January Regi onal Statistics Individual Test βNOTAβ means none of the above. 1. Calculate the mean of the following set of data: 66, 44, 37, 51, 26, 43, 79, 31, 86, 55, 69, 73 A) 53 B) 54 C) 55 D) 56 E) NOTA 2 Steve is interested in the proportion of people at his school th at prefer Chipotle over Moeβs. He randomly selects ten homerooms and pools all the students in those ten homerooms to create his sample. Which o f the following best describes Steve βs sampling technique? A) SRS B) stratified C) convenience D) cluster E) NO TA 3 A boxplot was created for a set of data and is shown below. How many of the following statements are true? I. The distribution is right skewed. II. The mean is greater than the median. III. The range of the distribution is 15. A) 0 B) 1 C) 2 D) 3 E) NOTA 4. An unfair, six - sided die is weighted such tha t the probability of rolling a k is defined by the following function: π ( π = π ) = 8 π β π 2 77 for all integers k such that 1 β€ π β€ 6 . What is the probability of rolling a prime number? A) 30 77 B) 37 77 C) 6 11 D) 7 11 E) NOTA 5. Mr. Farmerβs midterm exam grades are normally distributed with a mean M and a standard deviation S . Albert scores an 81.04 and is at the 90 th percentile of his class. Lokbondo scores a 71.79 and is at the 42 nd percentile of his class. Rounding M and S to the nearest integer, evaluate the sum M + S A) 78 B) 79 C) 80 D) 81 E) NOTA January Regi onal Statistics Individual Test 6. Which of the following statements is FALSE? A) A matched pairs design is a form of blocking. B) A control is often used in experiments to s erve as a point of comparison for the treatments. C) Rand omization in an experiment help s directly reduce response bias. D) Replication in an experiment serves to minimize chance variation. E) NOTA 7. Let X be a binomial distribution with a mean of 31.92 and a variance of 7.6608 . What is the number of trials in X? A) 42 B) 132 C) 134 D) need more information E) NOTA Use the following information to answer questions 8 - 11 Kyle is interested in the palm fronds found in a nearby park. He collects and a sampl e of 9 palm fronds and records the length (X) of weight (Y) of each one presented in the table below. X (cm) 151.7 169.4 124.1 138.5 177.4 155.2 126.9 117.6 141.7 Y (kg) 4.3 2 4.91 3.96 4.11 5.21 4.35 3.84 3.42 4.48 8. Kyle performs a linear regression of Y on X using the data he obtained. What is the value of the x - intercept of his regression model? Do not round in your calculation of the regression line but r ound your final answer to two decimal places. A) 0.03 B) 0.62 C) - 0.04 D) - 24.56 E) NOTA 9. Kyle finds the coefficient of determination of his original data set to be π 0 2 . He realizes he lives in the US and wants to convert his units from the metric to the US system. He takes his data and transforms the X variable by converting centimeters to inches and the Y variable by converting kilograms into pounds. He then performs a linear regression of X on Y and finds the new coefficient of determination to be π 1 2 . What is π 1 2 in terms of π 0 2 ? Use the following conversio ns: 1 cm = 0.4 inches, 1 kilogram = 2.2 pounds. A) 11 2 π 0 2 B) 2 11 π 0 2 C) 121 4 π 0 2 D) 4 121 π 0 2 E) NOTA 10. Suppose Kyle finds another palm frond with a length of 14 7.2 cm and a weight of 8.71 kg and wants to see how accurate his model is. Kyle includes this palm frond in his data and recalculates the least - squares regression line. Calculate the residual a ssociated with this new palm frond using the new regression line. Do not round in your calculation of the regression line but r ound your final answer to two decimal places. A) - 4.36 B) 3.92 C) 4.36 D) 4.79 E) NOTA January Regi onal Statistics Individual Test 11. The ne w observation found in question 10 can best be classified as an___________ and would be expected to have a relatively _________ impact on the slope of the regression model, if included in the data set. A) outlier; small B) outlier; large C) influential obs ervation, small D) influential observation, large E) NOTA 12. The time that it takes to complete the 100 yard dash for a physical education class is normally distributed with a mean of 14.32 seconds and a standard deviation of 2.37 seconds. What is the cutoff time, in seconds, to qualify for the track team if you must be faster th an 91 percent of all students taking the class? Round your answer to 2 decimal places. A) 11.14 B) 12.16 C) 16.48 D) 17. 50 E) NOTA 13. Suppose there are five identical boxes arranged in a single line. Each box contains either a toy or nothing. The probability that there is a toy in a given box is p Assuming that the presence of a toy in any one box is independent of the others, what is the probability, in terms of p , that no two adjacent boxes contain toys ? A) β 4 π 5 + 5 π 4 B) 4 π 5 β 5 π 4 + 1 C) β 5 π 5 + 10 π 4 β 10 π 2 + 5 π D) β π 5 + π 4 + 3 π 3 β 4 π 2 + 1 E) NOTA Use the following information to answer questions 14 - 15. Eight TI - NSpire calculators are to be randomly distributed to four distinct math classrooms at a local h igh s chool. Unfortunately, it is known that four of the eight calculators are defective. 