Math 10 - Exam 1 Tpics Types and Levels f data Categrical, Discrete r Cntinuus Nminal, Ordinal, Interval r Rati Descriptive Statistics Stem and Leaf Graph Dt Plt (Interpret) Gruped Data Relative and Cumulative Relative Frequencies Histgram Ogive Mean, Median, Mde Skewness Range, Variance, Standard Deviatin Empirical Rule Z-Scres Percentiles, Quartiles Interquartile Range Bx Plt Crrelatin Bivariate Data Scatterplt Crrelatin Cefficient Outliers Identifying Effect f utliers n Descriptive Statistics Experimental Design Steps f a Statistical Prcess Observatinal Study Representative Sample Sampling Methds Experiment Explanatry Variable Respnse Variable Blinding Placebs Prbability Empirical, Classical r Subjective Terms and Laws f Prbability Events and Outcmes Sample Space Cmplement Unins and Intersectins Additive Rule Cnditinal Prbability Tree Diagram Multiplicative Rule Independence Changing the cnditinality Cntingency (Tw way) Tables Marginal Prbabilities Jint Prbabilities Cnditinal Prbabilities Cnstructing table Discrete Randm Variables Mean and Standard Deviatin Prbability distributin functin (pdf) Prbability prblems Binmial Distributin Cntinuus Randm Variables Mean and Standard Deviatin Prbability density functin (pdf) Prbability and Percentile prblems fr Nrmal Distributin Central Limit Therem pdf f the randm variable X (3 imprtant parts) pdf f sample prprtin ˆp Prbability Questins Yu must bring a picture ID t the exam. Yu may bring 4 pages f HANDWRITTEN ntes t the exam. Bring yur prbability tables (Binmial Nrmal, etc) Bring Pencil, Calculatr and yur ntes t the exam n sharing is allwed during the exam. N cell phne calculatrs. Cell Phnes, ipds, PDAs, and ther electrnic devices must be turned ff and put away. Manage yur time s yu can attempt every questin.
Practice Questins fr Exam 1 1. 10% f American adults have Type II diabetes. A test has been develped that has a 80% chance f crrectly detecting this disease, but has a false psitive rate f 15%. a. Draw a tree diagram f all pssibilities, where the first branch represents persn having Type II diabetes (psitive D+ r negative D-) and the secnd branch represents the test (psitive T+ r negative T-). b. What percentage f American adults will TEST psitive fr the Type II diabetes? c. Given an adult tests psitive fr the disease, what is the prbability the adult actually has Type II diabetes? 2. The data shwn in the scatter plt is the distance traveled and the airfare fr 12 flights n Delta Airlines: a. Which f the fllwing is a reasnable estimate f the crrelatin cefficient? (Circle ne answer) 1.0 0.8 0.0-0.5 b. What des this graph tell us abut distance and airfare c. What is the type and level f distance traveled? Type (Circle One) Categrical Discrete Cntinuus Level (Circle One) Nminal Ordinal Interval Rati 3. Yu have a 70% chance f being n time t class tday and a 80% chance f being n time t class tmrrw. Assume these tw days are independent events. a. Find the prbability f being n time t class bth tday and tmrrw. b. Find the prbability f being n time t class at least nce tday r tmrrw. 4. The fllwing data represent the daily births at a hspital fr 20 days 14 15 15 17 17 19 19 21 23 25 26 27 31 35 36 47 48 59 70 99 a) Cnstruct a stem and leaf diagram f the data b) Calculate the interquartile range fr this data set. c) Calculate the median fr this data set. d) Withut calculating, what can yu say abut the mean births fr this Hspital.(check ne answer belw)? The mean is greater than the median. The mean is less than the median. The mean is abut the same as the median. Nne f the abve n way t knw withut calculating. 5. The fllwing data represents the hurs per week wrked utside f schl by 200 randmly selected night students at a cmmunity cllege: Hurs Frequency Relative Freq C.R.Freq 1-8 20 9-16 30 17-24 50 25-32 60 33-40 30 41-48 10 a) In the space abve, determine the relative frequencies and cumulative relative frequencies. b) Sketch a relative frequency histgram, shwing all hrizntal and vertical labels. c) Sketch a cumulative relative frequency give, shwing all hrizntal and vertical labels. d) Estimate the median frm the graph. e) What percentage f the night students wrk 32 hurs per week r less? f) Withut calculating but explaining yur reasning, which f the fllwing is a reasnable estimate fr the standard deviatin? a) 0.5 b) 1 c) 10 d) 50
6. Determine if each f the fllwing data are categrical, cntinuus r discrete (circle ne fr each) a. Number f fatalities frm a tsunami: categrical cntinuus discrete b. Time spent in traffic: categrical cntinuus discrete c. Number f Sngs n yur I-pd: categrical cntinuus discrete d. Yur student number categrical cntinuus discrete e. Names f cities in Califrnia with a Walmart: categrical cntinuus discrete f. Price per galln f gasline: categrical cntinuus discrete g. Number f Curses taken in a year. categrical cntinuus discrete h. Tns f steel used by a manufacturer: categrical cntinuus discrete 7. 1000 students (500 mrning, 300 afternn, 200 night) were asked hw ften they use the campus library. The results are summarized in the table belw: Never uses library Smetimes uses library Frequently uses libray Ttal Mrning 200 250 150 600 Afternn 80 145 75 300 Night 80 10 10 100 Ttal 360 405 235 1000 a. Find the fllwing prbabilities: i) A randmly selected student never uses the library. ii) iii) A randmly selected student is a night student and frequently uses the library. Given the student is an afternn student, the student never uses the library. b. Are Afternn Student and Never uses library Independent Events? Justify and explain yur answer. c. Wuld the prbabilities generated frm this data be classical, empirical r subjective prbability? 8. These descriptive statistics and bxplts were generated frm data representing calries per serving fr three types f htdgs: All Beef, Mixed Meat and Pultry. a. Cmpare the mean t the median calries fr the Meat grup. Is the result cnsistent with the shape f the bx plt? Explain yur answer. b. If the data is apprximately bell shaped, between what tw values f calries wuld yu expect t find abut 95% f the Beef data? c. Which f the three grups has the mst variability in calries per serving? Explain yur answer. d. Hebrew Natinal All Beef Htdgs had 190 calries per serving. Calculate and interpret the z-scre fr Hebrew Natinal Htdgs using the Beef Categry data. e. Determine the prbability a randmly selected Pultry Ht Dg exceeds 113 calries. f. Cmpare the three grups and draw at least tw cnclusins frm the results.
