QBA 201 Final, Spring 2014

x School of Business ESSE A Lebanese American University Sample Final Exam QBA 201 Managerial Statistics 1. (10 Points) Grades of students in Managerial Statistics course are normally distributed with mean of 80 points and standard deviation of 16 points. a) One student is selected at random. What is the probability that this student scored between 40 and 100 points? b) What is the grade G above which 93.7% of the students score? 2. (10 Points) The average annual salary in Lebanon was $12200. Assume that the salaries were normally distributed with standard deviation of $2500. a) Find the probability that, for a randomly selected sample of 25 individuals, the mean salary was less than $13000. b) Find the probability that, for a randomly selected sample of 16 individuals, the total salaries was more than $180000. 3. (10 Points) A survey found that out of 200 workers, 170 said they were interrupted three or more times an hour by phone messages. Find the 80% confidence interval of the population proportion of workers who are interrupted three or more times an hour. 4. (15 Points) The number of cars sold annually by used car salespeople is normally distributed. A random sample of 10 salespeople was taken, and the number of cars each sold is listed here. Find 99% confidence interval estimate of the population mean. 79 43 58 66 101 63 79 33 58 70 Page 1 of 2 5. (15 Points) A study of 25 statistical professors showed that they spent, on average, 9.5 minutes correcting a student’s test. a) Find the point estimate of the mean b) Find 98% confidence interval of the mean time if the population standard deviation is 2.6 minutes. Interpret. 6. (10 Points) A researcher is interested in estimating the average salary of teachers in a large school. She wants to be 95% confident that her estimate is correct. If the standard deviation is $1000, how large a sample is needed to be accurate within $200? 7. (15 Points) A researcher claims that the coffee drinker consumes an average of 3.1 cups per day. A sample of 9 drinkers revealed they consumed the following amounts of coffee, reported in cups. 3.1 33 35 26 43 3.7 38 31 41 If the population standard deviation is 0.54, test the researcher’s claim using a 0.01 significance level. 8. (15 Points) A restaurant chain claims that the mean waiting time of customers is less than 3 minutes. While examining the waiting time, the manager found, in a random sample of 41 customers, that the sample average is 2.7 minutes and the sample standard deviation is 1.2 minute. At the 0.1 significance level, test the claim. Page 2 of 2 | Key Formulas | : LX Population mean: = -— } Sample mean: X = Lx n | | X(X—-4)* N Population standard deviation: 0 = Sample standard deviation: S$ = Or use equivalently: ny x? — (Xx)? n(n —1) X- UL Standard normal value: Z = a X-p la Z-value of X, when y and o known: Z = ZO 2 Sample size for estimating mean: 1 = (=) 22 Sample size for proportion: n = p(1 — p) (2) Confidence interval for u, with o known: X-z <X+z als als Confidence interval for y, with o unknown: | | | | > Ss 4 Ss —~t—o=<u< an X-t SHS X+t Tn Xx Sample proportion: