) accurate predictions can be made for Y even if extrapolation is involved. D) the scatterplot of Y vs X also shows a linear pattern. E) the residuals plot for regression of Y on X shows a curved pattern. 18) It's easy to measure the circumference of a tree's trunk, but not so easy to measure its height. Foresters developed a model for ponderosa pines that they use to predict the tree's height (in feet) ^ from the circumference of its trunk (in inches): ln h = -1.2 + 1.4(ln C). A lumberjack finds a tree with a circumference of 60"; how tall does this model estimate the tree to be? A) 11' B) 93' C) 83' D) 19' E) 5' 18) 4
19) Two variables that are actually not related to each other may nonetheless have a very high correlation because they both result from some other, possibly hidden, factor. This is an example of A) a lurking variable. B) extrapolation. C) leverage. D) regression. E) an outlier. 20) If the point in the upper right corner of this scatterplot is removed from the data set, then what will happen to the slope of the line of best fit (b) and to the correlation (r)? 19) 20) A) b will decrease, and r will increase. B) both will increase. C) both will decrease. D) b will increase, and r will decrease. E) both will remain the same. 21) A company sponsoring a new Internet search engine wants to collect data on the ease of using it. Which is the best way to collect the data? A) simulation B) sample survey C) observational study D) experiment E) census 22) The January 2005 Gallup Youth Survey telephoned a random sample of 1028 U.S. teens and asked these teens to name their favorite movie from 2004. Napoleon Dynamite had the highest percentage with 8% of teens ranking it as their favorite movie. Which is true? I. The population of interest is all U.S. teens II. 8% is a statistic and not the actual percentage of all U.S. teens who would rank this movie as their favorite. III. This sampling design should provide a reasonably accurate estimate of the actual percentage of all U.S. teens who would rank this movie as their favorite. A) I, II, and III B) III only C) I and II D) II only E) I only 21) 22) 5
23) Suppose your local school district decides to randomly test high school students for attention deficit disorder (ADD). There are three high schools in the district, each with grades 9-12. The school board pools all of the students together and randomly samples 250 students. Is this a simple random sample? A) No, because we can't guarantee that there are students from each school in the sample. B) Yes, because each student is equally likely to be chosen. C) Yes, because they could have chosen any 250 students from throughout the district. D) Yes, because the students were chosen at random. E) No, because we can't guarantee that there are students from each grade in the sample. 24) A basketball player has a 70% free throw percentage. Which plan could be used to simulate the number of free throws she will make in her next five free throw attempts? I. Let 0,1 represent making the first shot, 2, 3 represent making the second shot,, 8, 9 represent making the fifth shot. Generate five random numbers 0-9, ignoring repeats. II. Let 0, 1, 2 represent missing a shot and 3, 4,, 9 represent making a shot. Generate five random numbers 0-9 and count how many numbers are in 3-9. III. Let 0, 1, 2 represent missing a shot and 3, 4,, 9 represent making a shot. Generate five random numbers 0-9 and count how many numbers are in 3-9, ignoring repeats. A) II and III B) I, II, and III C) I only D) II only E) III only 25) More dogs are being diagnosed with thyroid problems than have been diagnosed in the past. A researcher identified 50 puppies without thyroid problems and kept records of their diets for several years to see if any developed thyroid problems. This is a(n) A) randomized experiment B) retrospective study C) prospective study D) blocked experiment E) survey 26) A chemistry professor who teaches a large lecture class surveys his students who attend his class about how he can make the class more interesting, hoping he can get more students to attend. This survey method suffers from A) nonresponse bias B) response bias C) none of these D) undercoverage E) voluntary response bias 23) 24) 25) 26) 27) Placebos are a tool for 27) A) blinding B) control C) blocking D) sampling E) randomization 6
