11/2/09 - Eleanor Roosevelt High School



11/2/09

AP Statistics

HOW (Take-Home Test)

Due Mon. 11/9/09, 8:30 in my mailbox

Multiple-Choice

Show all work

Each question is worth 3 points

Name:______________________________

1. Which one of the following would be a correct interpretation if you have a z-score of +2.0 on an exam?

(A) It means that you missed two questions on the exam.

(B) It means that you got twice as many questions correct as the average student.

(C) It means that your grade was two points higher than the mean grade on this exam.

(D) It means that your grade was in the upper 2% of all grades on this exam.

(E) It means that your grade is two standard deviations above the mean for this exam.

2. A music education specialist speaking on a local newscast has advocated that young children learn to play a musical instrument. The author cited a study of 650 randomly selected high school sophomores and juniors, which reported that students who play a musical instrument, score on average 51 points higher an academic achievement test than students who do not play an instrument. Which of the following is a correct statement?

(A) Since playing a musical instrument seems to improve achievement scores for high school students, the effect should be similar for young children.

(B) Playing a musical instrument will cause a student to score higher on this achievement test.

(C) The study was an experiment rather than an observational study.

(D) The study is a matched pairs study.

(E) There seems to be a relationship between playing musical instruments and obtaining a higher score on the achievement test.

3. What is the purpose of the randomization of treatment to subjects in an experiment?

(A) To eliminate confounding variable in the experiment.

(B) To create roughly equivalent groups before treatments are administered

(C) To prevent certain groups in the population from being systematically excluded in the experiment.

(D) To reduce bias in the selection of the subjects to be included in the experiment.

(E) To eliminate the need for blinding in an experiment.

4. A child is 40 inches tall, which places her in the top 10% of all children of similar age. The heights for children of this age form an approximately normal distribution with a mean of 38 inches. Based on this information, what is the standard deviation of the heights of all children of this age?

(A) 0.20 inches (B) 0.31 inches (C) 0.65 inches (D) 1.21 inches (E) 1.56 inches

5. A recent study was conducted to see if a soy-protein powder would be effective in increasing bone density in 200 randomly selected women aged 60 to 75 who lived in Canada. To what population can the result of this experiment be generalized?

(A) All women who would use this soy-protein powder.

(B) All women in Canada who would use this soy-protein powder.

(C) All women who are between 60 and 75 years of age who would use this soy-protein powder.

(D) All women in Canada who are between 60 and 75 years of age who would use this soy-protein powder.

(E) No one, since the women volunteered to be a part of the study.

6. A newspaper wants to determine the level of support in a large town regarding the construction of a new library in the downtown location. Which one of the following represents a stratified sample method?

(A) Randomly select four residential blocks in the town and ask everyone who lives on those blocks.

(B) Select every 4th person who enters the current library until the desired number of people are selected.

(C ) Take an SRS of people from the city phone directory

(D) Take a random sample of the residents from each of the northwest, northeast, southeast, and southwest quadrant of the city.

(E) Number the residents of the town using the latest census data. Use random number generator to pick the sample.

7. A group of twelve people work in a large office building. They all decided they wanted to lose weight by increasing their physical activity. Six of them decide to walk up and down the four flights of stairs each workday rather than taking the elevator. The other six decide to walk a half hour each day during their lunchtime. At the end of a 20-week period it was found that those who walked a half hour at lunch lost more weight, on average, than those who walked up and down the flights of stairs. Which one of the following is a TRUE statement?

(A) This was an observational study since it was not randomly decided which person participated in which activity.

(B) This was an experiment since the participants were divided into two equal groups.

(C ) Since the people chose which physical activity they engaged in, nothing can be concluded about which type of physical activity is more effective in reducing weight.

(D) This was a block design since there are two treatments involved.

(E) We can use these results to conclude that if everyone in this building were to walk a half hour at lunch each day they achieve, on average, about the same weight loss as this group.

8. The frequency table below summarizes the times in the last month that patients at the emergency room of a small-city hospital waited to receive medical attention.

|Waiting Time |Frequency |

|Less than 10 minutes |5 |

|At least 10 but less than 20 minutes |24 |

|At least 20 but less than 30 minutes |45 |

|At least 30 but less than 40 minutes |38 |

|At least 40 but less than 50 |19 |

|At least 50 but less than 60 |7 |

| | |

Which of the following represents possible values for the median and mean waiting time for the emergency room last month?

