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Statistics Assignment Full-Length Practice Exam Page 1 of 23 Multiple-Choice Section (90 minutes) Choose the one best answer for each of the following questions. Do not send your multiple choice answers back to your instructor. Only send your freeresponse answers (next section) to your instructor. It's important to stay within the time limit to see how you'd do under real test conditions. If you can't finish all the questions in 90 minutes, go back later and do the problems you weren't able to finish. 1. A five-number summary of a univariate data set is determined to be [10, 15, 25, 45, 85]. These data are to be used to construct a (modified) boxplot. Which of the following statements are true? I. The mean is probably greater than the median. II. There is at least one outlier. III. The data are skewed to the right. A. I only B. II only C. III only D. I and III only E. I, II, and III 2. You have a rather strange die: Three faces are marked with the letter A, two faces with the letter B, and one face with the letter C. You roll the die until you get a B. What is the probability that the first B appears on the first or the second roll? A. .333 B. .704 C. .556 D. .037 E. .296 _____________ © Copyright 2000 Apex Learning Inc. All rights reserved. This material is intended for the exclusive use of registered users only. No portion of these materials may be reproduced or redistributed in any form without the express written permission of Apex Learning Inc. Statistics Assignment Full-Length Practice Exam Page 2 of 23 3. You are going to construct a 95% confidence interval for the difference between two independent sample means. There are 12 subjects in one sample and 11 in the other. You think that the two populations have the same standard deviation, and so decide to use a pooled estimator of the population variance. How many degrees of freedom would you use for this t procedure? A. 21 B. 23 C. 10 D. 12 E. 22 ˆ = 19.41 + .17 x . What is the 4. The regression line for this bivariate data set is y residual for the point with an x-value of 68? x y A. 30.97 B. 3.03 C. 34 56 28 45 25 68 34 49 30 58 32 63 36 66 23 62 29 D. –30.97 E. –3.03 _____________ © Copyright 2000 Apex Learning Inc. All rights reserved. This material is intended for the exclusive use of registered users only. No portion of these materials may be reproduced or redistributed in any form without the express written permission of Apex Learning Inc. Statistics Assignment Full-Length Practice Exam Page 3 of 23 5. Which of these distributions has the largest standard deviation? Assume that the range is the same for each histogram shown here. A. B. C. D. E. _____________ © Copyright 2000 Apex Learning Inc. All rights reserved. This material is intended for the exclusive use of registered users only. No portion of these materials may be reproduced or redistributed in any form without the express written permission of Apex Learning Inc. Statistics Assignment Full-Length Practice Exam Page 4 of 23 6. Randomization is important in experiments because: A. it makes treatment and control groups equal in size. B. it ensures that there are enough subjects in all treatment groups. C. it masks the placebo effect. D. it controls for any bias the experimenter may have. E. it helps ensure that treatment and control groups are as alike as possible. 7. You have a rather strange die: Three faces are marked with the letter A, two faces with the letter B, and one face with the letter C. If you were to roll this die, what is the probability that at least one of the first two rolls would be a B? A. 5/9 B. 1/3 C. 1/9 D. 4/9 E. 7/9 8. You want to see if a coin is fair. You flip it 5 times and count the number of heads. If H is the number of heads obtained in five flips of the coin, what is the P-value of the test when H equals 4? A. 5/32 B. 6/32 C. 7/32 D. 8/32 E. 9/32 9. You are going to construct a 99% t confidence interval for a population mean based on a sample of size 22. What is the critical value of t (t*) you will use to construct the interval? A. 2.819 B. 2.845 C. 2.080 D. 2.831 E. 2.518 _____________ © Copyright 2000 Apex Learning Inc. All rights reserved. This material is intended for the exclusive use of registered users only. No portion of these materials may be reproduced or redistributed in any form without the express written permission of Apex Learning Inc. Statistics Assignment Full-Length Practice Exam Page 5 of 23 10. Franny is told that the z-score for her SAT test score was 1.2 compared to all twelfth-grade