14. What is t he probability that e ach of the four classrooms classroom receives one of the defective calculators? Round your answer to four decimals. A) 0.0088 B) 0.0143 C) 0.0625 D) 0.0938 E) NOTA 15. If the calculators are to be distributed in a way such that exactly one of the classroom s gets 3 calculators, two of the classrooms get 2 calculators, and one of the classroom s gets 1 calculator, how many possible ways can this be accomplished? A) 1680 B) 15360 C) 20160 D) 30720 E) NOTA January Regi onal Statistics Individual Test 16. Which of the following statements about the normal distribution? I. The mean is 0. II. The standard deviation is 1. III. It is bimodal. IV. The probability under the curve is equal to 1. A) I, II, III, and IV B) I, II, and IV C) III and IV D) IV only E) NOTA 17. Karen collects data on t he zip code where each student in her school lives . Which of the following is the best graphical technique to analyze the data? A) scatterplot B) pie chart C) boxplot D) stem - and - leaf plot E) NOTA Use the following information to answer questio ns 18 - 19. Consider the following continuous function: π ( π₯ ) = { ππ₯ , 0 < π₯ < 4 π , 4 < π₯ < 6 0 , πππ ππ€ β πππ 18. Find the sum of the values c and d that make f(x) a valid probability density function. A) 3 8 B) 3 16 C) 1 16 D) 5 8 E) NOTA 19 Using the values of c and d from question 18, find the value of x that correspond to the 75 th percentile. A) 4 B) 4.5 C) 5 D) 5.5 E) NOTA 20. In a left skewed distribution, the 50 th percentile is ______ than the mean and ______ than the median. A) greater, greater B) greater, less C) less, greater D) less, less E) NOTA January Regi onal Statistics Individual Test 21. A random variable X has an expected value of 3 and variance of 4. Calculated the expected value and variance of 5 + 3X . Answers are given in the form (expected value, variance) A) ( 14 , 12) B) ( 14 , 36) C) (9, 12) D) (9, 36) E) NOTA Use the following information to answer questions 22 - 24 A recently published article claims that listening to classical music while taking a test improves standardized test scores. The article also claims t hat chewing mint - flavored gum while taking a test improves standardized test scores. Scientists decide to test this claim. They sample students from high schools across Florida and administer a pretest to all the students in the sample . They then randomly assign each student to either listen to classical music, punk rock music, or rap music. They also assign each student to chew mint - flavored gum or fruit - flavored gum. The students then took a posttest and statistical analysis was done on the difference s between each studentβs pretest and posttest scores. 22. Let X be the number of factors in the experiment and Y be the total number of treatments in the experiment . Find the tenths digit of ln( XY ) A) 3 B) 4 C) 7 D) 8 E) NOTA 23. Which is the experimental unit in this design? A) differences between pretest and posttest scores B) high schools across Florida C) students D) type of music and type of gum combination E) NOTA 24 . How many of the following statements are true regarding this experimental design? I. This experimental design is missing a control group. II. The experimental design lacks blocking. III. The experiment can be considered double - blind. IV. Random assignment of the students into treatment groups will lead to homogeneous groups and may compro mise the results of the experiment. A) 1 B) 2 C) 3 D) 4 E) NOTA 25. David is meeting his girlfriend for coffee at Starbucks at some time between noon and 1:00 PM. Unfortunately, they donβt remember the exact time they will meet so they each decide to show up at some random time in the interval independently of one another hoping to see the other one there. Once David arrives, he will wait 20 minutes for his girlfriend to show up before leaving. His girlfriend is not as patient and will only wait 10 minutes for David before leaving What is the probability the two will meet? A) 11 36 B) 31 72 C) 41 72 D) 25 36 E) NOTA January Regi onal Statistics Individual Test 26. Loksondo is practicing free throws for his upcoming basketball game. He decides to keep attempting shots until he makes one. Since he is still working on his game, his probability of making a free throw is less than fifty percent. If the probability that he makes his first free throw on his second try is 0.2244, what is probability he makes his first free throw on his fourth try? Assume each shot has constant probability and is independent of all other shots. Round your answer to four decimal places. A) .0259 B) .0503 C) .0977 D) .1481 E) NOTA 27. What is the probability of drawing either a diamond or a face card in a standard 52 - card deck? A) 19 5 2 B) 11 26 C) 25 52 D) 21 26 E) NOTA 28. A researcher wants to know the daily eating habits of people living in Florida. He takes an SRS of all the addresses in Florida and sends in a mail - in survey. At the end of his data collection period, he only receives only a mere 14% of the responses back . Which of the following biases is best represented in this example? A) nonresponse bias B) response bias C) wording bias D) undercoverage bias E) NOTA 29. It is known that 94% of the seniors at Cypress Bay High School have a deadly disease known as senioritis and 45% of the underclassmen have senioritis. All students that are not seniors are considered underclassmen. The student body at Cypress Bay consists of 23% seniors. If a randomly chosen student is found to have senioritis, what is the probability that he or she is a senior? Round your answer to four decimal places. A) .2162 B) .3465 C) .3842 D) .5627 E) NOTA 30. A game consists of throwing darts at a strange dartboard. The dartboard consists of a n inner circle inscribed in a square which is inscribed in an outer circle. 1 point is awarded for a dart thrown outside the square and within the outermost circle. 4 points are awarded for a dart thrown within the square but outside the innermost circle. 8 points are awarded for a dart thrown within the innermost circle. Assume that all darts thrown land somewhere on the board. What is the expected value of the game? A) 2 π + 6 π B) 4 π + 6 π C) 6 π + 6 π D) 6 π + 3 π E) NOTA