Math 243, Practice Exam 1

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Berniece Grace Harmon
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1 Math 243, Practice Exam 1 Questions 1 through 5 are multiple choice questions. In each case, circle the correct answer. 1. (5 points) A state university wishes to learn how happy its students are with their housing. They use random numbers to pick 30 freshman, 30 sophomores, 30 juniors, and 30 seniors, and then do phone interviews with each of these students. What sort of sample is this? (a) Voluntary response sample (b) Stratified random sample (c) Simple random sample (d) Convenience sample 2. (5 points) Examine the following normal density curve. Estimate the standard deviation σ (a) σ = 50 (b) σ = 20 (c) σ = 20 (d) σ = 0 (e) σ = 2.2 (f) σ =

2 3. (5 points) Examine the following scatterplot The correlation is: (a) Clearly less than 1 (b) Close to 1 (c) Clearly negative but not close to 1 (d) Near zero (e) Clearly positive but not close to 1 (f) Close to 1 (g) Clearly greater than 1 (h) Not defined 4. (5 points) In September 2001, Science News reports that a study of 8006 men over a 20 year period finds a strong correlation between higher rates of constipation and Parkinson s disease (a neurological disorder). The neurologists conducting this study do not believe that constipation causes Parkinson s disease. What is the most likely conclusion one can draw? (a) Constipation causes Parkinson s disease (b) Constipation is caused by Parkinson s disease (c) The correlation is caused by a lurking variable, such as diet or heredity. (d) The observed correlation is a mistake caused by too small a sample. (e) The conclusion is caused by using a convenience sample rather than a random sample.

3 Give short answers to the following questions. 5. (15 points) For a particular age group of adult males the distribution of cholesterol readings (in mg/dl) is approximately normally distributed with a mean of 210 and a standard deviation of 15. [On the real exam Table A from your book would be attached to the back. For now, just consult your book.] (a) What percentage of this population would have readings exceeding 220? (b) What percentage of this population would have readings between 190 and 200? (c) Between what values do the readings of the middle 95% of all readings fall? (d) What is the median of all cholesterol readings? (e) What is the first quartile of all cholesterol readings? 6. (12 points) A study of education followed a large group of fifth-grade children to see how many years of school they eventually completed. Let X be the highest year of school completed by a randomly chosen fifth-grader. (Students who go on to college are included in X = 12). The study found the following probability distribution of X: Final year Probability (a) What percent of fifth-graders eventually finished the 12th grade? (b) Find P (X 6). (Be careful: the event X 6 includes the value 6). (c) Find P (X > 6). (d) Find the probability that a randomly chosen fifth-grader completes at least one year of high-school. (High school begins with the 9th grade).

4 7. (10 points) The Wechsler Adult Intelligence Scale is a common IQ test for adults. The distribution of WAIS scores for persons over 16 years of age is approximately normal with mean 100 and standard deviation 15. (a) What is the probability that a randomly chosen individual has a WAIS score of 105 or higher? (b) A certain person s z-score on this test was 0.5. What was her score on the WAIS scale? 8. (15 points) We would like to understand whether the minimum wage affects the unemployment rate. We study minimum wages in each state of the U.S. and compare them with unemployment rates in each state. (a) Is this an observational or an experimental study? (b) What is the response variable? (c) What is the explanatory variable? (d) What are the individuals in this study? (e) Give a possible confounding variable. 9. (12 points) Here are the ages of the 20th century U.S. presidents at the time of their first inauguration: 46, 64, 69, 52, 61, 56, 55, 43, 62, 60, 51, 54, 51, 55, 56, 51, 42. (a) Give the 5-number summary for this data. (b) Draw a boxplot for this data. (c) What is the mean? (d) What is the standard deviation?

5 10. (15 points) The following data has been collected on five individuals for some explanatory variable x and some response variable y: Individual A B C D E x y (a) Draw a scatterplot on the axes provided. Be sure to label your axes, indicate the scales on both axes, and make an appropriate choice of which variable to put on which axis. (b) Find the equation of the least squares regression line and plot in on the graph above. (c) What percentage of the variation in y is explained by the variation in x? (d) What is the coorelation? (e) Use the least squares regression line to predict y when x = 15.

6 Answers: (1) b (2) c (3) c (4) c (5) (a) 25.46%; (b) 16.28%; (c) ; (d) 210; (e) 195. (6) (a) 75.2%; (b) 0.983; (c) 0.976; (d) (7) (a) ; (b) (8) (a) Observational study; (b) unemployment rate; (c) minimum range; (d) the 50 states; (e) One possibile answer is the overall wealth of the state. (9) (a) 42, 51, 55, 60.5, 69; (b) ; (c) ; (d) (10) (a) ; (b) y = 1.925x ; (c) 63.83%; (d) 0.799; (e) y =

Section 1.3 Exercises (Solutions)

Section 1.3 Exercises (Solutions) Section 1.3 Exercises (s) 1.109, 1.110, 1.111, 1.114*, 1.115, 1.119*, 1.122, 1.125, 1.127*, 1.128*, 1.131*, 1.133*, 1.135*, 1.137*, 1.139*, 1.145*, 1.146-148. 1.109 Sketch some normal curves. (a) Sketch