1. Bell Work1/29 1) From the sequence of random numbers, select 3 distinct numbers (no repeats) between 1 and 50, reading from left to right 9249907196 2363023185 92 | 49 | 90| 71 | 96 | 23 | 63 | 02 | 31 | 85 2) Determine whether the numerical value describes a statistic or a parameter Income and Education In a large sample of households, the median annual income per household for high school graduates is $19,856 (based on data from the U.S. Census Bureau). Politics Among the Senators in the current Congress, 44% are Democrats. Titanic A study of all 2201 passengers aboard the Titanic found that 711 survived when it sank.

2. Simulations Objectives: Perform a simulation by generating random numbers, and interpret the results Simulation simulations model real-world situations by using random-digit outcomes to mimic the uncertainty of a response variable of interest

3. If someone handed you a coin and told you that it’s biased toward usually landing heads, you might be skeptical. What would you do to test whether the coin was fair or not? Performing a Simulation

4. Suppose a basketball player has an 80% free throw success rate. How can we use random numbers to simulate whether or not she makes a foul shot? How many shots might she be able to make in a row without missing? Performing a Simulation 1)Identify the random event and the likelihood of the event 2)Identify the response variable 3)Explain how you will model the outcome 4)Run several trials 5)Collect and summarize the results of all the trials 6)State your conclusion Trial # Sequence of Random Numbers Trial Outcome 1 7 3 3 9 4 9 7 3 0 8 2 7 6 9 0 2 8 0 4 6 7 3 6 7 1 0 4 3 9 7 4 7 4 3 2 5 8 7 4 2 8 2 2 5 0 0 9 1 9 4 9 1 1 9

5. Performing a Simulation Suppose a cereal manufacturer puts pictures of famous athletes on cards in boxes of cereal. Twenty-percent of the boxes contain pictures of Tiger Woods, 30% a picture of David Beckham, and the rest a picture of Serena Williams. You want all three pictures. How many boxes of cereal do you expect to buy in order to get the complete set? Trial Number Sequence of Random Numbers Trial Outcomes: 9 6 2 9 9 0 7 1 9 6 7 1 6 2 2 3 5 9 4 0 0 3 2 7 2 4 1 2 3 0 4 6 3 7 6 3 5 9 4 0 2 0 0 6 4 5 8 5 9 6

6. Bell Work1/30 Modern Managed Hospitals (MMH) is a national for-profit chain of hospitals. Management wants to survey patients discharged this year to obtain patient satisfaction profiles. They wish to use a sample of such patients. Several sampling techniques are described below. Identify the sampling method for each. a)Obtain a list of patients discharged from MMH facilities. Divide the patients according to length of hospital stay (2 days or less, 3-7 days, 8-14 day, more than 14 days). Draw simple random samples from each group. b)Randomly select some MMH facilities from each geographic region, and then include all the patients on the discharge lists of the selected hospitals. c)Obtain a list of patients discharged from MMH facilities. Number these patients, and then use a random-number table to obtain the sample. d)At the beginning of the year, instruct each MMH facility to survey every 500 th patient discharged. e)Instruct each MMH facility to survey 10 discharged patients this week and send in the results.

7. Performing a Simulation Suppose a basketball player has an72% free throw success rate. How can we use random numbers to simulate whether or not she makes a foul shot? How many shots might she be able to make in a row without missing? Trial # Sequence of Random Numbers Trial Outcome 1 37757 82846 4398 2 32693 27879 4228 3 33027 15275 7198 4 67444 76039 9529 5 13172 21304 0596

8. M&Ms The Mars candy company starts a marketing campaign that puts a plastic game piece in each bag of M&Ms. 25% of the pieces show the letter “M”, 10% show the symbol “&”, and the rest just say “Try again”. When you collect a set of three symbols “M”, “&”, and “M” you can turn them in for a free bag of candy. About how many bags will a consumer have to buy to get a free one? Use a simulation to find out. Performing a Simulation Trial # Sequence of Random Numbers Trial Outcome 1 33925 25430 60175 97662 49816 07941 2 30933 35846 30645 13054 99732 57715 3 01830 92309 37457 63487 42282 69693 4 37901 40569 78997 16044 61578 70032 5 38110 99649 22197 58546 82826 64928

