(3 pts) 1. Which statements are usually true of a left-skewed distribution? (circle all that are correct)

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1 STAT Practice Exam I Name (print): Section: This is a practice exam - it s a representative sample of problems that may appear on the exam and also substantially longer than the in-class exam. It s best to do large portion of your studying before taking this exam. Please how your work whenever calculations are necessary. Use at three decimal places when working with proportions and use at least two decimal places when working with all other numbers. Put answers in boxes if provided. For multiple choice questions, circle all correct answers. I. (15 points - 3 points each) (3 pts) 1. Which statements are usually true of a left-skewed distribution? (circle all that are correct) (a) The mean is larger than the median. (b) Q 1 is closer to the median than Q 3. (c) The IQR is skewed to the left. (d) The mean is smaller than the median. (e) About 68% of the distribution is within 1 standard deviation of the mean. (f) None of the above. (3 pts) 2. Which of the following statements about the correlation coefficient r is not true (circle all that are correct): (a) A correlation of r = 1 indicates perfect positive linear association. (b) The correlation is not appropriate as a measure of association for nonlinear relationships between two quantitative variables. (c) The correlation r measures the strength of the linear association between two quantitative variables. (d) The correlation r is unitless. (e) None of the above. (3 pts) 3. The five-number summary of credit hours for 24 students in an introductory class is: (13, 15, 16.5, 18, 22). From this information, determine which statement is true: (a) There are no outliers in the data. (b) There is at least one small outlier in the data. (c) There is at least one large outlier in the data. (d) There are both small and large outliers in the data. (3 pts) 4. All but one of the statements below contain a mistake. Circle the one statement that could be true: (a) The correlation r between cigarette smoking and gender is large. (b) The correlation between age and weight of a newborn baby is r =.83 ounces each day. 1

2 (c) The correlation between a person s age and vision is r = (d) The correlation between the species of a tree and its height is r =.56. (e) The correlation between blood alcohol level and reaction time is r =.73. (3 pts) 5. Suppose that a normal model describes the acidity (ph) of rain water, and that water tested after a storm had a z-score of 1.2. This means that the acidity of rain water (circle one): (a) was 1.2 ph units greater than average rainwater. (b) had a ph of 1.2 times that of average rainwater. (c) varied with a standard deviation of 1. (d) had a ph of 1.2. (e) had a ph 1.2 standard deviations greater than the average acidity (ph) of rainwater. (f) None of the above. II. (22 points) Statistics Canada provides data on the Canadian population (in thousands). The table below Language Province or Territory English French Total Only Only Both Neither Yukon Territory Nova Scotia Quebec Manitoba Total displays data from four provinces or territories in Canada and the language status of the citizens. Citizens either reported speaking only English, only French, both English and French, or neither language. (4 pts) 6. Of the Canadian citizens that only speak English, what proportion either live in the Yukon Territory or Nova Scotia? (circle one): (a) (b) (c) (d) (e) (f) None of these (4 pts) 7. What proportion of Canadian citizens in this example are from Quebec and only speak French? Circle the closest proportion: (a) (b) (c) (d) (e) (f) None of these (6 pts) 8. Give the conditional distribution of the language variable among those who live in Quebec, placing your final answer in the box below. 2

3 (4 pts) 9. The observational units in this study are the (circle one): (a) Language Categories (b) Canadian Citizens (c) Canadian Provinces and Territories (d) # citizens in each category (e) Percentages (f) None of these (4 pts) 10. The most appropriate visual display for exploring the marginal distribution of the Language variable would be a (circle one): (a) Bar chart (b) Stem and leaf plot (c) Boxplot (d) Histogram (e) None of these III (20 points): In 1882, Michelson was attempting to measure the speed of light. He ran multiple experiments, using different techniques. The following sorted data display observations from two such techniques, each containing 20 trials. The measurements are in km/sec and have 299,000 km/sec subtracted from them to make calculations more manageable.(the speed of light is now estimated with much better precision to be 299, km/sec.) Experiment A Experiment B (5 pts) 11. Calculate the five number summary of the observations for Experiment A and report it below. (4 pts) 12. Test for outliers in the Experiment A data using the criteria discussed in class. Report any outliers. 3

4 Speed of Light Experiments (3 pts) 13. Using information gathered in the previous two problems, draw a boxplot for the data from Experiment A beside the boxplot of the Experiment B data. (8 pts) 14. In the context of the problem, compare the key features of the two distributions. Speed of Light Estimate (km/sec) 299, Experiment A Experiment B IV (22 points): A scientist at the University of Montana studies the electrical activity of cells in the brain. In order for a signal to be sent within the brain, a channel must be opened, allowing electricity to cross the cell s membrane. This scientist knows that the opening time of a channel closely follows a normal model with a mean of 4.0 milliseconds and a standard deviation of.8 milliseconds. (8 pts) 15. What is the IQR of the opening times of a channel? (6 pts) 16. This scientist knows an electrical signal is sent when a channel opens for at least 5 milliseconds. Based on this knowledge and the information provided in the problem, what proportion of channels produce an electric signal? 4

5 (4 pts) 17. Using the rule, find the 84th percentile of the distribution of opening times. (4 pts) 18. Suppose this scientist discovers that a new drug adds 2 milliseconds to the opening time of all channels, allowing more electricity to travel across the membrane. For example, a channel ordinarily having an opening time of 3 milliseconds would now have an opening time of 5 milliseconds with the new drug. Which of the following gives the appropriate normal distribution for these new opening times using the drug (circle one)? (a) Normal (µ = 6 milliseconds, σ = 0.8 milliseconds) (b) Normal (µ = 4 milliseconds, σ = 2.8 milliseconds) (c) Normal (µ = 6 milliseconds, σ = 1.6 milliseconds) (d) Normal (µ = 6 milliseconds, σ = 2.8 milliseconds) (e) Normal (µ = 4 milliseconds, σ = 0.8 milliseconds) (f) None of these V. (21 points) Several years ago, round-trip flights leaving Missoula to various cities at the start of Thanksgiving break were reported by in the table to the right. Missoula to: Distance (Miles) Fare ($) The scatterplot shown below was created to examine Albuquerque the relationship between the distance traveled from Baltimore Missoula and ticket price. Boston Price (dollars) Scatterplot of Airline Ticket Prices from Missoula vs. Distance Chicago Dallas Denver Kansas City Los Angeles Nashville New Orleans New York City Philadelphia Portland Saint Louis Salt Lake City San Francisco Seattle Distance (miles) 5

6 (3 pts) 19. What is the explanatory variable in this problem? (6 pts) 20. Describe the relationship between ticket price and distance traveled. (7 pts) 21. The correlation coefficient for the relationship between these two variables is r =.829. In addition, the following summary statistics were calculated for both variables. Use the information to find the regression equation for predicting ticket price from distance traveled. Express this equation in the context of the problem and draw the corresponding line in the scatterplot above. Sample Size Mean Median Standard Deviation IQR Distance Traveled From Missoula (miles) Ticket Cost (in Dollars) (5 pts) 22. Using the model you produced in the previous question, predict the ticket cost for a city 1800 miles from Missoula. Formulas z = y µ σ r = 1 n 1 x x s x y y s y ŷ = b 0 + b 1 x, b 1 = r s y s x and b 0 = y b 1 x y = y n s = (y y) 2 n 1 Range = Max Min IQR = Q 3 Q 1 6