Study guide Exam 1Solutions - Study guide exam 1 STA 270...

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Unformatted text preview: Study guide, exam 1 STA 270 Daugherty Terms, concepts and skills required: Descriptive Statistics and inferentiai Statistics Numerical, discrete , continuous, and categoricai data types Calculate and interpret relative frequency. Define and use the term frequency distribution. Use reiative frequencies to calcuiate proportions. Know how to construct and describe bar charts, pie charts, stem and leaf displays, histograms, boxplots, scatterpiots Know the difference between an observational study and an experimental study Define and use the terms sample and population Be able to identify obvious cases of sampiing bias. Define a sirnpie random sample ofsize n. Calculate the sample mean, trimmed mean, median, variance, standard deviation, quartiles, IQR, z~ scores,sampie proportion, outliers, correiation, least squares line, slope and intercept and interpret those vaiues. Know the difference between a sampie mean and a population mean. Know the mathematical notation for everything. Sample questions: {5) 1. Describe the two main branches of Statistics 5673? 33W" 2?: if 1g” g TWT'EST'IC S _‘ Tiff-a“ oiiunaulfg in? 7;va iii" “5 ‘9 3 “Mimi-"M I” 3- 47'1""de at: barn . WWT‘ML s‘r'n- T”£S‘T"‘rc a : “Fr-i a mac or- I c e.- G t“: Man I“? raga”; i3 c923 Fifi-9W“ t”? gfl"mififltfim 7a ri Pofac/W‘rcatj (15) 2. George wants to know how the students at his university feel about tuition rates. To determine this, he asks the thirty students in his music theory ciass to teil him if they feit tuition rates at the university were too high or ifthey were reasonable. After tailying his results, George estimates that 73% of students in the university consider tuition to be too high while 27% think tuition is reasonabie. 3. identify the population under study. gTu‘bWTS am) THE magma/ti S; T e b. Edentifythe sample under study. _ _ He“ 3%} s'tvbwrs. area “Fr-IE“ m Whit. “Wreath” amass. c. is George’s conciusion justified? Why or why not? N C“ . I a“ 1:193 was. 2: men. s/ Trig; T T‘War" m u s I. <3. “rite—sate aw S W bet/’1’”; ii cZi‘f" tZe'iQrces 9VTW‘7”); V3» d. Give George a suggestion as to now he might improve his study. (3 Evita?" (L0 m. b s EXEC i f} iii-1w 250.44 s Awe/t pur- i? (jar/t ’i’i-iz’“ 53'11737fi % 9. .. M. _ C}; biz—fl $5.34!” (12} 3. Avery smaEI data set has oniy three vaEues. Two ofthe values are 1 and 6 .The sampEe mean has been calculated and it is 4. x :4 X121 X226 x3=? n: a. Whatisthemissingvalue,x3? a rm ~ ‘ X . ‘ M M J t i xségm We? sziewivc+x3 a} " WWW“ b. Suppose we add a fourth data point X; 2 25. What is the value of the sample mean using the 4 data points? What does this iilustrate about the effect of extreme values on the sample mean? la 6 + 5*“ .z. 29” . W WWW-:1, 5' 0?. Z 5 “TM?” mmm I .S “I'm Ft. amt: airs E ‘r E eram w a. v.55” (15) 4. A hospitai emergency room physician in a major city in the United States recorded the wait times for patients visiting the emergency room. He recorded the time that the patient came in and the time when the patient was first attended to by a physician to determine the length of the wait. He _ conducted this study in one 24 hour period from 10:00 PM December 31“ 2008 to 10:00 PM January 1St 2009, recording the wait time for each patient who visited. During that period, 200 patients visited the emergency room. l Wait Time (inutes i o_;<5 ___ 64 0.32 _ ' M _ 5_< 10 42 0.21 : 10-< 15 0“<35 .. . .. . “to a. Complete the table by tilting in aii the missing vaioes. b. What proportion of the wait times were greater than or equal to 20 minutes? ,Meou +.0i§ 3 i095?“ c. The Physician would like to estimate the average wait time for this emergency room on a typicai day. Wouid this be a good sample to use to make this estimation? Explain. Wit; ‘9 or... g... g; 119L753» W “Tic! {57".} 5/1) iv 5w varies EV a?