Test 1 Chapters 1, 2, 3
Introduction to Statistics / Math 13 − 12777 −Summer 2008 (Prof. Latham)

1. For each of the variables described below, indicate whether the variable is a quantitative or a categorical (qualitative) variable. Also, indicate the level of measurement for the variable: nominal, ordinal, interval, or ratio. Make sure your responses are the most specific possible. Indicate your choice for each by circling the appropriate answer. Variable Type of variable Level of measurement

2. Which of the following variables are best thought of as continuous, which discrete? Indicate your choice for each by circling the appropriate answer. (a) The number of personal telephone calls made tomorrow at Bingley Corporation. Discrete Continuous

(b) The number of defective compact discs in a batch of discs. Discrete Continuous

(a) Distance (in miles) Nominal from home to the Quantitative Ordinal nearest all−night Categorical Interval Ratio convenience store (b) Temperature (in degrees Celsius) Nominal Quantitative Ordinal Categorical Interval Ratio Nominal Quantitative Ordinal Categorical Interval Ratio

(c) The time for a participant to identify the color of the letters when the word red is shown in green letters on a computer screen. Discrete Continuous

(c) Closing price (in dollars) of a stock

(d) The number of tickets purchased by a caller on a Rose Bowl ticket hotline. Discrete Continuous

(d) Letter grade (A, B, Nominal C, D, or F) Quantitative Ordinal Categorical Interval Ratio 3. In a recent phone survey, people were asked to state their favorite type of television show. The pie chart below summarizes the responses of those surveyed. addDivNode(455); 4. The pie chart below shows how the annual budget for a certain company is divided by department. If the total budget is , what amount is budgeted for Editorial and Sales combined? addDivNode(476);

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(a) Which category was chosen by approximately one−fourth of those surveyed? (b) Approximately what percentage of those surveyed chose Other or Drama? Write your answer as a multiple of − that is, . (c) If of those surveyed chose Documentary,

approximately what percentage chose Other? 5. Qwan Corporation has four departments. The double bar graph below shows how many male and female employees are in each department. Use this graph to answer the questions. 6. Below are the times (in days) it takes for a sample of customers from Andrew's computer store to pay their invoices. 19, 15, 43, 39, 14, 14, 14, 42, 42, 42, 38, 38, 34, 34. Draw the histogram for these data using an initial class boundary of and a class width of . Note that you can add or remove classes from the figure. Label each class with its endpoints.

(a) Estimate the number of females in Production. (b) Which departments have more males than females? (c) Which department has the most employees total?

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7. Methadone is a synthetic drug whose effect on the body is similar to that of morphine and heroin. Methadone has been used to help people control their addictions to these other drugs. Recently, the governor of Florida vetoed a million−dollar appropriation for several Methadone clinics in the state. Had Methadone use gotten out of hand? The following histogram summarizes information from a study of Florida Methadone clinic patients. (Florida's projected mean daily dosage per Methadone clinic patient was about milligrams.)

8. The stem−and−leaf display below gives the test scores for the students in Prof. Jones' economics class. Use the display to answer the following questions. Test scores

Key:

means a score of

.

(a) What was the highest score in the (b) What was the lowest score overall? (c) How many students scored in the

s?

s?

Based on the histogram, find the proportion of daily dosages in the sample that are at least milligrams. Write your answer as a decimal, and do not round your answer. 9. From the time of early studies by Sir Francis Galton in the late nineteenth century linking it with mental ability, the cranial capacity of the human skull has played an important role in arguments about IQ, racial differences, and evolution, sometimes with serious consequences. (See, for example, S.J. Gould, "The Mismeasure of Man," .) Suppose that the mean cranial capacity measurement for modern, adult males is 10. Four distributions, labeled (a), (b), (c), and (d), are represented below by their histograms. Without performing any calculations, order the respective means , , , and of the distributions.

cc

(cubic centimeters). Complete the following statements about the distribution of cranial capacity measurements for modern, adult males.
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(a) According to Chebyshev's theorem, at least _____% of the measurements lie within 1.5 standard deviations of the mean, cc. a. 56% b. 75% c. 84% d. 89%

(b) Suppose that the distribution is bell−shaped. If approximately 99.7% of the measurements lie between 463 cc and 1705 cc, then the approximate value of the standard deviation for the distribution, according to the empirical rule, is _____.

11. The following list contains the average annual total returns (in percentage points) for mutual funds. The mutual funds appear in an online brokerage firm's "all−star" list. 11, 16, 12, 37, 1, 33, 15, −4, 36.

