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Statistics 108, Exam 1, Fall 2008 Name (print):_____________________ I confirm that I am allowed only a calculator and one 3-by-5 inch note card of notes for this exam. I will not look at anybody else’s exam and I will take all necessary efforts to prevent others from seeing my exam. The consequence of using additional test aids, copying from others, or allowing others to copy my work will result in disciplinary action. I have read and agree with the above statement. Signature: _____________________ 1. 4pts. Answer:_____________. Using the values 𝑥1 = 2, 𝑥2 = 8, and 𝑦1 = 3, 𝑦2 = 1, calculate ∑ 𝑦𝑖 (𝑥𝑖 − 𝑥̅ )2 . Show your work. For the following blanks, fill in whether the random variable is nominal, ordinal, continuous or discrete. 2. 1pt. Answer:_____________ The brand of automobile (Toyota, Ford, etc.) 3. 1pt.Answer: _____________ Amount of pain after surgery (None, Some, Much) 4. 1pt.Answer: _____________ Semester grade in a class (A,B,C,D,F) 5. 1pt.Answer: ______________ Number of typographical errors in a page (0, 1, 2, etc.) Circle whether the item is a parameter or a statistic. 6. 1pt. statistic parameter: The mean weight of all 18 year old white men in America. 7. 1pt. statistic parameter: The mean height of the 29 males in this class. 8. 1pt. statistic parameter: The probability of a coin toss being heads. The below steam-and-leaf plot shows the body temperature (in Fahrenheit) of 104 students. Leaf Unit = 0.10 2 94 66 4 95 12 6 95 69 10 96 1334 17 96 6778999 33 97 0000011122233344 50 97 55566777888888999 (23) 98 00000001111111222233344 31 98 5555556666777889 15 99 0022233444 5 99 57 3 100 4 2 100 5 1 101 4 9. 2pts.Answer: ______________ How many students had body temperatures of 98.6 degrees? Name:_______________ Boxplot of EurekaPrecip, LAPrecip 80 70 60 Data 50 40 30 20 10 0 EurekaPrecip LAPrecip The above boxplot graph shows 101 years of precipitation (rain in inches) data for Eureka and Los Angeles. 10. 2pts.Answer:__________________ What is the approximate median rainfall for Eureka? 11. 2pts.Answer:__________________ Which city has the greatest range? 12. 2pts.Answer: __________________ Showing your calculations, give an estimate for the interquartile range for Eureka. \ 13. 3pts. Answer:________________El Nino years are when the water near the equator is far above normal. La Nina years are when the water near the equator is far below normal. Neutral years are when the water temperature is intermediate. Over a 101 year period, 33 years were classified as being El Nino years, 23 years as La Nina, and 45 years as neutral. If a pie chart were to be drawn, how many degrees would the La Nina slice require? Show your calculations. 14. 2 pts. A study was performed to investigate how many miles Americans drive on a typical week day. Researchers performed a telephone survey where, on a Wednesday, they asked 200 men and 200 women about how many miles they had driven on the previous Tuesday. 50 of the 400 people were randomly selected from rural areas and the remaining people were from urban areas. Circle which of the following sampling methods was used: (A) Systematic Sampling (B) Stratified Sampling. 2 Name:_______________ 15. Using the six data values: 3, 8, 6, 4, 3, 0, calculate: (show your work) a. 4pts. Mean = b. 3pts. Median = c. 2pts. Mode = Scatterplot of Age vs Height 55 50 45 Age 40 35 30 25 20 1450 1500 1550 Height 1600 1650 16. 2pts. Which number is the closest to the sample correlation between Age and height? (i) -35 (ii) -1 (iii) -0.8 (iv) 0 (v) +0.8 (vi) +1 (vii) +35 17. 2pts. Suppose the odds are 2:3 that you will win a game. What is the probability that you will win the game? 18. Suppose a jar contains 3 black marbles and 3 white marbles. Suppose 2 marbles are randomly sampled from the jar without replacement. What is the probability of getting 1 white and 1 black marble? Show your work. 3 Name:_______________ Scatterplot of Price vs Salary 120 110 100 Price 90 80 70 60 50 40 30 0 20 40 60 80 100 Salary Price = 42.6 + 0.694 Salary The above graph shows the relationship between average working salary and cost of living (Price) for 46 major cities around the world. The salaries and cost of living are scaled to where Zurich, Switzerland is 100 for both cost of living and salary. The equation for the regression line is given below the graph. Madrid, Spain had a salary level of 50 and a Price of 93.8. 19. 3pts. Calculate the regression line’s predicted Price for Madrid. 20. 2pts. Calculate the residual value for Madrid. 21. 2pts. For the Price vs. Salary scatter plot, circle the number that is closest to the correlation is: (i) -42.6 (ii) -1 (iii) -0.8 (iv) 0 (v) +0.8 (vi) +1 (vii) +42.6 4 Name:_______________ The below table shows the counts of left-handed and right-handed students and their eye colors. Tabulated statistics: eyes, hand Rows: eyes blue brown green All Columns: hand left right All 2 5 3 10 23 22 12 57 25 27 15 67 Cell Contents: Count 22. 3pts. Use the table to estimate 𝑃(𝑏𝑟𝑜𝑤𝑛 𝑒𝑦𝑒𝑠)= 23. 3pts. Use the table to estimate 𝑃(𝑏𝑟𝑜𝑤𝑛 𝑒𝑦𝑒𝑠 |𝑙𝑒𝑓𝑡 ℎ𝑎𝑛𝑑𝑒𝑑) = Histogram of LAPrecip 25 Frequency 20 15 10 5 0 5 10 15 20 LAPrecip 25 30 35 24. 2pts. The above histogram shows precipitation amounts (inches) in Los Angeles for 101 years. The median precipitation was 13.5 inches. Compared to the median of 13.5 inches, the mean is: circle (a) more, (b) less, or (c) about the same? 5 Name:_______________ 25. 2pts. In the above Venn Diagram, shade in the region represented by 𝐴̅ ∩ 𝐵̅ 26. 2pts. In the above Venn Diagram, shade in the region represented by𝐴̅ ∪ 𝐵̅. 6