9. Frm samples f a ttal f 2100 yung (18-24 year ld) White, Black and Latin men taken in January 2010 in the U.S., the unemplyment rate f each sample was determined as given in the fllwing table. (2013, Urban Institute, The Labr Market Perfrmance f Yung Black Men Race/Ethnicity Unemplyment Rate in the Great Recessin). The study used stratified sampling. The Urban Institute cncluded that yung black men have a higher unemplyment during the recessin than their white and Latin peers. White 15.6% a. What is the ppulatin and what is the sample? Black 30.0% b. Identify the steps f the statistical prcess: Hispanic 26.9% Ask a questin that can be answered with sample data. Determine the infrmatin needed. Cllect sample data that is representative f the ppulatin. Summarize, interpret and analyze the sample data. State the results and cnclusin f the study. 10. A study was cnducted t examine the effects f active recvery (AR), massage (MR), and cld water immersin (CR) n perfrmance f repeated buts f high-intensity cycling separated by 24 hurs. A sample f physically active men aged 18 30 were randmly assigned t ne f fur grups. Each grup perfrmed an intense 18-minute cycling wrkut after which each underwent a 15-minute recvery perid. In the 15 minutes, the first grup (AR) cntinued t cycle at a lw level, the secnd grup (MR) received leg massage, the third grup (CR) immersed their legs in a bath f cld water. The last grup simply sat and rested. The next day the subjects did the same intense 18-minute cycling wrkut. Each exercise was dne n a cycle ergmeter s that the wrk level (measure in kiljules) was calculated fr each. The researchers fund that n the secnd day, that there was n difference in the perfrmance level f the subjects in the AR, MR and CR, but that the subjects wh just sat in a chair t rest did less wrk than the ther grups. (Jurnal f Strength and Cnditining Research (2004; 18 [4], 855-60). a. What is the explanatry variable? b. What is the respnse variable? c. Which grups are the treatment grups? d. Is there a cntrl grup? If s, which ne? e. Is there blinding in this experiment? Explain yur answer. 11. 70% f students at a large New Yrk University receive sme financial aid. a. If 4 students are randmly selected, determine the prbability that exactly 2 students in the sample receive sme financial aid. b. If 4 students are randmly selected, determine the prbability that less than 2 students in the sample receive sme financial aid.. 12. The randm variable X fllws the prbability distributin functin as shwn t the right: a. Determine P(X=3) b. Determine the ppulatin mean. c. Determine the ppulatin variance
13. 40% f students at a cllege use the cafeteria. a. If 9 students are randmly sampled, determine the prbability that less than 3 use the cafeteria. If 9 students are randmly sampled and X represents the number f students in the sample wh use the cafeteria, find the mean and standard deviatin f X. 14. Accidents in a pwer plant ccur at a Pissn rate f 1.39 per year a. Find the prbability f at least 2 accidents ccurring at the plant in the next year. b. Find the prbability that the plant has zer accidents in tw year. 15. Find the 30 th percentile fr each f the cking time fr atmeal which fllws a Nrmal Distributin with a mean f 4 and a standard deviatin f 3 16. Students exam scres fr a curse fllw a Nrmal Distributin with μ=70 and σ=10. a. Find the prbability a randmly selected student scres a 75 r mre. b. Find the exam scre which is the 25 th percentile f this distributin. c. Yu take a randm sample f 40 students. Find the prbability the sample mean is between 68 and 72. d. Wuld yur answer fr part c be different if the prbability distributin f exam scres did nt fllw a Nrmal distributin? Explain yur answer. 17. The age f a grve f walnut trees fllw a Nrmal Distributin with μ=50 years and σ=15 years. a. Find the prbability that the age f a randmly selected tree is between 40 and 70 years. b. Find the prbability f a randmly selected tree has lived exactly 45.231789 years. c. Find the 30 th percentile f this distributin. 18. 35% f students at De Anza Cllege plan t transfer t San Jse State. 200 students are randmly selected and the sample prprtin ˆp will be calculated. a. Determine the expected value and standard deviatin f the sample prprtin. b. Determine that the cnditin fr nrmality is satisfied. c. Determine the prbability the sample prprtin exceeds 0.40.