12. A job placement agency advertised that last year its clients, on average, had a starting salary of . Assuming that average refers to the mean, which of the following claims must be true based on this information? Note: More than one statement could be true. If none of the statements is true, mark the appropriate box.

(a) What is the median of this data set? If your answer is not an integer, round your answer to at least one decimal place. (b) What is the mean of this data set? If your answer is not an integer, round your answer to at least one decimal place. (c) How many modes does the data set have, and what are their values? Indicate the number of modes by selecting the appropriate line, and then indicate the value(s) of the mode(s), if applicable. 1. zero modes 2. one mode: _____ 3. two modes: _____

_____

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13. An intelligence test that has a maximum time for completion of minutes was recently administered to a group of people. Their

14. The following data are the distances from the workplace (in miles) for the employees of a small business: 5, 14, 10, 12, 9. Assuming that these distances constitute an entire population, find the standard deviation of the population. Round your answer to at least two decimal places. (If necessary, consult a list of formulas.)

respective times for completion (in minutes) were as follows: 22, 26, 32, 33, 33, 34, 36, 38, 38, 39, 39, 39, 39, 41, 42, 42, 42, 42, 43, 43, 43.

(a) For these data, which measures of central tendency take more than one value? Choose all that apply. 1. Mean 2. Median 3. Mode 4. None of these measures (b) Suppose that the measurement 22 (the smallest measurement in the data set) were replaced by 8. Which measures of central tendency would be affected by the change? Choose all that apply. 1. Mean 2. Median 3. Mode 4. None of these measures (c) Suppose that, starting with the original data set, the smallest measurement were removed. Which measures of central tendency would be changed from those of the original data set? Choose all that apply. 1. Mean 2. Median 3. Mode 4. None of these measures
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Figure 1

(d) The relative values of the mean and median for the original data set are typical of data that have a significant skew to the left. What are the relative values of the mean and median for the original data set? Choose only one. 1. Mean is greater 2. Median is greater 3. Cannot be determined 15. Here are the shopping times (in minutes) for a sample of shoppers at a particular shoe store: 33, 41, 21, 43, 22. Find the standard deviation of this sample of shopping times. Round your answer to at least two decimal places. (If necessary, consult a list of formulas.) 16. Loretta, who turns eighty this year, has just learned about blood pressure problems in the elderly and is interested in how her blood pressure compares to those of her peers. Specifically, she is interested in her systolic blood pressure, which can be problematic among the elderly. She has uncovered an article in a scientific journal that reports that the mean systolic blood pressure measurement for women over seventy−five is mmHg, with a standard deviation of mmHg. Assume that the article reported correct information. Complete the following statements about the distribution of systolic blood pressure measurements for women over seventy−five.

(a) According to Chebyshev's theorem, at least 84% of the measurements lie between _____mmHg and _____mmHg. (Round your answer to 1 decimal place.) (b) According to Chebyshev's theorem, at least _____% of the measurements lie between 119.4 mmHg and 146.2 mmHg. a. 56% b. 75% c. 84% d. 89% (c) Suppose that the distribution is bell−shaped. According to the empirical rule, approximately _____% of the measurements lie between 119.4 mmHg and 146.2 mmHg. a. 68% b. 75% c. 95% d. 99.7% (d) Suppose that the distribution is bell−shaped. According to the empirical rule, approximately 99.7% of the measurements lie between _____mmHg and _____mmHg.

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17. The following data are the ages (in years) of algebra teachers in a school district. 38, 30, 31, 55, 57, 41, 48, 42, 41, 56, 30, 43, 25, 34, 32, 44, 39, 58. Construct a box−and−whisker plot for the data. addDivNode(412);

18. The following are ages of Declaration of Independence.

of the signers of the

27, 27, 44, 43, 54, 69, 36, 46, 32, 35, 52, 38, 39, 42, 40, 49. Find th and th percentiles for these ages.

(If necessary, consult a list of formulas.)

19. A sample of

customers was taken at a local

computer store. The customers were asked the prices of the computers they had bought. The data are summarized in the following table. Number of computers 7 10 14 13 Price (in dollars) 1400 1800 2700 2050

20. Students at a major university in Southern California are complaining about a serious housing crunch. Many of the university's students, they complain, have to commute too far to school because there is not enough housing near campus. The university officials' response is to perform a study. The study, reported in the school newspaper, contains the following histogram summarizing the commute distances for a sample of students at the university:

Find the mean price for this sample. Round your answer to the nearest dollar.

Based on this histogram, estimate the standard deviation of the sample of distances. Carry your intermediate computations to at least four
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decimal places, and round your answer to at least one decimal place. (If necessary, consult a list of formulas.)

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