Name Student ID # Class Section Instructor Math 1070 Spring 2011 EXAM Dept. Use Only Exam Scores Problem Points 1. 20 2. 20 3. 20 4. 20 5. 20 TOTAL Score Show all your work and make sure you justify all your answers.
Math 1070 Exam 1. This practice exam may have general misspeeellings, and some obvious errors. 2. The table below is the hourly wage of the individuals John 12 Spock 125 Sally 20 Jack 36 Berry 25 Kelly 19 Nick 55 Jacque 10 Chester 15 Bella 40 (a) Make a five number summary, and make a box plot. 1
(b) Compute the variance and stanard deviation. (c) Are there any suspect outliers? 2
3. Be comforptable with box plots and pie charts. 4. Explain how it is possible that the mean value of the savings of individuals aged 30 to 50 is 150000, but the median value is 40000. 3
5. For the Standard normal distribution the z-score 1.2 in table A represents the what area under the normal distribution. Write this in terms of a probability, and in terms of a picture. 6. For a symmetric distribution the mean is 5. What is the median? 4
7. The running times of a mile for college professors follows a normal distribution with mean of 11 and standard deviation of 2.4. (a) Find a range in which 95 percent of all professor will finish the mile. (b) Ifyouwantedtorunfasterthanthe90thpercentilehowfastwould you have to run? (c) Professor MacArthur runs a 6 minute mile. What percent of Professors run a mile faster than 6 minutes. 5
(d) What percent of Professors run a mile in 7 to 9 minutes? (e) If 100 running times were observed in race of college professor what distribution would the average follow? (f) What is the probability that the average running time of a college professor is between 7 and 9 minutes. (g) What is the probability that the average running time of a college professor is not between 7 and 9 minutes 6
8. Emissions of sulfur dioxide by industry set off chemical changes in the atmosphere that result in acid rain. The acidity of liquids is measured by ph on a scale of 0 to 14. Distilled water has a ph of 7, and lower ph values indicate acidity. Normal rain is somewhat acidic, so acid rain is sometimes defined as rainfall with a ph below 5. The ph of rain at one location varies amoung rainy days according to a normal distribution with mean 5.4m and standard deviation.54. What proportion of rainy days have rainfall with ph below 5. 7
9. The table below is the hours worked in a given day for the individuals in column one and their hourly wage is given in column two. (a) Make a scatter plot. Spock 12 10 Jacque 5 20 Chester 4 25 Bella 8 15 8
(b) Compute the average and stanard deviation. (c) Compute the correlation 9
(d) Find the equation of the regression line (e) Use the regrssion line the predict the hours worked for an individual makeing 50 dollars an hour. (f) Compute the residual for Spock. (g) Is correlation positive or negative. Explain what this means in words. 10
10. problem 33 on page 119. 11. Is it possible to have a regression of 2, or 1.2 or 0 or.788? 11
12. In Professor Friedman s class the correlation between the students total score prior to the final examination and their final examination score is r =.6. The pre-exam totals for all the students in the course have a mean of 280 and standard deviation of 30. The final exam score have a mean of 75, and standard deviation of 8. Julie had a total of 300 before the final exam. (a) What is the equation of the regression line. 12
(b) Use the regression line to predict Julie s final exam score. (c) Julie does not think that this method accurately predicts how well she did on the final exam. Use r 2 to argue that her actual score could be much higher than the predicted value. 13
13. An online poll showed that 97 percent of online repondents opposed issuing drivers s lienses to illegal immigrants. National random samples taken at the time showed that only about 70 percent of the respondents are opposed to this. Explain briefly to someone who knows no statistics why random samples report public opinion more reliably than the online poll. 14
14. Some people think that red wine protects moderate drinkers from heart disease better than other alcoholic beverages. This calls for a randomized comparative expirment. Ther subjects were healthy men aged 35 to 65. They were randomly assigned to drink a red wine (9 subjects), drink white wine (9 subjects), drink white wine and also take polyphenols from red wine (6 subjects), take polyphenols alone (9 subjects), or drink vodka and lemonade (6 subjects). Outline the design of the expirment and randomly assign the 39 subjects to the 5 groups. Use table B starting at line 107, taking the first two digits. 15
15. Suppose that Starbucks is releasing a new line of blended coffee called mocha light. You wonder if Starbucks customers like the new mocha light as much as regular the regular mocha. (a) Describe a matched pair design to answer this question. Be sure the include proper blinding of your subjects. 16
(b) You have 20 regular customers on hand. Use table B starting at line 141 (taking the first two digits) to do the randomization that your design requires. 17
16. See problem 46 and 47. 17. Be prepared for a question related to the law of large numbners (in particular how to estimate parameters), central limit theorem, and what a statistic is. 18
18. Consider the expirment of tossing two regular dice. (a) What is the sample space. (b) What is the probability that the number you roll is 11? (c) What is the probability that the number you roll is any number between a 3 and 10? 19
(d) What is the probability that the number you roll is less than a 9? (e) What is the probability that the number you roll is less than or equal to 9? 20
19. The number of accidents per week at a hazardous intersection varies with mean 2.2, and standard deviation of 1.4. This distribution takes only whole number values so it is not a normal distribution. (a) What is the approximate distribution of X. Where X is the mean number of accidents per week at an intersection during a year. (b) What is the approximate probability that X is less than 2? (c) What is the probability that there are fewer than 100 accidents at this intersection in a year. 21
20. see problems 37 and 38 on page 312 22