girls who took the test. Which of the following best describes what this means? A. Only 1.2% of the twelfth-grade girls taking this test had scores higher than Franny. B. Franny's score is 1.2 points higher than the average score for all twelfth-grade girls who took the SAT. C. Franny received 1,200 on the SAT. D. Franny's score is 1.2 standard deviations above the mean of twelfth-grade girls who took the SAT. E. Franny's score is 1.2 times greater than the average score for all twelfth-grade girls who took the SAT. 11. A double-blind experimental design is: A. one in which neither the experimenter nor the subject are aware of which treatment the subject receives. B. one whose purpose is to standardize responses of the various treatment groups. C. one in which the subject is unaware of whether they are receiving the treatment or not, but the researcher is aware. D. one in which groups are matched on a specific set of criteria so as to eliminate any obvious differences between the groups. E. another way to describe an experiment in which no placebo is used. 12. Sometimes t procedures are referred to as robust. Which of the following best describes what this means? A. They are not affected by extreme values. B. They can be used in many different situations, unlike less robust measures. C. They are still useable even when the assumptions necessary for their use are violated. D. They do not require that samples be drawn from normal populations. E. They can be used even if the population standard deviation is unknown. _____________ © Copyright 2000 Apex Learning Inc. All rights reserved. This material is intended for the exclusive use of registered users only. No portion of these materials may be reproduced or redistributed in any form without the express written permission of Apex Learning Inc. Statistics Assignment Full-Length Practice Exam Page 6 of 23 13. A Statistics teacher decides to give A's only to students who score in the top 15% on the final exam. The scores are normally distributed with a mean of 78 and a standard deviation of 7 (this is also the population standard deviation). To the nearest integer value, what is the lowest score a student could earn and still receive an A? A. 79 B. 80 C. 82 D. 83 E. 85 14. From the data in this table, what is P(B | E)? C D E Total A. 12/35 B. 12/55 C. 23/70 A B Total 23 15 12 50 32 15 23 70 55 30 35 120 D. 35/70 E. 23/35 15. Which of the following are true statements? I. An observational study differs from an experiment in that only experiments have distinct groups upon which measurements are made. II. A sample survey is one type of experiment. III. Experiments, but not observational studies, can point to cause-and-effect relationships. A. I only B. II only C. III only D. II and III only E. I, II, and III _____________ © Copyright 2000 Apex Learning Inc. All rights reserved. This material is intended for the exclusive use of registered users only. No portion of these materials may be reproduced or redistributed in any form without the express written permission of Apex Learning Inc. Statistics Assignment Full-Length Practice Exam Page 7 of 23 16. Consider the following set of sample data: 21, 24, 25, 32, 35, 31, 29, 28. Which of the following will give a 95% confidence interval for the mean of the population from which this sample was drawn? A. 28.125 ± 1.96 (4.61/ 8 ) B. 28.125 ± 2.365(4.31/ 8 ) C. 28.125 ± 2.306(4.61/ 8 ) D. 28.125 ± 2.365(4.61/ 8 ) E. 28.125 ± 2.306(4.31/ 8 ) 17. Which of the following are necessary in order to use a normal approximation to the sampling distribution of a sample proportion? I. The population from which the sample was drawn must be at least 10 times larger than the sample. II. The population from which the samples are drawn must be normal. III. The sample must be a simple random sample from the population. A. I only B. II only C. III only D. I and III only E. II and III only 18. What are the mean and median of the data presented in the table below? Value 15 18 19 23 27 A. 21.7, 23 B. 21.7, 19 C. 21.7, 20 Relative Frequency .15 .10 .20 .25 .30 Cumulative Frequency .15 .25 .45 .70 1.00 D. 20.4, 23 E. 20.4, 19 _____________ © Copyright 2000 Apex Learning Inc. All rights reserved. This material is intended for the exclusive use of registered users only. No portion of these materials may be reproduced or redistributed in any form without the express written permission of Apex Learning Inc. Statistics Assignment Full-Length Practice Exam Page 8 of 23 19. A population is strongly skewed to the left with a mean of 18 and a standard deviation of 4. You draw samples of size 4 from this population and calculate the mean of each sample. Which of the following shows the mean, standard deviation, and shape of the sampling distribution of the sample mean? A. 18; 4; skewed to the left B. 18; 2; approximately normal according to the Central Limit Theorem C. 18; 2; skewed to the right D. 18; 2; skewed to the left E. 18; 4; approximately normal according to the Central Limit Theorem. 