Midterm Ch What is the difference between an observational study and well designed experiment?

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1 Midterm Ch. 1-8 AP STATS Name Date Per 1. What is the difference between an observational study and well designed experiment? 2. A high school statistics class wants to conduct a survey to determine what percentage of students in the school would be willing to pay a fee for participation in after-school activities. They assign every student a number and use the random number generator on the calculator to select 20 students. This plan is an example of which type of sampling? a. Cluster b. Convenience c. Simple random d. Stratified random e. Systematic 3. A new medication has been developed to treat sleep-onset insomnia (difficulty in falling asleep). Researchers want to compare this drug to a drug that has been used in the past by comparing the length of time it takes subjects to fall asleep. Of the following, which is the best method for obtaining this information? a. Randomly assign the subjects to two groups, giving the new drug to one group and the old drug to the other group, then compare the results. b. Have subjects choose which drug they are willing to use, the compare the results. c. Assign the two drugs to the subjects on the basis of their past sleep history without randomization, then compare the results. d. Give the new drug to all subjects on the first night. Give the old drug to all subjects on the second night. Compare the results. e. Randomly assign the subjects to two groups, giving the new drug to one group and no drug to the other group, then compare the results. 4. In which of the following situations would you not be able to use a census? a. To determine what proportion of licensed bicycles on a university campus are mountain bikes b. To determine what proportion of students in high school support the beach volleyball club c. To determine what proportion of deer in the Tahoe forest are bucks d. To determine what proportion of registered students enrolled in college live with their parents e. To determine what proportion of single-family dwellings in small town have patio covers 5. Which of the following is a characteristic of stratified random sampling? a. Convenience sampling is part of the sampling procedure b. The population is divided into groups of units that are heterogenous on some characteristic c. The strata are not based on facts known before the sample is selected. d. Each individual member of the population belongs to one and only one of the strata. e. Every possible subset of the population, of the desired sample size, has an equal chance of being selected.

2 6. Automobile brake pads are either metallic or nonmetallic. An experiment is to be conducted to determine whether the stopping distance is the same for both types of brake pads. In previous studies, it was determined that car size (small, medium, large) is associated with stopping distance, but car type (sedan, wagon, coupe) is not associated with stopping distance. This experiment would best be done a. without blocking d. by blocking on stopping distance b. by blocking on car size e. by blocking on brake pad type c. by blocking on car type 7. Use the following boxplot to answer the following I. The 75 th percentile rank is 400 II. The mean score is 500 III. The interquartile range is 300 a. I only d. II and III b. II only e. None are true c. III only 8. A group of students has 60 houseflies in a large container and needs to assign 20 to each of three groups labeled A, B, C for an experiment. They can capture the flies one at a time when the flies enter a side chamber in the container that is baited with food. Which of the following methods will be most likely to result in three comparable groups of 20 houseflies each? a. When each fly is caught, roll a die. If the die shows a 1 or 2, the fly is labeled A. If the die shows a 3 or 4, the fly is labeled B. If the die shows a 5 or 6, the fly is labeled C. Repeat this process for all 60 flies. b. When each fly is caught, roll a die. If the die shows and even number, the fly is labeled A. If the die shows an odd number, the fly is labeled B. When 20 flies have been labeled A and 20 flies have been labeled B, the remaining flies are then labeled C. c. Label the first 20 flies caught as group A, the second 20 as group B, and the third 20 caught as group C. d. Write the letters A, B, C on separate slips of paper. Randomly pick one of the slips of paper and assign the first 20 flies caught to that group. Pick another slip and assign the next 20 flies caught to that group. Assign the remaining flies to the remaining group. e. Place each fly in its own numbered container (numbered from 1 to 60) in the order that it was caught. Write the numbers from 1 to 60 on slips of paper, put the slips in a jar, and mix them well. Pick 20 numbers out of the jar. Assign the flies in the containers with those numbers to group A. Pick 20 more numbers and assign the flies in the containers with those numbers to group B. Assign the remaining 20 flies to group C.

