AP Statistics Test #1 (Chapter 1)

Transcription

1 AP Statistics Test #1 (Chapter 1) Name Part I - Multiple Choice (Questions 1-20) - Circle the answer of your choice. 1. You measure the age, marital status and earned income of an SRS of 1463 women. The number and type of variables you have measured is (a) 1463; all quantitative. (b) four; two categorical and two quantitative. (c) four; one categorical and three quantitative. (d) three; two categorical and one quantitative. (e) three; one categorical and two quantitative. 2. Consumers Union measured the gas mileage in miles per gallon of model automobiles on a special test track. The pie chart below provides information about the country of manufacture of the model cars used by Consumers Union. Based on the pie chart, we may conclude that: (a) Japanese cars get significantly lower gas mileage than cars of other countries. This is because their slice of the pie is at the bottom of the chart. (b) U.S cars get significantly higher gas mileage than cars from other countries. (c) Swedish cars get gas mileages that are between those of Japanese and U.S. cars. (d) Mercedes, Audi, Porsche, and BMW represent approximately a quarter of the cars tested. (e) More than half of the cars in the study were from the United States. 3. A researcher reports that, on average, the participants in his study lost 10.4 pounds after two months on his new diet. A friend of yours comments that she tried the diet for two months and lost no weight, so clearly the report was a fraud. Which of the following statements is correct? (a) Your friend must not have followed the diet correctly, since she did not lose weight. (b) Since your friend did not lose weight, the report must not be correct. (c) The report only gives the average. This does not imply that all participants in the study lost 10.4 pounds or even that all lost weight. Your friend s experience does not necessarily contradict the study results. (d) In order for the study to be correct, we must now add your friend s results to those of the study and recompute the new average. (e) Your friend is an outlier. 4. Normal body temperature varies by time of day. A series of readings was taken of the body temperature of a subject. The mean reading was found to be 36.5 C with a standard deviation of 0.3 C. When converted to F, the mean and standard deviation are ( F = C(1.8) + 32). (a) 97.7, 32 (b) 97.7, 0.30 (c) 97.7, 0.54 (d) 97.7, 0.97 (e) 97.7, 1.80

2 5. The following is a histogram showing the actual frequency of the closing prices on the New York exchange of a particular stock. Based on the frequency histogram for New York Stock exchange, the class that contains the 80th percentile is: (a) (b) (c) (d) (e) Which of the following is likely to have a mean that is smaller than the median? (a) The salaries of all National Football League players. (b) The scores of students (out of 100 points) on a very easy exam in which most get nearly perfect scores but a few do very poorly. (c) The prices of homes in a large city. (d) The scores of students (out of 100 points) on a very difficult exam in which most get poor scores but a few do very well. (e) Amounts awarded by civil court juries. 7. There are three children in a room, ages three, four, and five. If a four-year-old child enters the room the (a) mean age will stay the same but the variance will increase. (b) mean age will stay the same but the variance will decrease. (c) mean age and variance will stay the same. (d) mean age and variance will increase. (e) mean age and variance will decrease. 8. The weights of the male and female students in a class are summarized in the following boxplots: 8. Which of the following is NOT correct? (a) About 50% of the male students have weights between 150 and 185 pounds. (b) About 25% of female students have weights more than 130 pounds. (c) The median weight of male students is about 162 pounds. (d) The mean weight of female students is about 120 pounds because of symmetry. (e) The male students have less variability than the female students.

3 9. When testing water for chemical impurities, results are often reported as bdl, that is, below detection limit. The following are the measurements of the amount of lead in a series of water samples taken from inner-city households (ppm). 5, 7, 12, bdl, 10, 8, bdl, 20, 6 Which of the following is correct? (a) The mean lead level in the water is about 10 ppm. (b) The mean lead level in the water is about 8 ppm. (c) The median lead level in the water is 7 ppm. (d) The median lead level in the water is 8 ppm. (e) Neither the mean nor the median can be computed because some values are unknown. 10. Ms. Myers precalculus class had a standard deviation of 2.4 on a trigonometry test, while Ms. Gentry's precalculus had a standard deviation of 1.2 on the same test. What can be said about these two classes? (a) Ms. Myers class is more homogeneous than Ms. Gentry's class. (b) Ms. Gentry's class is more homogeneous than Ms. Myers class. (c) Ms. Gentry's class did less well on the test than Ms. Myers class. (d) Ms. Myers class performed twice as well on the test as Ms. Gentry s class. (e) Ms. Myers class performed 1.2 points better on the test as Ms. Gentry s class. 11. The following is the DataDesk statistical summary of thegold medal performance in the men's long jump (measured in inches) for the modern Olympic series starting in Approximately what percent of the data lie between 298 and ? (a) 25% (b) 33% (c) 50% (d) 67% (e) 75% 12. Weights of seals are given in the following histogram. For this data, which values are appropriate estimates of the data s mean and standard deviation? (a) 100, 50 (b) 100, 100 (c) 200, 50 (d) 200, 100 (e) 300, A data set with seven data points has a mean of 5. One of the seven values in the data set is 8. What numerical contribution did the data point 8 make to the variance? (a) 1.25 (b) 1.50 (c) 1.75 (d) 2.00 (e) 2.25