20. What is the "five-number summary" of the data given in the table below? Value 15 18 19 23 27 Relative Frequency .15 .10 .20 .25 .30 Cumulative Frequency .15 .25 .45 .70 1.00 A. 15-18-19-23-27 B. 15-18-19-23-23 C. 15-18-23-27-27 D. 15-18-18-23-27 E. 15-19-23-23-27 _____________ © Copyright 2000 Apex Learning Inc. All rights reserved. This material is intended for the exclusive use of registered users only. No portion of these materials may be reproduced or redistributed in any form without the express written permission of Apex Learning Inc. Statistics Assignment Full-Length Practice Exam Page 9 of 23 21. Given the tree diagram shown here, what is P(A | E)? C A B D E .7 .3 .3 C .1 D E A. 7/11 B. 3/4 C. 4/7 .4 .3 .5 .4 D. 3/10 E. .21 22. Researchers conduct a study to determine whether an online statistics course is superior to an in-class course in terms of success on the AP Exam. They compare the scores of 150 students, 75 of whom took each type of course. The online students did better, on average, so the researchers publish an article recommending that students who want to do well on the AP Exam should consider the online course rather than a course at their school. Which of the following statements is true? A. The results of this study are meaningless because this was an observational study and not an experiment. B. Self-selection is not a factor when comparing the performance of the two groups. C. This is an example of the placebo effect. D. Though there is a relationship between the type of course and performance, this study does not show that there is a cause-and-effect relationship. E. There is too much sampling error in this type of study to be able to make conclusions. _____________ © Copyright 2000 Apex Learning Inc. All rights reserved. This material is intended for the exclusive use of registered users only. No portion of these materials may be reproduced or redistributed in any form without the express written permission of Apex Learning Inc. Statistics Assignment Full-Length Practice Exam Page 10 of 23 23. The table below gives (in seconds) the time required for six right-handed people to complete a test of dexterity, first with their left hand, then with their right. You want to perform a t test to see if there is a significant difference between the times required for the left and right hands. The appropriate number of degrees of freedom for this test is: Alice Bob Carrie Doug Eleanor Frank A. 6 B. 12 C. 11 Left Hand 23 Right Hand 19 19 17 26 20 22 18 18 20 19 20 D. 10 E. 5 24. Two variables are related so that the slope of their regression line is 6, and so that sy = 4.2 and s x = .35 . What is r, the correlation coefficient for the two variables? A. 1/12 B. 72 C. .6 D. .5 E. .54 _____________ © Copyright 2000 Apex Learning Inc. All rights reserved. This material is intended for the exclusive use of registered users only. No portion of these materials may be reproduced or redistributed in any form without the express written permission of Apex Learning Inc. Statistics Assignment Full-Length Practice Exam Page 11 of 23 25. All 32 seniors at a High School took both the AP Exam in Statistics and the AP Exam in Calculus. Their mean score on the Statistics exam was 2.57 with a standard deviation of .7. Their mean score on the Calculus exam was 2.78 with a standard deviation of .64. If we combine these tests into a single score, the correct mean and standard deviation are: A. 5.35; .7 +.64 B. 5.35, .7 + .64 C. 5.35, .72 + .642 D. 5.35, .72 + .642 E. The mean is 5.35, but you cannot determine the standard deviation from this information. 26. You want to research a new pill you hope will relieve the effects of arthritis in persons over 50 years of age. You divide your volunteers into two groups: one consisting of people aged 50-60 and one consisting of people over 60. You further divide each of those groups by gender. The members of each of these four groups are randomly assigned to treatment and control groups with the treatment group receiving the new pill and the control group receiving the placebo. The basic design of this study is: A. double-blind, blocked by age and gender. B. comparative randomized, blocked by age, gender, and type of medication. C. randomized and stratified. D. completely randomized. E. comparative randomized, blocked by age and gender. 