(A) median = 27 minutes and mean = 24 minutes

(B) median = 28 and mean = 30 minutes

(C ) median = 31 minutes and mean = 35 minutes

(D) median = 35 minutes and mean = 39 minutes

(E) median = 45 minutes and mean = 46 minutes

9. Company A has 500 employees and company B has 5000 employees. Union negotiators want to compare the salary distributions for the two companies. Which one of the following would be most useful for accomplishing this comparison?

(A) Dotplots for A and B drawn on the same scale.

(B) Back-to Back stemplots for A and B

(C ) Two frequency histograms for A and B drawn on the same scale.

(D) Two relative frequency histograms A and B drawn on the same scale.

(E) A scatterplot of A versus B

10. Two machines are used to produce bolts for a company. To determine the number of defects, randomly selected batches of 1200 bolts are examined and the number of defective bolts in each batch counted. The following are the stem-leaf plot and some summary statistics for the number of defective bolts in 40 batches from each of the two machines.

|Machine A | |Machine B |

| | 1 |1 |

|99888 |1 |57778899 |

|443333222 |2 |001124444 |

|88887776666655555 |2 |55677889 |

|432111100 |3 |00001123 |

| |3 |66880 |

| |4 |0 |

| |4 |7 |

Variable N Median Minimum Maximum Q1 Q3

Machine A 40 26.0 18.0 34.0 23 28

Machine B 40 25.50 11.0 47.0 20 30.75

Based on the plot and the summary statistics, which is statement below is TRUE?

(A) The output from Machine B exhibits less variability than that of Machine A.

(B) The distribution of the number of defective chips from Machine A is more skewed than the distribution of defective chips from Machine B.

(C) The mean number of defective chips from Machine A is more than the mean number of defective chips for Machine B.

(D) The IQR of the distribution of the number of defects from Machine B is less than the IQR of the distribution of the number of defects from Machine A

(E) The data value of 47 is an outlier in the distribution of defective chips from Machine B.

Free-Response

Each question is worth 10 points

1. In hilly area farmers often contour their fields to reduce the erosion due to water flow. This might have the unintended effect of changing the yield since the rows may not be aligned in an east-west direction to take advantages of the direct sunlight.

The following summary statistics show the yields in hundreds of bushels per acre of randomly selected plots of land along hillsides as well as level plots of land nearby with similar soil characteristics.

Level |Minimum |Q |Median |Q |Maximum |Mean |Std Dev |Number | |Hilly |10.9 |13.3 |29.2 |58.1 |100.0 |35.7 |20.4 |12 | |Level |10.9 |18.5 |39.3 |61.5 |118.0 |48.6 |22.1 |12 | |

(a) Draw parallel boxplots that compares the yield for the two types of land.

(b) Based on your boxplots write a few sentences comparing the distribution of corn yields for the level and hilly areas.

(c) What measure of central tendency would you use to represent the distributions of both the level and hilly areas?

(d) Are there any outliers?

2. A large company that manufactures herbal products plans to test the effectiveness of a new product that it would like to market as a preventive for the common cold. It recruits 400 college-age students and randomly divided them into two groups of 200.

Each student will receive a daily injection of a nasty cold virus for a period three days. This injection will be in the form of a nasal spray. Five days before the nasal injections of the cold virus begins, 200 of the students are directed to consume two cups per day of a liquid drink containing the herbal product.- one cup in the morning and one cup in the evening. The other 200 will follow the same schedule but will be given a placebo liquid. Researchers will record the number of students who develop colds in each group.

(a) In this an experiment or an observational study? Justify your answer.

(b) Why is a placebo necessary in this case? Explain your answer

(c) Would double blinding be necessary in this study? Explain

3. a. The amount of time spent by a statistical consultant with a client at their first meeting is normally distributed with a mean value of 60 min and a standard deviation of 10 min.

What percent of the times spent on the consultant’s first meetings with clients exceed 45 min?

b. Given that 10% of the nails made using a certain manufacturing process have a length less than 2.48 inches, while 5% have a length greater than 2.54 inches, what are the mean and standard deviation of the lengths of the nails? Assume that the lengths have a normal distribution.

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