9. M&Ms The Mars candy company starts a marketing campaign that puts a plastic game piece in each bag of M&Ms. 25% of the pieces show the letter “M”, 10% show the symbol “&”, and the rest just say “Try again”. When you collect a set of three symbols “M”, “&”, and “M” you can turn them in for a free bag of candy. Determine how likely it would be for you to win a free bag, if you were to buy 8 bags of M&Ms. Use a simulation to find out. Trial # Sequence of Random Numbers Trial Outcome 1 78315 45640 00915 06600 2 50731 26955 13878 92091 3 51603 20567 27148 27436 4 54877 55683 60025 33519 5 40525 43024 29093 43755 6 56204 79209 59490 18523 7 91204 22078 53945 55041 8 93249 50123 82582 33693 9 54260 12027 24457 81561 Performing a Simulation No Yes No

10. Bell Work 1/30 Your state’s BigBucks Lottery prize has reached $100,000,000, and you decide to play. You have to pick five numbers between 1 and 60, and you’ll win if your numbers match those drawn by the state. You decide to pick your “lucky” numbers using a random number table. Which numbers do you play, based on these random digits? 43680 98750 13092 76561 58712 {43, 09, 50, 13, 27} Tell whether the variable should be treated as categorical or quantitative a)Eye color b)Grade level ( Freshmen, Sophomore, Junior, & Senior) c)GPA d)Student ID number

11. You take a quiz with 6 multiple choice questions. After you studied, you estimated that you would have about an 80% chance of getting any individual question right. What are your chances of getting them all right? Performing a Simulation Trial # Sequence of Random Numbers Trial Outcome 1 07196 98642 2 23185 56282 3 14125 38872 4 71622 35940 5 72753 32616 6 89059 43528 7 39717 37348 8 62162 75182 9 43796 75336 10 95232 18232 No Yes No Yes No Yes No

12. A friend of yours who took the multiple choice quiz got all 6 questions right, but now claims to have guessed blindly on every question. If each question offered 4 possible answers, do you believe her? Explain, basing your argument on a simulation involving at least 10 trials Performing a Simulation Trial # Sequence of Random Numbers Trial Outcome 1 71401 68430 19843 2 65773 15770 51360 3 48799 29287 55763 4 42320 52078 79161 5 51658 86940 17216 6 97992 63475 15639 7 74560 76580 16398 8 13892 70250 66846 9 94818 63008 91280 10 24049 17301 91033 No

13. A proud legislator claims that your state’s new law against talking on a cell phone while driving has reduced cell phone use to less than 12% of all drivers. While waiting for your bus the next morning, you notice that 4 of the 10 people who drive by are using their cell phones. Does this cast doubt on the legislator’s figure of 12%? Use a simulation to estimate the likelihood of seeing at least 4 of 10 randomly selected drivers talking on their cell phones if the actual rate of usage is 12%. Performing a Simulation Trial # Sequence of Random NumbersTrial Outcome 1 10317 43005 53454 60016 2 00584 49564 50366 80564 3 06087 39180 35123 04954 4 74602 09381 67512 26696 5 93581 15821 59794 48388 6 05720 87311 22125 67801 7 58711 33353 58357 00371 8 05579 67731 51700 75015 9 18834 20819 79343 60952 10 41171 91506 63920 76435 Explain your conclusion clearly

14. A basketball player with a 65% shooting percentage has just made 6 shots in a row. The announcer says this player “is hot tonight! She’s in the zone!” Assume the player takes about 20 shots per game. Is it unusual for her to make 6 or more shots in a row during a game? Performing a Simulation Trial # Sequence of Random NumbersOutcome 1 11255 17942 21535 71187 00176 40726 58466 02744 2 25877 84786 25891 88643 09003 27922 56673 02725 3 09547 66274 09154 06118 59209 53626 59186 16000 4 04221 39859 14551 47991 01486 87565 93179 36158 5 12320 04778 20858 49424 75929 46735 66343 65195 Yes No Yes No