27. The final exam scores in freshman English at a large high school are normally distributed with a mean of 84% and a standard deviation of 14. If 450 students took the exam, approximately how many students scored between 70% and 80%? A. 103 B. 125 C. .2289 D. 99 E. 95 _____________ © Copyright 2000 Apex Learning Inc. All rights reserved. This material is intended for the exclusive use of registered users only. No portion of these materials may be reproduced or redistributed in any form without the express written permission of Apex Learning Inc. Statistics Assignment Full-Length Practice Exam Page 12 of 23 28. You want to construct a 95% confidence interval for the proportion of patients who will experience adverse reactions to a new medication. Because side effects can be rather severe, you desire a margin of error of no more than .05. You have no idea, prior to doing the research, of what the true proportion might be. What is the minimum number of subjects you will need in your study? A. 384 B. 385 C. 19.6 D. 1537 E. 390 29. A binomial event is observed 50 times. The probability of the event being successful is .3. Let X equal the count of successes of the event during the 50 trials. What are µ X and σ X ? A. 15; 3.24 B. .3; .15 C. 15; 10.5 D. .15; 3.24 E. 15; 3.87 _____________ © Copyright 2000 Apex Learning Inc. All rights reserved. This material is intended for the exclusive use of registered users only. No portion of these materials may be reproduced or redistributed in any form without the express written permission of Apex Learning Inc. Statistics Assignment Full-Length Practice Exam Page 13 of 23 30. You want to obtain a simple random sample of size 30 of all students in the junior class. Assume there are 150 boys and 150 girls in the class. Which of the following methods will produce such a sample? I. Number the students from 1 to 300. Randomly select one of the first 10 students, then take every tenth student on the list after that. II. Number the students from 1 to 300. Use a random number generator to select 30 numbers from 1 to 300. Your sample consists of the students whose names correspond to the generated numbers. III. Number the boys from 1 to 150 and number the girls from 151 to 300. Randomly select 15 boys by using a random number generator to pick 15 numbers from 1 to 150. Then select 15 girls by using a random number generator to pick 15 numbers from 151 to 300. A. I only B. II only C. III only D. II and III only E. I, II, and III 31. A study found that the hours students spend watching television and their grade point averages (GPAs) have a correlation of r = –.71. Given this information, which of the following statements is most accurate? A. About 71% of students' GPAs depend on hours spent watching television. B. About half of the variation in GPAs can be explained by hours spent watching television. C. A student could improve his/her GPA by watching less television. D. There is a cause-and-effect relationship between watching television and success in school. E. For each decrease in one hour of television watching, there will be a corresponding increase of .7 in a student's GPA. _____________ © Copyright 2000 Apex Learning Inc. All rights reserved. This material is intended for the exclusive use of registered users only. No portion of these materials may be reproduced or redistributed in any form without the express written permission of Apex Learning Inc. Statistics Assignment Full-Length Practice Exam Page 14 of 23 χ2 32. You conduct a test for independence to see if political affiliation is related to gender in a medium-sized Midwestern town. The test is based on data from a survey asking respondents to indicate their preference for one of four political 2 parties. Your X value is 5.21. What P-value is associated with this value? A. .05 < p < .10 B. p > .25 C. .15 < p < .20 D. .025 < p < .05 E. .02 < p < .025 33. Two variables appear to be exponentially related. A researcher takes the natural logarithm of each y-value and computes the equation for the regression of ln y on x. The resulting equation is ln y = 2.35 + 4.48x. To the nearest integer, what is the predicted value of y when x equals .65? A. 5.262 B. 182,810 C. 172 D. 188 E. 193 34. You have a table of random single-digit numbers that has an equal number of every digit from zero to nine. If you start