3 9. Consider the following two histograms, then decide which of the statements are false a. Both sets are symmetric b. They have different means and ranges c. They do not have the same variance d. They do not have the same standard deviation e. Only one set has gaps and clusters 10. Which of the following statements about comparative bar charts are true? I. A comparative bar chart can be used for only for numerical data. II. A comparative bar chart works best for small number of observations. III. The vertical axis of a comparative bar chart is always relative frequency. 11. Which of the following can a stem-and-leaf plot display? I. gaps in the data II. potential outliers III. symmetry 12. Which of the following statements about histograms are true? I. The upper limit of a class interval corresponds to less than, while the lower limit corresponds to greater than or equal to. II. The bars of each class interval need not share a side with adjacent class interval bars. III. Relative frequency histograms and frequency histograms have the same shape and proportions. 13. When a set of data has suspect outliers, which of the following are preferred measures of central tendency? a. mean and variance b. mean and range c. median and interquartile range d. median and range e. mean and standard deviation

4 14. The following double bar graphs shows the choice of heating fuel for new homes completed during the indicated years. In each pair the top bar indicates electricity while the lower bar indicates gas % 58% % 59% % 60% % 65% % 66% Which of the following are false statements? I. The percentage of new homes using fuels other than electricity and gas has stayed the same from one year to another. II. The percentage of new homes using electricity has never risen from one year to another. III. The percentage of new homes using gas has increased every year. a. I b. II c. III d. I, II, and III e. None of the above gives the complete set of true responses. 15. If quartiles Q 1 30and Q3 50, which of the following must be true? I. The standard deviation is at most 10. II. The mean is 40. III. The median is between 30 and 50. a. I only b. II only c. III only d. All are true. e. None are true.

5 16. The stem plot below displays the weights (in ounces) of a random sample of tomatoes grown on a local farm. Weights of Tomatoes (oz) 2L 2H 3L 3H 4L 4H 5L 5H 6L 6H stem: ones leaf: tenths Which of the following are false statements based on the display? I. The range of the data is 4.2 ounces. II. The tomato data is negatively skewed. III. A typical tomato weighs about 4 ounces. a. I c. III b. II d. I, II, and III e. None of the above gives the complete set of true responses. 17. Which of the following are false statements? I. While the range is not affected by outliers, the interquartile range is. II. The range of the sample data set is never greater than the range of the population. III. The interquartile range is half the distance between the first quartile and the third quartile. a. I only b. II only c. III only d. I and II e I and III 18. Suppose the average score on a national test is 800 with a standard deviation of 50. If each score is increased by 25, what are the new mean and standard deviation? 19. Suppose the average score on a national test is 800 with a standard deviation of 50. If each score is increased by 25%, what are the new mean and standard deviation?

6 20. A 1995 poll by the Program for International Policy asked respondents what percentage of the U.S. budget they thought went to foreign aid. The mean response was 12%, and the median was 17%. (The actual amount is less than 1%.) What do these responses indicate about the likely shape of the distribution of all responses? a. The distribution is uniform between 12% and 17%. b. The distribution is skewed to the left. c. The distribution is symmetric around 14.5%. d. The distribution is skewed to the right. e. The distribution is bell-shaped with a standard deviation of 2.5%. 21. Assuming that batting averages have a bell-shaped distribution, arrange in descending order: I. An average at the first quartile, Q 1. II. An average with a z-score of -1. III. An average with a percentile rank of 20%. a. I, II, III b. I, III, II c. II, I, III d. II, III, I e. III, II, I 22. Which of the following are false statements? I. If the sample has variance zero, the sample mean and the sample median are equal. II. If the sample has variance zero, the variance of the population is also zero. III. If the population has variance zero, the variance of the sample is also zero. a. I and II b. I and III c. II only d. I, II, and III e. None of the above gives the complete set of true responses. 23. A stemplot for the 1988 per capita personal income for the 50 states is , 7 0, 2, 2, 5, 5, 6, 7, 7, 7, 8, 8 3, 7, 7 1, 6, 7, 8, 9 0, 0, 0, 2, 4, 4, 5, 5, 9 2, 4, 4, 5, 6, 8, 8, 9 4, 6, 6, 7 9 0, 3, 3, Stem: thousands Leaf: hundreds Which of the following best describes these data? a. Symmetric distribution with outliers on high end b. Symmetric distribution, median greater than mean c. Symmetric distribution, mean greater than median d. Skewed distribution, median greater than mean e. Skewed distribution, mean greater than median