28) Double-blinding in experiments is important so that I. The evaluators do not know which treatment group the participants are in. II. The participants do not know which treatment group they are in. III. No one knows which treatment any of the participants are getting. A) II only B) I, II,and III C) I only D) III only E) I and II 28) 29) Which of the following is not required in an experimental design? 29) A) control B) randomization C) All are required in an experimental design. D) replication E) blocking 30) A researcher wants to compare the effect of a new type of shampoo on hair condition. The researcher believes that men and women may react to the shampoo differently. Additionally, the researcher believes that the shampoo will react differently on hair that is dyed. The subjects are split into four groups: men who dye their hair; men who do not dye their hair; women who dye their hair; women who do not dye their hair. Subjects in each group are randomly assigned to the new shampoo and the old shampoo. This experiment A) is completely randomized. B) has two factors (shampoo type and whether hair is dyed) blocked by gender. C) has two factors (gender and whether hair is dyed) blocked by shampoo type. D) has three factors (shampoo type, gender, whether hair is dyed). E) has one factor (shampoo type), blocked by gender and whether hair is dyed. 30) Use the following information for questions 1-2: In an AP* Stats class, 57% of students eat breakfast in the morning and 80% of students floss their teeth. Forty-six percent of students eat breakfast and also floss their teeth. 31) What is the probability that a student from this class eats breakfast but does not floss their teeth? 31) A) 11% B) 91% C) 57% D) 34% E) 9% 32) What is the probability that a student from this class eats breakfast or flosses their teeth? 32) A) 9% B) 34% C) 91% D) 11% E) 57% 33) Five juniors and four seniors have applied for two open student council positions. School administrators have decided to pick the two new members randomly. What is the probability they are both juniors or both seniors? A) 0.444 B) 0.395 C) 0.722 D) 0.506 E) 0.569 34) A fair coin has come up "heads" 10 times in a row. The probability that the coin will come up heads on the next flip is A) It cannot be determined. B) 50%. C) less than 50%, since "tails" is due to come up. D) greater than 50%, since it appears that we are in a streak of "heads." 35) According to the National Telecommunication and Information Administration, 56.5% of U.S. households owned a computer in 2001. What is the probability that of three randomly selected U.S. households at least one owned a computer in 2001? A) 18.0% B) 91.8% C) 82.0% D) 43.5% E) 56.5% 33) 34) 35) 7
36) According to the National Telecommunication and Information Administration, 50.5% of U.S. households had Internet access in 2001. What is the probability that four randomly selected U.S. households all had Internet access in 2001? A) 6.5% B) 93.5% C) 50.5% D) 49.5% E) 12.6% 36) 37) Which of these has a Binomial model? 37) A) the number of aces in a five-card Poker hand B) the number of people we survey until we find someone who has taken Statistics C) the number of sodas students drink per day D) the number of people we survey until we find two people who have taken Statistics E) the number of people in a class of 25 who have taken Statistics 38) Which of these has a Geometric model? 38) A) the number of people we survey until we find two people who have taken Statistics B) the number of aces in a five-card Poker hand C) the number of people we survey until we find someone who has taken Statistics D) the number of sodas students drink per day E) the number of people in a class of 25 who have taken Statistics 39) BatCo, a company that sells batteries, claims that 99.5% of their batteries are in working order. How many batteries would you expect to buy, on average, to find one that does not work? A) 5 B) 2000 C) 200 D) 995 E) 100 40) Some marathons allow two runners to "split" the marathon by each running a half marathon. Alice and Sharon plan to split a marathon. Alice's half-marathon times average 92 minutes with a standard deviation of 4 minutes, and Sharon's half-marathon times average 96 minutes with a standard deviation of 2 minutes. Assume that the women's half-marathon times are independent. The expected time for Alice and Sharon to complete a full marathon is 92 + 96 = 188 minutes. What is the standard deviation of their total time? A) 4.5 minutes B) 6 minutes C) 20 minutes D) 2 minutes E) It cannot be determined. 39) 40) 8