4 14. In a frequency distribution of 3000 scores, the mean is 78 and the median as 95. One would expect this distribution to be: (a) skewed to the right (b) skewed to the left (c) symmetrical and mound-shaped (d) symmetrical and uniform (e) bimodal 15. A study was conducted on the weights of three different species of fish found in a lake in Finland. These three fish (bream, perch and roach) are commercial fish. Their weights are displayed in the boxplots below. Which of the following statements comparing these boxplots is NOT correct? (a) The median weights of the three species differ. (b) The spread of roach is less than the spread of the other two species. (c) The distributions of weights are approximately symmetric for all three species. (d) There are no outliers in weight for the three species. (e) The variability in the weights for the three species exceeds the variation in the three species means. 16. The mean age of 12 of the members attending a mathematics department faculty meeting is 37. Mr. Myers, who is 50, arrives late. What is the average of all 13 members? (a) 37 (b) 38 (c) 39 (d) 40 (e) Which of the following are true statements? I. The standard deviation is the square root of the variance. II. The standard deviation is zero only when all values are the same. III. The standard deviation is strongly affected by outliers. (a) I and II (b) I and III (c) II and III (d) I, II, and III (e) None of the above gives the complete set of true responses. 18. The stemplot displays the 1988 per capita income (in hundreds of dollars) of the 50 states. Which of the following best describes the data? (a) Skewed distribution, mean greater than median (b) Skewed distribution, median greater than mean (c) Symmetric distribution, mean greater than median (d) Symmetric distribution, median greater than mean (e) Symmetric distribution with outliers on high end

5 Part II Free Response (Questions 1-3) Show your work and explain your results clearly. 1. The test grades for a certain class were entered into a Minitab worksheet, and then Descriptive Statistics were requested. The results were: MTB > Describe 'Grades'. N MEAN MEDIAN TRMEAN STDEV SEMEAN Grades MIN MAX Q1 Q3 Grades You happened to see, on a scrap of paper, that the lowest grades were 35, 57, 59, 60,... but you don t know what the other individual grades are. Nevertheless, a knowledgeable user of statistics can tell a lot about the dataset simply by studying the set of descriptive statistics above. (a) Write a brief description of what the results tell you about the distribution of grades. Be sure to address: the general shape of the distribution unusual features, including possible outliers the middle 50% of the data any significance in the difference between the mean and the median (b) Construct a modified boxplot for these data.

6 2. Ogives of Distributions of Arithmetic Test Scores for Seventh and Eighth Graders (Connect 7s with a smooth curve for seventh-grade ogive and connect 8s with a smooth curve for eighth-grade ogive.) PERCENT TEST SCORE (a) What is the estimated percent of eighth-grade pupils whose arithmetic scores fall below the median score for grade seven? Justify your answer. (b) What is the shape of the distribution of the eighth-grade test scores? Justify your answer.

7 3.. During the early part of the 1994 baseball season, many sports fans and baseball players noticed that the number of home runs being hit seemed to be unusually large. Here are the data on the number of home runs hit by American and National League teams. American League 35, 40, 43, 49, 51, 54, 57, 58, 58, 64, 68, 68, 75, 77 National League 29, 31, 42, 46, 47, 48, 48, 53, 55, 55, 55, 63, 63, 67 (a) Construct an appropriate graph for comparing the number of home runs hit in the two leagues. (b) Calculate numerical summaries of the number of home runs hit in the two leagues. Which of these numbers would be most appropriate for comparing the two leagues? Explain. (c) Are there any outliers in either of the two data sets? Justify your answer numerically. (d) Write a few sentences comparing the distributions of home runs in the two leagues.