Final Exam with Answers - Statistics and Society | STAT 11300, Exams of Statistics

Download Final Exam with Answers - Statistics and Society | STAT 11300 and more Exams Statistics in PDF only on Docsity! Stat 113K SAMPLE Exam #2 Name: _________________ 1. A substance used in biological and medical research is shipped by airfreight to users in cartons of 1,000 ampules. The data given in the scatterplot below, involving 10 shipments, were collected on the number of times the carton was transferred from one aircraft to another over the shipment route and the number of ampules found to be broken upon arrival. The regression equation is also given in the plot. Use this information to answer the following questions. Airfreight breakage Number of broken ampules = 4(Number of transfers) + 10.2 R2 = 0.9009 0 5 10 15 20 25 0 0.5 1 1.5 2 2.5 3 3.5 Number of aircraft transfers N um be r o f a m pu le s br ok en u po n ar riv al (a) Predict the number of broken ampules for a shipment involving 2 aircraft transfers. 18.2 (b) By what amount does the number of broken ampules increase (or decrease) when the number of transfers increases by 1 transfers. Please indicate if the number of broken ampules increases or decreases. The number of broken ampules increases by 4. (c) By what amount does the number of broken ampules increase (or decrease) when the number of transfers decreases by 2 transfers. Please indicate if the number of broken ampules increases or decreases. The number of broken ampules decreases by 8. (d) Predict the number of broken ampules for a shipping route that includes 5 aircraft transfers. Is this a reasonable prediction? Explain. 30.2, but this is not a reasonable prediction because 5 transfers is outside the range of data. 2. Multiple Choice. A high correlation between two variables does not always mean that changes in one cause changes in the other. The best way to get good evidence that cause-and- effect is present is to (circle the correct answer): (a) select a simple random sample from the population of interest. (b) carry out a randomized comparative experiment. (c) make a scatterplot and look for a strong association. (d) make a histogram and look for outliers. 3. Suppose that it is known that the true proportion of registered American voters who believe that their local representative should be reelected is 0.55. However, the Pew Research Center does not know this, and they survey a simple random sample of 2000 people in order to estimate the true proportion. The sample proportion found from taking this survey approximately follows a normal distribution. For this survey of 2000 people, the standard deviation for the result will be 0.011. a. What is the probability that the sample proportion will be between 0.561 and 0.57? 0.1246 b. What is the probability that the sample proportion will be greater than 0.565? 0.0869 a. What proportion of the distribution is between 160 and 190 cm? 0.7485 b. What proportion of male college students have heights above 140 cm? 0.9938 c. The middle 80% of college students will have heights between _154.64_ cm and _185.36_cm. d. The bottom 40% of male college students will be less than how many cm tall? 167 cm 9.) The correlation between a person’s height and weight is .89. What percent of variability in weight can be explained by the regression line with height as the explanatory variable? 79.21% 10.) Use the scatterplot below to answer the following two questions. y = 24.241 + 2.2034x r2 = 0.4391 25 27 29 31 33 35 37 39 41 43 45 2 3 4 5 6 7 8 9 X Y a. In the above graph there is one outlier. If we remove the outlier from the dataset and fit the regression line again, what will happen to the r2 value? It will increase. b. What will happen to the slope of the line? It will increase. For each of the graphs below, match one of the correlations from the list below. Only use each of the possible values once. Graph A r = _0.5_ Graph B r = _0.88_ Graph C r = _0_ Possible values: r = .88 r = 0 r = .5 r = -.18 r = 1 A 0 2 4 6 8 10 12 14 16 18 4 6 8 10 12 14 16 X Y B 20 25 30 35 40 45 50 55 2 3 4 5 6 7 8 9 10 X Y C 0 2 4 6 8 10 12 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 X 4). (21 pts) The following scatterplot shows data collected by a lending firm studying the relationship between the number of children in a household and the amount of debt the household is willing to carry relative to their annual income expressed as a ratio (for instance, a household with an annual income of $50,000 and a total debt of $100,000 has a debt to income ratio of 2). The regression equation is given on the plot. Use this information to answer the following questions. Number of Children vs Debt to Income Ratio y = 2.3 + 1.02x r2 = 0.6534 0 2 4 6 8 10 12 14 0 1 2 3 4 5 6 7 8 9 10 11 Number of Children D eb t t o In co m e R at io (a) (4 pts) Find the predicted debt to income ratio for a household with 7 children. 9.44 (b) (2 pts) Find the predicted debt for a household with 7 children and an annual income of $225,000. 2,124,000 (c) (3 pts) Give the numerical value for the percent of variability in debt to income ratio explained by a linear association with number of children. 65.34 (d) (4 pts) If a family with 2 children will have exactly one more child, what can they expect their debt to income ratio to increase by? 1.02 (e) (4 pts) Give the correlation between number of children in a household and the debt to income ratio of that household. 0.808 (f) (4 pts) Suppose you are from a household with 11 children. Based on the above graph, can you justifiably predict your family's debt to income ratio? Yes or No. Explain. No that's extrapolation beyond the range of the data. 5). (9 pts) A balanced die has 6 faces, each of which has an equal probability of being rolled. John rolls 3 balanced dice and calculates the sum of the three faces. There are 6*6*6 = 216 possible outcomes. a) (3 pts) What is the probability that three 6s are rolled? 0.0046 b) (3 pts) What is the probability that the three faces sum to 3? 1/216 c) (3 pts) What is the probability that one 2 and two 1s are rolled? 3/216 = 0.013 6). (11 pts) The following table gives the final grade distribution for an introductory statistics class of 700 students. The numerical values correspond to a 4 point grading scale. Letter Grade A B C D F Numerical Grade 4 3 2 1 0 Proportion of students 0.1 0.2 0.45 0.2 ?? a) (2 pts) What is the probability that a randomly selected student from this class received an F as the students final grade? 0.05 b) (3 pts) After the semester ended, suppose you were to randomly select a student from the class. What do you expect his final numerical grade to have been? 2.1 c) (3 pts) What was the probability that a randomly selected student’s numerical grade was at least a 2? 0.75 d) (3 pts) Given that you know your final grade was an A or a B, what is the conditional probability that your final grade was an A? 1/3