1b) =.215 1c).080/.215 =.372

Transcription

1 Practice Exam 1 - Answers 1. / \.1/ \.9 (D+) (D-) / \ / \.8 / \.2.15/ \.85 (T+) (T-) (T+) (T-) b) =.215 1c).080/.215 = 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) b. What des this graph tell us abut distance and airfare As distance ges up price ges up. 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. 0.7 x 0.8=0.56 b. Find the prbability f being n time t class at least nce tday r tmrrw = The fllwing data represent the daily births at a hspital fr 20 days a) Cnstruct a stem and leaf diagram f the data b) Calculate the interquartile range fr this data set. Q1 = 18, Q3 = 41.5 IQR = = 23.5 c) Calculate the median fr this data set. Median = 25.5 d)make a bx plt fr the data

2 e) Right fence = (23.5) = s 99 is an utlier f) Withut calculating, what can yu say abut the mean births fr this Hspital.(check ne answer belw)? The mean is greater than the median. Data is skewed right 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 Ttal 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. median = 24.5 e) What percentage f the night students wrk 32 hurs per week r less? 0.80 (crf) 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) is the nly answer that makes sense since the range is 48 and the range is between 4s and 6s.

3 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 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 Afternn Night Ttal a. Find the fllwing prbabilities: i) A randmly selected student never uses the library. 360/1000=.360 ii) iii) A randmly selected student is a night student and frequently uses the library. 10/1000=.010 Given the student is an afternn student, the student never uses the library. 80/300=.267 b. Are Afternn Student and Never uses library Independent Events? Justify and explain yur answer. N. P(Never) P(Never Afternn) ( ) c. Wuld the prbabilities generated frm this data be classical, empirical r subjective prbability? Empirical based n data 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. Mean>median, but it is difficult t read the skewness frm graph s its unclear. 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? (111.57, ) c. Which f the three grups has the mst variability in calries per serving? Explain yur answer. Meat highest Standard deviatin 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. Z=1.46 Hebrew natinal calries are abve average. e. Determine the prbability a randmly selected Pultry Ht Dg exceeds 113 calries. 50% (half the data is abve the median) f. Cmpare the three grups and draw at least tw cnclusins frm the results. Chicken dgs are lwer in calries. Meat and Beef are abut the same. (ther answers k).

4 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? Sample: 2100 yung (18-24) year ld men in the U.S. Ppulatin: All yung (18-24) year ld men in the U.S. Black Hispanic 30.0% 26.9% b. Identify the steps f the statistical prcess: Ask a questin that can be answered with sample data. Is there a difference in unemplyment rates f yug men due t race/ethnicity? Determine the infrmatin needed. Emplyment Status and Race/ethnicity Cllect sample data that is representative f the ppulatin. Stratified Sampling will prduce a representative sample Summarize, interpret and analyze the sample data. The tabled data shws yung male unemplyment rate fr Black at 30%, Hispanic at 26.9% and White at 15.6% State the results and cnclusin f the study. Yung black men have a higher unemplyment during the recessin than their white and Latin peers. 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 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], ). a. What is the explanatry variable? The recvery methds: AR, MR, CR r rest b. What is the respnse variable? The difference in wrk dne by the cyclists between the first and secnd days. c. Which grups are the treatment grups? AR, MR, CR d. Is there a cntrl grup? If s, which ne? Yes, rest nly grup. e. Is there blinding in this experiment? Explain yur answer. Nt pssible, since participants knw what recvery methd they are receiving.

5 11. 70% f students at a large New Yrk University receive sme financial aid. (use binmial table n=4, p=.7) a. If 4 students are randmly selected, determine the prbability that exactly 2 students in the sample receive sme financial aid. P(X=2) =.265 b. If 4 students are randmly selected, determine the prbability that less than 2 students in the sample receive sme financial aid. P(X<2) = P(0) + P(1) = The randm variable X fllws the prbability distributin functin as shwn t the right: a. Determine P(X=3) P(3)=0.3 b. Determine the ppulatin mean. µ=2 c. Determine the ppulatin variance σ 2 = % 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 Deleted b. 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. µ=3.6 students σ = Find the 30 th percentile fr the cking time fr atmeal which fllws a Nrmal Distributin with a mean f 4 and a standard deviatin f 3 30 th percentile fr Z is th percentile fr X is (3) = 2.44 minutes 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. P(X > 75) = P[Z > (75-70)/10 ] = P(Z > 0.5) = b. Find the exam scre which is the 25 th percentile f this distributin.: (10) = 63.3 c. Yu take a randm sample f 40 students. Find the prbability the sample mean is between 68 and ( 68 72) P < X < = P < Z < = ( 1.26 < < 1.26) = P Z 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. NO, because f the CLT. 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 P ( 40 < X < 70) = P < Z < = P( 0.67 < Z < 1.33) = b. Find the prbability f a randmly selected tree has lived exactly years. 0, makes n sense c. Find the 30 th percentile f this distributin (15) = 42.2 years

6 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. ( 0.35)( ) μp ˆ = p = 0.35 σ pˆ = = b. Determine that the cnditin fr nrmality is satisfied. np =.35(200) = 70 n(1-p0 =.65(200) = 130 Bth values are at least 10, s cnditin fr nrmality is satisfied. c. Determine the prbability the sample prprtin exceeds P( pˆ > 0.40) = PZ > ( 0.35)( ) 200 = P Z > 1.48 = = ( )