7 24. Which of the following statements are true? I. If a distribution is skewed to the right, its median is often greater than its mean. II. If the right and left sides of a histogram are mirror images of each other, the distribution is symmetric. III. A distribution spread far to the left is said to be skewed to the left. a. II only b. I and II c. I and III d. II and III e. None of the above gives the complete set of true responses. 25. The following graph shows the cumulative proportions with regards to outstanding balances on credit cards. Cumulative Proportion A correlation and regression analysis reveals that r = 0.72 and r 2 = 0.53 when 60 pairs of observations, (x,y) are considered. Therefore, we can conclude that a. x causes y to occur b. there is a strong nonlinear relationship between x and y c. there is a moderate linear relationship between x and y d. there is a strong linear relationship between x and y 27. A least squares regression line was fitted to the weights (in pounds) versus age (in months) of a group of many young children. The equation on the line is yˆ x where ŷ is the predicted weight and x is the age of the child. A 23 month old child in this group has an actual weight of 28 pounds. What is the residual weight, in pounds, for this child? 28. A delivery service places packages into large containers before flying them across the country. These filled containers vary greatly in their weight. Suppose the delivery service s airplanes always transports two such containers on each flight. The two containers are chosen so their combined weight is close to, but does not exceed, a specified weight limit. A random sample of flights with these containers is taken, and the weight of each of the two containers on each selected flight is recorded. The weights of the two containers on the same flight a. will have a correlation of 1 b. will have a correlation of 0 c. will have a positive correlation that is less than 1 d. will have a negative correlation e. cannot be determined from the information given What is the approximate value of the median? a. $500 d. $2500 b. $800 e. $4000 c. $2000

8 29. The graphs of the sampling distributions, I and II, of the sample mean of the same random variable for samples of two different sizes are shown above. Which of the following statements must be true about the sample size of distribution I? a. The sample sizes cannot be compared based on theses graphs. b. The sample size of I is equal to the sample size of II. c. The sample size of I is less than the sample size of II. d. The sample size of I is greater than the sample size of II. e. The sample size does not affect the sampling distribution. 30. The linear correlation coefficient was reported to equal -1. Which of the following is not true? a. A computation error was made in computing r. b. The two variables are negatively correlated. c. All of the sample data points fall along a straight line that has a negative slope. d. The coefficient of determination equals 100%. 31. If the slope of the regression line is negative and the coefficient of determination is.81, then find Pearson s correlation coefficient 32. Two measures x and y were taken on 18 subjects. The first of two regressions, Regression I, yielded yˆ x and had the following residual plot. The second regression, Regression II, yielded residual plot. log y log x and had the following Which of the following conclusions is best supported by the evidence above? a. There is a nonlinear relationship between x and y, and Regression I yields a better fit. b. There is a nonlinear relationship between x and y, and Regression II yields a better fit. c. There is a negative correlation between x and y. d. There is a linear relationship between x and y, and Regression I yields a better fit. e. There is a linear relationship between x and y, and Regression II yields a better fit.

9 33. In a study of the performance of a computer printer, the size (in kilobytes) and the printing time (in seconds) for each of 22 small text files were recorded. A regression line was a satisfactory description of the relationship between size and printing time. The results of the regression analysis are shown below. Which of the following statements are true? I. There s a strong positive linear correlation since the correlation coefficient is.935 II. The regression equation is y= x III. The regression equation is y= x a. Only I d. I and III b. Only II e. none of the responses are correct c. Only III 34. Dennis is planning to fly from New York to Los Angeles and will take the Airtight Airlines flight that leaves at 8 A.M. The Web site he used to make his reservation states that the probability that the flight will arrive in Los Angeles on time is Of the following, which is the most reasonable explanation for how that probability could have been estimated? a. From the fact that, of all airline flights in the United States, 60% arrive on time b. From the fact that, on all previous days this particular flight had been scheduled, it had arrived on time 60% of those days c. By using an extended weather forecast for the date of her flight, which showed a 40% chance of bad weather d. By making assumptions about how airplanes work, and factoring all of those assumptions into an equation to arrive at the probability e. From the fact that, of all airline flights arriving in California, 60% arrive on time