“ a "7“;er We UL e we?” 3’ ‘5‘ {3 W 225s W‘s-“n r": (x as” at? it 7'" 1”!" '17 ‘9 ‘4 M ‘r’. d. Describe the shape ofthe histogram for this data. (The actuai histogram is not part ofthe response for this question. You may want to make a very quick, very rough sketch in order to answer the question. if you do so, that sketch wili not be evaluated) It" “5% Unify/meme web Has: A Poszrri/é' Wows (15) 5. Please answer the following questions True (T) or False (F). In addition, write a sentence explaining your choice in each case. a. The mean and the median are always equal. , H F:th a"- n 6 emails “ism a SET WILL Prin aw- h'rr-"rfmw; - WM W33 Flies "r7116 M {film} film}; W) shawl; b. if a histogram has a long tail to the left and tall bars on the right, it is negatively skewed. A professor giving a very easy test would expect to see a negatively skewed histogram of the scores. Trivia“. M erase “T2397 WCWLD Pitched?” FEW Lew Qcm’iafi Ma fl- LST'oF Hirer-law sacs»ng c. A few outliers have little or no effect on the value of the median. "l 91W" n We mats Ma) -: .9 Wu were 6‘- ?“E'b {5’ ‘r 8‘ Jim We at” Will L. U S (18) 6. The following data represents the number of customers entering a store in the last 20 days. 105, 105, 104, 101,l§é:§g3:7,77, 7.2,&.o,l7o,)59, 68, 5:7,lav, ss 54, 23, 2, 1 mwmmmflr . j is w....g-j«~m_..._.%__3 3. Calculate the sample median. 70 b. Calculate the 30% trimmed mean. <3- 7 l- 7:? + 7.2. 4 76 r 7W“ 6- ‘5? M ‘3’ t5 ‘7 "r" -wwwméw-m—mmww 5' 7 Z. S» __......._._._. c. Construct a skeletal boxplot of the 20 values. Please display the numbers used to construct the bokplot. 4; l ‘70 645 w; l; W.‘_...,___.,..... , E Lmh “.mfi WMLNII “Mimi”...wa """" Mai”.mmmsu_,.m.i._m~m_mlwckmiww~—~W with”... £2 '0 :0 so ‘10 Q2 so '76 @s a we W ficwwmmg d. Are there any outliers in this data set? if 50, list them. more: 96 em :- 33” ls-rrtwrszs’ 6%ng T <33— Tl nub 2; mail?" (sane—E163 q {3 If, S ng C 1; Li 3 (10) 7. High temperatures (of) for Phoenix in August were recorded. The mean for this data set is _X_ 2 98.6 and the Standard Deviation, s = 5.3 One day in August, the high was 96 degrees. Calculate the z—score for this observation. was e z 5’. G _ - ms! fi/ ng Write a sentence describing the meaning of the z-score you caicuiated. % 3956,4528 31$ .9“?! s-vabaeb, Bet/Jarroer Eglwn} 77%”rmen4) .— {10) 8. CaicuEate the Standard deviation for the following sampie of heights in inches: #2” 63f72+6fi 474 “ Height in X w .WW Tmmmh .._ l ches Lra n 63 flx‘u'fif" (/90! What is the interpretation of this standard deviation? “TV i’IcaLt v fil- iiE'reil‘r 1w TALZS i>’i'7"'>‘i S 5" 7" 33$ i+7Qé :rwcflfi; Awdt’ FREWW77wf nn mm (4 wear” ' 2. The data below were gathered on a random sampie of 7 male black-footed albatrosses of known age. in an effort to monitor diseases ofthese animals, biologists would like to be able to estimate the age of animais that have died by flattening their gonads and measuring the resulting area. Gonad size vs. Age in Stack-footed albatrosses eonad Size 2o: — a)? = 4491428571; (sq mml th —— 50(3) —— 37) = 1271781429; Eager/:96,- Zy = 34.75; 2 szy = 5557912288 a) What is the value of the correlation coefficient for these data? 5.93"??rzz if” w WW; M—W C7 26 J 57,2905; WILD Eli/45. EN M were. of- Amb V 5 suggestive LIA/M View raw; Mr? B 67"‘5115‘53’0 b} What is the equation ofthe least squares line describing the relationship between 401M???) 5” 1725' (in/’5 fie-F”. .2: i (g‘ ,r m :i’" r"- : ‘ "‘- F‘ b“ — La 4»H«e‘--~-e~m»fiw~- « 517% 79iflm ,3- a Zb’g q: 3" [0 y ~» —- “83 W r' . .a ‘ . ' ' W‘ "héi'qp Zi >4 1‘2 ‘ih‘f’i 7.1412? 997/ w} 7 7 c4 x=Gonad Size and y=Age. 9’ ; flé + I g; X c} if these aibatrosses are representative ofthe population, what would you predict to be the age of a male albatross with a gonad size 01°50 so. mm? Show any caiculations below. 4 46-6/9 .i-gzss(m):'7.i% Yams 01> i d) The iargest albatross gonad size in the sampie was 96 sq mm, with an age of 23.64 years. These animais are thought to live for up to 40 years. Would it be reasonable to use the equation from part (b) above to predict the age for a gonad size of 150 sq mm? Why or why not? N6“ « l 50 M v: 1 If. Es {WE “tr-lam Ledge." are («l-6“ bat-e user) "TO edafis‘m i231? ‘T [PI->125“ i i ...
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