at the first digit on the table and begin moving to the right, what is the probability that you do not land on an even number (2, 4, 6, or 8) until the fifth digit? A. .4 B. .0768 C. .05184 D. .01024 E. .031104 _____________ © Copyright 2000 Apex Learning Inc. All rights reserved. This material is intended for the exclusive use of registered users only. No portion of these materials may be reproduced or redistributed in any form without the express written permission of Apex Learning Inc. Statistics Assignment Full-Length Practice Exam Page 15 of 23 35. It is appropriate to use a matched pairs experimental design when: A. both treatment and control groups are similar. B. each subject is to receive both treatments. C. you need a special technique for establishing a control group. D. a comparative randomized design is not feasible. E. you need a control for confounding variables. _____________ © Copyright 2000 Apex Learning Inc. All rights reserved. This material is intended for the exclusive use of registered users only. No portion of these materials may be reproduced or redistributed in any form without the express written permission of Apex Learning Inc. Statistics Assignment Full-Length Practice Exam Page 16 of 23 36. Use this computer output to determine r, the correlation coefficient between Method 1 and Method 2. Descriptive Statistics Variable METHOD 1 METHOD 2 Variable METHOD 1 METHOD 2 N 12 12 Mean Median 64.42 66.50 63.25 63.50 Min 52.00 53.00 Max 74.00 73.00 Q1 57.25 55.75 TrMean 64.70 63.30 StDev 7.10 7.28 SEMean 2.05 2.10 Q3 70.25 69.75 Regression Analysis The regression equation is Predictor Constant METHOD 2 s = 6.892 A. .241 B. .380 C. .058 Coef 40.98 0.3705 R-sq = Stdev 18.17 0.2856 t-ratio p 2.25 0.048 1.30 0.224 R-sq(adj) = 5.8% D. .145 E. .027 _____________ © Copyright 2000 Apex Learning Inc. All rights reserved. This material is intended for the exclusive use of registered users only. No portion of these materials may be reproduced or redistributed in any form without the express written permission of Apex Learning Inc. Statistics Assignment Full-Length Practice Exam Page 17 of 23 37. Which of the following gives a 99% confidence interval for the slope of the regression line from this computer output? Descriptive Statistics Variable METHOD 1 METHOD 2 Variable METHOD 1 METHOD 2 N 12 12 Mean Median 64.42 66.50 63.25 63.50 Min 52.00 53.00 Max 74.00 73.00 Q1 57.25 55.75 TrMean 64.70 63.30 StDev 7.10 7.28 SEMean 2.05 2.10 Q3 70.25 69.75 Regression Analysis The regression equation is Predictor Constant METHOD 2 s = 6.892 Coef 40.98 0.3705 R-sq = A. 40.98 ± 3.169(.286) B. .371 ± 3.055(.286) C. .371 ± 3.169(6.892) Stdev 18.17 0.2856 t-ratio p 2.25 0.048 1.30 0.224 R-sq(adj) = 5.8% D. .371 ± 3.055(40.98) E. .371 ± 3.169(.286) _____________ © Copyright 2000 Apex Learning Inc. All rights reserved. This material is intended for the exclusive use of registered users only. No portion of these materials may be reproduced or redistributed in any form without the express written permission of Apex Learning Inc. Statistics Assignment Full-Length Practice Exam Page 18 of 23 38. Look at the scatterplot pictured here. Regarding the point marked A, which of these are true? I. A is better described as an influential point rather than an outlier. II. Removing A from the scatterplot would cause the correlation to increase. III. Removing A from the scatterplot would cause the slope of the regression line to decrease significantly. A. I only B. I and II only C. II only D. II and III only E. III only 39. The IQs of students at a very prestigious technical university are normally distributed with a mean of 124 and a standard deviation of 8. What is the probability that a person selected at random from this population will have an IQ below 100? A. .023 B. .0013 C. .005 D. .9987 E. 0 _____________ © Copyright 2000 Apex Learning Inc. All rights reserved. This material is intended for the exclusive use of registered users only. No portion of these materials may be reproduced or redistributed in any form without the express written permission of Apex Learning Inc. Statistics Assignment Full-Length Practice Exam Page 19 of 23 40. A survey of 40 people finds that 22 prefer Sugar Crunchies breakfast cereal to Honey Yummies. Another completely independent survey finds that 24 of 50 people surveyed prefer Sugar Crunchies to Honey Yummies. For a significance test of the hypothesis H0 : p1 = p2 , where p1 is the proportion favoring Sugar Crunchies from the first survey population, and p2 is the proportion from the second