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Introduction to Statistics Sample Exam Chapters 1 - 4 1. To estimate the percentage of Regis College students who use illegal drugs, a uniformed police oﬃcer approached students outside the student center, asked their names, and then asked whether they had used illegal drugs in the last month. She continued asking students until she had 40 responses. (a) What is the population for this survey? (b) What is the sample for this survey? (c) What factors make this survey subject to bias? (d) Describe another way of collecting the data, and mention at least one advantage and at least one disadvantage of your method. 2. Fairﬁeld College is considering a new course evaluation form for all the classes taught on campus. One concern is the amount of time necessary to ﬁll out the form. A random sample of 30 students were asked to ﬁll out the form for the class they had at 10:00 a.m. The times in minutes to ﬁll out the form were as follows: 18 19 8 12 18 20 15 17 19 23 22 30 21 16 44 17 15 12 18 26 51 23 35 31 42 5 2 3 9 12 Compute the ﬁve number summary and make a box and whisker plot for this data. Be sure to indicate the scale. Describe the shape of the display; is it skewed one way or the other? 3. The Richter scale is used to measure the magnitude of earthquakes. A sample of 15 earthquakes occurring in the United States had Richter scale ratings of 6.0 2.1 1.3 5.1 3.4 2.1 1.4 1.5 2.0 3.1 4.6 1.2 1.8 2.7 3.5 Compute the ﬁve number summary and the interquartile range. Make a box and whisker plot. Is this data skewed right or left? 4. We wish to make a histogram representing the following data. 63 21 13 51 34 21 14 15 20 31 46 12 18 27 35 4 34 24 54 10 15 22 18 42 If we wish the histogram to have 6 bars, what should the class width be? 5. The frequency table for the data in problem 4 above is shown below. Fill in the blank entries. Class Limits Class Boundaries Midpoint Freq. Rel. Freq. Cumulative Freq 8.5 4 16.7% 4 9 37.5% 3 16 4 16.7% 20 6. The histogram below shows the frequencies of the number of houses sold in a month by a particular realty company. Use the information from the histogram to compute the sample mean and sample standard deviation. Organize your work in a table showing all your calculations. 7. The Richter scale is used to measure the magnitude of earthquakes. A sample of 6 earthquakes occurring in the United States had Richter scale ratings of 6.0 2.1 1.3 5.1 3.4 2.1 Compute the sample mean and standard deviation for this data. 8. A population of golﬁsh in a large ﬁsh tank was studied and the mean length was found to be 6 centimeters with a standard deviation of 1.1 cm. A separate study looked at the lengths of sharks found in ﬁshermen’s nets. This second study found that the mean length of the sharks measured was 8 feet with a standard deviation of 2.1 feet. Compute the coeﬃcient of variation for the length of goldﬁsh and for the length of sharks. Which data set is more spread out? A sample of a trout population from a lake was measured and the mean length was found to be 8 inches with a standard deviation of 1.5 inches. Is the distribution of lengths of trout more like the distribution of lengths of goldﬁsh or the distribution of lengths of sharks? Explain. 9. (a) Find a Chebyshev interval which will contain at least 75% of the lengths of trout in the previous problem. (b) Find a Chebyshev interval which will contain at least 88.9% of the lengths of sharks in the previous problem. (c) Find a Chebyshev interval which will contain at least 93.8% of the lengths of goldﬁsh in the previous problem. 10. Is the data represented by the following box and whisker plot skewed left or right? 10 15 20 25 30 35 40 45 (True or False) More than half of the data is larger than the median. (True or False) Exactly half of the data is inside the box. (True or False) The left whisker represents the ﬁrst quartile. (True or False) There is more data in the right whisker than in the left whisker. 11. We’ve got 20 cookies in a jar. There are 14 chocolate chip and 6 oatmeal raisin. If you draw one cookies at random from the jar, what is the probability that it is oatmeal raisin? 12. In another cookie jar we have 6 chocolate chip, 4 oatmeal raisin, and 3 sugar cookies. If you take one cookie at random out of this jar, what is the probability that it is either oatmeal raisin or a sugar cookie? Are these mutually exclusive events? 13. In yet another cookie jar we have 10 chocolate chip cookies, 3 of which are burnt, 12 oatmeal raisin, 5 or which are burnt, and 9 sugar cookies, 4 of which are burnt. If you draw one cookie at random from this jar, what is the probability that it is either a sugar cookie or a burnt cookie (of any kind). Are these events mutually exclusive? 14. If we draw one cookie from the jar in problem 11, and one cookie from the jar in problem 12, what is the probability that they are both chocolate chip? 15. The results of an extensive medical study to determine the eﬃcacy of a new medical test for a common medical condition are summarized in the following table. Condition Condition Present Absent Row Total Test Result + 63 96 159 Test Result - 252 564 816 Column Total 315 660 975 Find (a) P (A), (b) P (A, given +), (c) P (+), (d) P (P and +), (e) P (+ given P ) (f) P (+ given A) Mean and Standard Deviations: x (x − x)2 Sample Data x= n s= n−1 xf (x − x)2 f Grouped Data x= n s= n−1 n= f Chebyshev Intervals: at least 75% µ − 2σ to µ + 2σ at least 88.9% µ − 3σ to µ + 3σ at least 93.8% µ − 4σ to µ + 4σ

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posted: | 10/8/2009 |

language: | English |

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