10 35. Vaughn interviewed 100 people and classified them according to their attitude toward small cars and their personality type. The results are shown in the table below. Personality Type Type A Type B Total Attitude Positive Toward Neutral Small Cars Negative Total Which of the following is true? a. The proportion that has a positive attitude toward small cars is higher among people with a type B personality type than among people with a type A personality type. b. More than half of the 100 respondents have a type A personality type and a positive attitude toward small cars. c. Of the three attitude groups, the group with the negative attitude has the highest proportion of type A personality types. d. Of the three attitude groups, the group with the neutral attitude has the highest proportion of type B personality types. e. For each personality type, more than half of the 100 respondents have a neutral attitude toward small cars. 36. An experiment has three mutually exclusive outcomes, A, B, and C. If P(A) = 0.15, P(B) = 0.60, and P(C) = 0.25, which of the following must be true? I. P(A or C) = P(A) + P(C) II. B and C are independent. III. P(A and C) = 0 a. I only c. I and III only e. I, II, and III b. I and II only d. II and III only 37. Suppose that 40 percent of the subscribers to a cable television service watch the shopping channel at least once a week. You are to design a simulation to estimate the probability that none of the five randomly selected subscribers watches the shopping channel at least once a week. Which of the following assignment s of the digits 0 through 9 would be appropriate for modeling an individual subscriber s behavior in this simulation? a. Assign 0 as watching the shopping channel at least once a week and 1, 2, 3, 4, and 5 as not watching; ignore digits 6, 7, 8, and 9. b. Assign 0, 1, 2, 3 as watching the shopping channel at least once a week and 4, 5, 6, 7, 8, and 9 as not watching. c. Assign 0, 1, 2, 3, 4 as watching the shopping channel at least once a week and 5, 6, 7, 8, and 9 as not watching. d. Assign 0, 1, 2, 3, 4, 5 as watching the shopping channel at least once a week and 6, 7, 8, and 9 as not watching. e. Assign 4 as watching the shopping channel at least once a week and 0, 1, 2, 3, 5, 6, 7, 8, and 9 as not watching.

11 38. 80% percent of the people who have a particular disease will have a positive result on a given diagnostic test. 85% percent of the people who do not have the disease will have a negative result on this test. Suppose 7% of the population has the disease. Given a person tested positive, what is the probability that they do not have the disease? 39. An urn contains exactly three balls numbered 1, 2, and 3 respectively. Random samples of two balls are drawn from the urn with replacement. The average, x-bar = (x 1 + x 2 )/2, where x 1 and x 2 are the numbers on the selected balls, is recorded after each drawing. Which of the following describes the sampling distribution of x-bar? 40. Traffic data revealed that 35 percent of automobiles traveling along a portion of an interstate highway were exceeding the legal speed limit. Using highway cameras and license plate registration, it was also determined that 52 percent of sports cars were also speeding along the same portion of the highway. What is the probability that a randomly selected car along the same portion of the highway was a speeding sports car? a b c d e. It cannot be determined from the information given. 41. Which of the followings are discrete? I. Digital watch readings II. The body temperature of a walrus. III. The number of shoes in a factory. a. III only b. II and III only c. I, II, and III d. I and III only

12 42. The number of points, X, scored in a game has the probability distribution below, The number of points obtained in one game is independent of the number of points obtained in a second game. When the game is played twice, the sum of the number of points for both times could be 0, 1, 2, 3, or 4. If Y represents the sampling distribution of the sum of the scores when the game is played twice, for which value of Y will the probability be the greatest? a. 0 b. 1 c. 2 d. 3 e The probability of being a 2 nd grader in a public school in Placer County is.80. If three 2 nd graders are independent and randomly selected, what is the probability that the first one is from a private school and the next two are from a public school? 44. The probability of adults liking Giants Orange is.75. If 7 adults are randomly selected, what is the probability that 4 like Giants Orange? 45. Given the probability distribution, find the mean and standard deviation. X P(x) % of grocery stores have Cinnamon Cheerios. If Brandon needs to go from store to store until he finds Cinnamon Cheerios, what is the probability he will find it on exactly the fourth store, if he stops looking when he finds it? 47. The mean bowling score for Kiah is 123 with a X which separates the top 30% from the rest? of 5.6.What is the mean bowling score 48. The mean length between elbow and wrists is 15.0 with a standard deviation of 2.6. Find the probability of having such a length < 14.2 from a sample of 40 people. 49. The probability of an AP Statistics student taking the AP test is.96. If a random sample of 300 students is taken, find the probability that (.93 < pˆ <.99) Answers: 1. In an experiment, you intentionally force a treatment on the subjects. 2. C 3. A 4. C 5. D 6. B 7. E 8. E 9. B 10. none 11. I,II,III 12. I,III 13. C 14. A 15. C 16. C 17. E , , B 21. B 22. C 23. E 24. D 25 B 26. C D 29. D 30. A B 33. D 34. B 35. D 36. C 37. B B 40. E 41. D 42. C ,