survey population, what is the standard error of the difference between the proportions? A. B. 1 ö æ 22 öæ 24 öæ 1 + ç ÷ç ÷ç ÷ è 40 øè 50 øè 40 50 ø 23 ö 22 ö æ 23 öæ æ 22 öæ ÷ ÷ç1 − ÷ ç ÷ç1 − ç 50 ø 40 ø è 50 øè è 40 øè + 50 40 C. 1 ö æ 46 öæ 44 öæ 1 + ç ÷ç ÷ç ÷ è 90 øè 90 øè 40 50 ø D. 1 ö æ 22 öæ 24 öæ 1 + ç ÷ç ÷ç ÷ è 90 øè 90 øè 40 50 ø E. 23 ö 22 ö æ 23 öæ æ 22 öæ ÷ ÷ç1 − ÷ ç ÷ç1 − ç 50 ø 40 ø è 50 øè è 40 øè + 90 90 _____________ © Copyright 2000 Apex Learning Inc. All rights reserved. This material is intended for the exclusive use of registered users only. No portion of these materials may be reproduced or redistributed in any form without the express written permission of Apex Learning Inc. Statistics Assignment Full-Length Practice Exam Page 20 of 23 Free-Response Section (90 minutes) After you finish answering these questions, correct your own work using the answer key provided, then send your corrected work back to your instructor. You'll be scored on whether you did the work, not on how many questions you answered correctly. Questions 1-5 should take about 10-15 minutes each. Question 6 is an "Investigative Task," and should take about 20-30 minutes. You should do all you can in no more than 90 minutes. It's important to stay within the time limit to see how you'd do under real test conditions. Read over all the questions first, and do the questions you feel most confident about. Then go back and do the questions you're less confident about. Stop at 90 minutes, and then use the answer key to correct your work. If you can't finish all the questions in 90 minutes, go back later and do the problems you weren't able to finish. 1. You draw samples of size n from the population of all pennies in circulation. The random variable of interest is the mean age of the pennies in the sample (current year pennies are considered to be zero years old). The distribution of ages of pennies (starting at 0) is known to be skewed markedly to the right. That is, there are more recently minted pennies than older pennies in the population. One scholar claims that the mean age of all pennies in circulation is 7.4 years with a standard deviation of 3.3 years. Assume that this scholar is correct. Discuss the mean, standard deviation, and shape of the sampling distribution of sample means of the ages of pennies for each of the given sample sizes. Where possible, give precise values. A. n = 5 B. n = 15 C. n = 40 2. A sports car manufacturer paints its cars silver, white, black, and red in the following proportions: Color: Proportion: Silver .2 White .3 Black .1 Red .4 We know that 40% of these cars are manufactured with tan leather upholstery while the remaining 60% are manufactured with gray leather. A. Assuming that the choice of exterior color and leather color are independent, what is the probability that a randomly selected sports car from this manufacturer will be white with gray upholstery? B. Assuming that we know the car has tan upholstery, what is the probability that the car is either silver or white? _____________ © Copyright 2000 Apex Learning Inc. All rights reserved. This material is intended for the exclusive use of registered users only. No portion of these materials may be reproduced or redistributed in any form without the express written permission of Apex Learning Inc. Statistics Assignment Full-Length Practice Exam Page 21 of 23 3. You are interested in conducting a survey at your school to determine if gender or ethnicity is related to perceptions about educational opportunity. The school has 1,800 students but you only have resources to interview 100. The student body is approximately equally divided between males and females. Twelve percent of the school's population is Asian American, 8% is African American, 10% is Native American, and 70% is Caucasian. You are interested in being able to generalize the results of your survey to the entire student body. A. Describe a technique for obtaining a sample of size 100 that would have a reasonable chance of producing results that could be generalized to the entire school. B. Suppose you sent the surveys out to classes and asked the students to complete them and return them to the main office. Would the returns be likely to be biased in any direction? If so, why? In what direction? C. Suppose you decide to conduct the survey by personal interview. Members of the student council, all of whom happen to be Caucasian, will conduct personal interviews with the selected students. One of the survey questions reads, "Do you agree or disagree with the following statement: All students, regardless of ethnicity, have equal opportunity to become part of student government." What potential bias is present in this question? 