poe;,"llcm =-~ o 7 '3 (p :. -'6 g ~!L.. I (q~3 -ICf 22. \'1 ~ meot \o-..n ::-\~ ~ Z _ i 1 -8 ~l{ (V\-t-I) =~ C'1J-:: ~..

Transcription

1 Statistics 1, Section 6 Exam 1 Name ~ _ October~ Calculators and one 8.5" by 11 " sheet ofhandwritten notes allowed Show all work and answers clearly in the space provided Questions 16 are worth 15points each; question 7 is 1 points. There are 1 points possible. 1. The values below are snow depths (in centimeters) measured at different locations..j9 ~ g ~!L.. I (q~3 ICf 22. a. Find the mean and median. '1 = ~ = 1 V\ ==,12:? 8 ~ meot \o..n ::\~ ~ Z _ i 1 b. Calculate the standard deviation using the formula s = XX )2 i? g \'2. 1(... IZ \'1 J,.' :. '6 8 ~l{ o 7 '3 (p 9 c. Calculate Ql poe;,"llcm =~ (V\tI) =~ C'1J:: ~.. ~s' ~1vVe...Q/Y\. '8' ~ l 2.. q \=8 t o~s (L~.'8) g t \ ::: 9

2 2. An experiment is conducted to determine which oftwo diets is more effective. The subjects are randomly assigned to Diet 1 or Diet 2. After six months on the assigned diet, the weight loss ofeach subject is measured. The boxplots below summarize the resulting data. \'aflatl~ Diet 2 ~ D r Ci~t1 fr 1C 2C 3 tf a. Use the boxplots to estimate the median weight loss for Diet 1 and Diet 2.!i'\ 1 = 9 vy\'2 = I2 '"" b. Which diet group had the largest interquartile range (IQR)? Estimate the IQR for this group. Explain what this IQR means in simple English (pretend you are explaining it to someone who has never taken statistics). ~\et 2 lrtcvo (~ IQR TQ 12== q, Q \ ~ ''1 5:::; l'z.. I 6), oj.., ef. 'TN. IQ~ is trw ~od OJ.., ~ m.\c(ctle SOr c u I~ ~. '5 c. Calculate the upper fence for the diet group from part (b). What is the upper fence used for? Q~ t I,S t Q R~, 1 + t, s( \ ~= '?:> ~ ~') ~~~~1~ 'h1j;jcuu.. d d. bo the boxplots indicate symmetric or s~ewed d~ta?. JaA4f. ~ fu.t; ~ JA ~.~d db 1Yv 16)( / ~ ttaf ~ve4, l/la. ~

3 3. The histogram and summary statistics below are for a data set consisting ofthe wealth in billions of dollars of233 billionaires. "I '. _. ri,r, I, Column n I Mean IVariance istd. Dev. Max IQl iq3 i +._+_.J! I, I,! wealth i 1.3 i 3, 1 I! I l I Fre:::l uenc" 1J.O 'Nealth a. Is there skewness in this data set? If so, toward wha.t values? ) ~wed +vvj(l~ W; 1 u~ (M~ b. The empirical rule states that approximately 68% of data fall within one standard deviation ofthe mean. 1. Calculate mean +/ one standard deviation for this data. (OK to round to the ii. iii. nearest tenths.) d r 'I ± ~ l ~. (D to ( 1 ~ ) Approximately what percent ofthe data points fall in this interval? (Hint: The height ofthe bar at 37 represents one person.) t d ~ +~Dt"25 :::: q Lf ~ lf~ Ie; Is your ansz;?~ii) consistent with the empirical rule? Ifnot, does this mean the empirical rule is not valid? Explain. ND. lv~ojl.f,j.r <1~ ~ & ~ol 6A ~.. dttja a}w w'th..urt ()")V.~ o.a..d.c::1&v~~ ~~ ~ ' w.f2, t1.(v1) tu.nj7at 1lf'CJ/6 WI ~ St~ I c/9u. c. This data set contams two outliers one person at 24 and one at 37 i hon tj]~ fu.;~' dollars. Suppose these two individuals had a fit ofgenerosity and each gave &<vay all but 15 billion dollars oftheir wealth. Would this change the standard deviation? If so, higher or lower? j/jy "IJ..k<.. W7J71Jd k.1ma ~ ()(A;( 7 trv ~,ao t7v J;e ~~ ~V'4. ~ tan~

4 4. There are three finalists in a beauty pageant: Flora, Sabrina and Janet. Assume the contestants are equally beautiful and talented so the judges randomly choose who will win first, second and third place. t:; Fi~st<c::.: a. List the sample space for this experiment. (Hint: Tree diagram) pn l../.j F S 1" / 5f='~:YiS PJ'S rj=~fstjfjs{s~j)s~fi ///_ I j"' Sr= J 1FS J JSFJ. F 5JF ~ 3" <:..5 fs F...) J ~S Male Female Protestant 3 2 Catholic 45 3 Jewish 45 3 Other 7 8 A worker is randomly selected from this business. What is the probability the worker is rv a. Catholic +2 \S ~.:..; ~lc; 4~ ~ b. Catholic, given the worker is a female oo{ l6~ t}c. Jewish and Mille It'Sb\5 J d. Jewish or Male, ~li:~o d\ S

5 ,~e. Are the events Jewish and Mal~ mutually exclusive? Why or why not?. d 1\Jo. ~ a.h..q. 4:5 ~flm ~ OAR.. Je.v\J""<.4..tl l:f!vi.pjjl,..tu, ~~.l2ftj:t:./~1 e CUY\o~,(J\ o...:f ~, f.. Male. given the woiker is Jewish Act./YV\..Q. h'vyl( ~ 4~r~ ' 6. Consider the bivariate data in the table below for this problem. X = price of a widget in dollars. Y= number ofwidgets sold (in thousands). x XC1 3 G 2 (;, =;).. ~ &7 a. Calculate the correlation coefficient for ~is data. Hint: The standard deviations ofx and yare and respectively. Sy.' = ~ ~~X 2~ _ ds ~ (ld~) _ :2S3 _ 5 ~. Y\ \ L{ l ~ 3 b. Calculate the best fit regression line. _~ ~r3 ' 'S.x""l := ~'1. = I,OQ a~~ hi =( I~) (1,)( J.1L =3 +~\ 5 ::: $"5 4 c. Use the line in part (b) to predict the numb. price is $2.5. C{ =. 5'. S ~ \ ~ ~ 3 ~ hrl cfvv)cvn91' ~ d. Interp'Yet the slope calculated in part (b). Ive a specific interpre Ion involving price ofwidgets and sales. ~ ~ ~ d;)(y M. lu/dc. ni ~JLe ~ r" ~ / ~a.hvj ~ ~ ojrlj1a.! 1 ~,

6 7. a. Match the correlation coefficient with the appropriate plot. Note there are more correlation coefficients than plots so some will not be used: 1.,.7,,.9, 1., 1.1. Plot2: r= ~ '1' _ oo~o o o't p, o~ :J~o o o % I I I I I I o 8 o Q:>o 7 x PloU: rill l. crv "', % I I I I I I x x b. Which of the above correlation coefficients would you prefer if you were interested in accurate prediction ofy for a given value ofx?