D = 2 [Confidence interval for proportion: | p(i-p) pi~p) — < 4 < 1 | pz n =PSPtre n . X-u Testing a mean, o known: Z = an | Testing a mean, o unknown: R- tat ln Variance of the distribution of difference in means: 2 i, B Esk. ~ yy To tn ie test of k z= ae wo-sam mean: wie: 2 = == ample test o ans, kno 2 14 92 ae ny nz . LX-X)Y-¥) Coefficient of correlation: 7 = ———— , (n-1)SxSy or use equivalently: a(S )-(S xe») fee HOs | oo Ey L | or use equivalently: b = | Intercept of the regression line: Q = L Linear regression equation: Y=a+bX Sy Slope of the regression line: ) = rs nl 2)- San) AZ) -alSx)-(Oa} y- bx \. Xe grade in QBRA 20 normaly distributed | BM=W Y =\b = X-AY <= %) Pl40 < x too) - P (0-80 < 2 an (\NO-3DdD lwo I =P(-2s0<27e \.as) = P(®e1.2S)_p (2<-2.S0) = O.34q4Y — 0.06259 = 0. SSQy lb) G= grade above which 1379, ef Te Students Score . PLx>@) = 93.79, e(2 re ) = 0. B70 2.X%= onnual ere in Lebanon, Normally distri uled M=\l100 Y= aSeo a)n=3s ere Af. | 0.00 V Ain iz \ be 0.445 P(K< 12000) _ VZ009 ~ 12,20 “PES BERR ) oo Reon) 0s G7 bo b) nab Total= Ex Fe SK a) P (Sx > 120,000) -e @s > ¥30,000 ) n \& af | or =p(X> \,aSo) -\.5 § =e (2> WAS ~ 12,2a0 ) 2s8o0/T = P(a> — \.52) Vl (PZZZZ 1.32. = \-p (@<-1s2) = |-0.0642 = 0.428] 3. C.-T. Aor pepulahon PrSpochon N=IH_YXS!ITO BO? | 1- K=O =) X= 0.2 —— Ae Le o.\ Y/2=0.1\ ,df.=a0 Af | +t, Z4/2=20\=| 232 So BBS ~ 1.282 CW\OIs) 2 Ce DIS 1.232 | (98) (oAs) “AAD SLOO d.. 3b VPS V.BY@W Accor ding to the Samele dato, , we OAL BO%s carbhidend hot thw Prspsrion “ Waens thoy wea wclerraoted ley dnone Messages %s between BIT J. and 87.239. 4 n=O Y=65 S= 19.22 V = Unknown =>Case 2. Confidence Interval for JU is - eta (Sir) ehe Ke t4 (Six) Ws = \-K=0.99 x= 0.0) K/2 = 0.005 Cx/2 = Lacs ; cleqee of frendar = n-\=4 a £ Lo. oS 4 3.250 99) 4 CT Aw MM Wi S- 3.95 /t8.axr ls S Te) SME tS 3.95 5 19.22 Wo" US.IS £ MS 348 According tp bur Sample data we at 44). conbdent thot “hw 0) numloer bf COAS sold is between 45.295 and StS, BS. n= ag X=Hts a) Point Estimate Br MA =p X= AS b) W7)s conf dence imerval V=2.6 = Tis known => |~ %=0.93 (case |) => K= 0.02 od/2 = 0.0 | Zk/y =2Zoo= 2.221, df\ “2p.0| (Af. =90) ot The 939, CTL. Coon dency ittervel ) Tor LU (case\) is’ qS-220/2b\e Y eqcy 229/26 )<4 = a) PAVSM < 107] Accordia th the sample Lata , Wwe are 43°), samme cantident that tu average Hime Ba statistics professor spend 5 carcecing O29 €xamis between % B.24 and (O.71 minutes. b N=? 95% confident => Sey, \= % \o00 E= $200 CReyword withio) W279 = \- eK = O.9S dit. tors m= 0.05 \ %/2 = 0.035 o-+—__, (2K /2 = Zo.orslide Ve d.f.=00 a am 0 fine . ~) _ (en 4b.04 e (200) V7 (abeows round up) ra i] 7. Claim: M=%.\ eee A=A Y%=35 =o S4 => Vis knowe = 2-teet Step. ty” he 3.4 (claim) HJ $3. two-tailed tect Step2. <= 0.0) Steps Test statistics far the Z- test is: A= %-M ~ 35-3) _ Qa VAT O84 [ra Srepy. Reject Wy if Zo<~ 2/2 or Dy > 2K/q area La K=O0.01, 2-test , degree of freedom= 00 , oe ©.005 2x/y = Zens, 2.S51L Zp z2.2Q oo he Steps: Since Zo does not fallin the recon Lon, We do avy elect thy According te the sample ,we tan conclude Shot thy overage cope drinker drinks on Ong. Z\ cups/dou