4. The following table gives the inflation rate and the corresponding prime lending rate for 7 different years. The equation of the regression line is: prime lending rate = 3.175 + .654(inflation rate). Inflation Rate (x) 3.3 6.2 11 9.1 5.8 6.5 7.6 Prime Lending Rate (y) 5.2 8 10.8 7.9 6.8 6.9 9 A. What is the predicted prime lending rate when the inflation rate stands at 6%? B. What is the value of the residual when the inflation rate is 5.8%? C. Interpret the slope of the regression line for this situation. D. An eager economist uses these data to predict that the prime lending rate would be 16.26 if the inflation rate rose to 20%. Comment on this prediction. _____________ © Copyright 2000 Apex Learning Inc. All rights reserved. This material is intended for the exclusive use of registered users only. No portion of these materials may be reproduced or redistributed in any form without the express written permission of Apex Learning Inc. Statistics Assignment Full-Length Practice Exam Page 22 of 23 5. The Director of Student Activities is concerned that she has not hired enough security for the Sadie Hawkins Day dance, and wants to know approximately how many students will be attending. If more than 25% of the student body is planning on going to the dance, she will need to hire more security. She sends out a survey to 300 students, and out of the 285 who respond, 82 say they plan to attend. A. On the basis of this survey, should the Director of Student Activities hire more security? Use appropriate statistical evidence to support your conclusion. B. There were 15 people who didn't return their surveys. Suppose they had. Is it possible that the Student Activities Director's decision would have been different? 6. Suppose you have a friend on the school basketball team but, unfortunately, he is not a good free throw shooter. Over the course of his career, he has only made 40% of his shots. Otherwise, he is a good player and gets fouled a lot so he shoots 10 free throws a game, on average. In the biggest game of the season, he does very well and makes 6 out of 10 free throw attempts. A. Assuming that each shot is independent, set up the expression you would use to determine the exact probability that your friend actually makes 6 or more free throws in a given game. B. Using the set of random numbers shown here, explain how you would set up a simulation to determine the probability of making 6 or more free throws out of 10 attempts if your probability of making any one free throw is .4. 98713 51623 21826 41970 04853 19464 65847 94930 19537 00796 57512 53436 96270 18910 78602 49898 08320 97988 17433 54962 84837 45677 37221 36753 42771 52245 46304 07174 41545 39128 38816 71946 51855 01058 96541 62042 17871 00969 47896 47221 76406 88983 24384 75215 39264 89744 25948 98095 35996 05585 C. Suppose you wanted to do a normal approximation to the binomial for this situation. What are the mean and standard deviation of the binomial distribution? Is the normal approximation justified in this situation? Explain why or why not? Would the normal approximation be justified if n = 100? D. One of your friend's attempts during a game is a "one-and-one." That is, if he makes one free throw, he is given the opportunity to take a second shot. Assuming each shot is independent, is he most likely to make 0, 1, or 2 points on a "one-and-one" opportunity. E. What is the probability that the first free throw he makes is his fourth attempt? _____________ © Copyright 2000 Apex Learning Inc. All rights reserved. This material is intended for the exclusive use of registered users only. No portion of these materials may be reproduced or redistributed in any form without the express written permission of Apex Learning Inc. Statistics Assignment Full-Length Practice Exam Page 23 of 23 TI-83 screens are used with the permission of the publisher. Copyright ã 1996, Texas Instruments, Incorporated. MINITAB is a trademark of Minitab, Inc., and is used herein with the owner's permission. Portions of MINITAB Statistical Software input and output contained in this course are printed with permission of Minitab, Inc. _____________ © Copyright 2000 Apex Learning Inc. All rights reserved. This material is intended for the exclusive use of registered users only. No portion of these materials may be reproduced or redistributed in any form without the express written permission of Apex Learning Inc.