Business Statistics I

Introduction to Statistical Modeling I

Carleton UNIVERSITY DURATION: 3 HOURS No. of Students: Department Name & Course Number: School of Mathematics and Statistics, STAT 2606 A Course Instructor(s) Agnes Benhin I AUTHORIZED MEMORANDA . NON-PROGRAMMABLE CALCULATORS ALLOWED -- Students MUST count the number of pages in this examination question paper before beginning to write, and report any discrepancy to a proctor. This question paper has 8 pages. This examination question paper MAY be taken from the examination room. In addition to this question paper, students require: an examination booklet a Scantron sheet yes0 no!:] yes!:] n00 -- This examination paper ~ be released to the library. ATTEMPT ALL QUESTIONS. All solutions must be shownclearlv. 1. A couple goes to a photographic studio to have their wedding picture taken. An individual photograph is a success if both people look "good". The probability that a person looks "good" in an individual photograph is 0.4. [8) a) b) What is the probability of a given photograph being "good"? What assumption has to be made to answer this question? If the photographer takes 7 photographs in all, what is the probability that at least one is a success? a", Mathematics and Statistics, STA T 2606 A, "Final Exam-August 2005", Page 2 2. If the income in a community is normally distributed, with a mean of $20,000 and a standard deviation of $2,000. a) What proportion of the members of this community earn between $18,500 and $21,500? b) What minimum income does a member of this community have to earn in order to be in the top 30%? c) Would it be correct to state that the average income of a random sample of 9 families is normally distributed with mean $20,000 and standard deviation $2,000/3? Why or why not? d) Find the probability that average income of a random sample of 81 families is less than $19,500. e) If the incomes were not normally distributed, which of your answers in (a), (b), (c), (d) above still hold? Why? 3. A nationally known insurance company has been advertising on TV that 9 out of 10 claims are in the return mail two days after receipt. Suppose that 1112 of 1250 claims were returned within two days. a) Test the appropriate hypothesis at the 0.05 level of significance. b) A new survey is to be taken in order to estimate the true proportion to within 0.03 with 99% confidence. How large a sample must be taken? 4. In a provincial survey, a random sample of 1250 adults was polled regarding their view on banning handgun sales. 650 of tem favoured a ban. At the 0.05 level of significance do the data provide sufficient evidence to conclude that more than 50% of all adults favour the ban? [9] 5. [8] It is reported that the biomass for tropical woodlands, thought to be about 35 kilograms per square meter (kg/m2). Suppose you measure the tropical biomass in 400 randomly selected square-meter plots and obtain x =31.75 and s = 10.5. Do the data present sufficient evidence to indicate that scientists are overestimating the mean biomass for tropical woodlands and that the mean is in fact lower than estimated? Use a = 0.05.

STAT | 2606 | Business Statistics I | exam | Carleton UNIVERSITY DURATION: 

For quetions I and 2, considerthe following MINITAB generated boxplots of coagulation timeo (in seconds) for sample of blood drawn from animals receiving thre different diets. denoted 1, 2 and 3. dl.ct' ' ii-" r ---r * E, r. l--------li- ',: f. 2 '": -----i.--;-=--------i--- : . 1. Consider the following 3 statements, and circle the correct answer below. I) The animal that had the longest coagulation time was given diet 3. II) The great€st variability in coagulation times occurs with diet 3. III) Diet I show evidence of right skewnessaod diet 2 shows evidence of teft skewnes. .A\ a) Only I is true. b) Only II is rrue. '[ ") bO, III is true. d) Only I and II are true. e) Only I and III are truL_/ 2. Consider the following 3 statements, and circle the correct answer below. I) Approximately 25Vo of the snimels on diet 2 had coagulations times in excess of 63 seconds. II) Diet t has the greatest upper (third) quartile of the 3 diets. III) We can deduce tbat the mean for diet I is less than 62 eecond6. ^Q) Only II is true. f)ttare fale€. c) Only IItr is true. 3. Consider the folloqrin MINITAB generated stenFandlesf plot of students' GPAs (Grade Point Average). Stcm-andJeaf of GpA N = l(F Leaf Unit : 0.f 0 111 2t3 a 1{{ 516 7 L 88 21 2 00000000000111111 35 2 1333333t333 {19 2 {{aartaa{555555 (11) 2 66666677777 a0 2 888889999999 2g 3 0000000000011111 12 I 2333 I I {{rl{ 4366? :. 18 a) Only I ie true. d) AII are true. r ) 5. The values of. P(22 > 1) and E(c) are repetively a) l/E and 1/4 b) rl4 and l/E c) l/E and 0 6. Suppce that P(l) = 0.4, P(Bc) : 0.7, and P(AU B) = 0.S8. Considerthe following3 statements, and circle the correct angwer below. I) Events z4and B are mutually exclusive. II) Events .4 and B are independent. m) P(/na) = o.tz Nnly III is true. b) Only II is true. c) Only I is rrue. ( d) 9"ty II andIII are tme. e) Only I andIII are true. 7. Given the daia: 3, -3, l, 6, -1, 6, the mean and the median are respectively a) 2 and -3 b) 0 and 2 c) o *na -1ffi)!nd 2 e) none of the above \-/ 8. FfeET the two points (2, 3) and (3.5,6), whereb > 3.2, the value of the correlation coefficienr t\ "),/r always I Yf is always -t c) is aiways either I or -1, dependingon the value of b d) can be any number in tbe range -l t,o I depending on the value of D What is tUe ta)9l.]\above data? a) 1.4 ( u1 o.z ) c) 2.2 \__/ lI P(x > 7.5)= .3923, what is p? a)ro.e b)5.8 {a ll For quetions 4 and 5 consider the discret€ random variable, o. which follows the distribution sbown below. a l-2 -l 0 | 2 P(x : a) | r/8 Ll4 r/a l/a p 4. What is the value of p? ,...q\ /\ a)la b)0 c)l {d)1/8 ) e)noneoftheabove \_-/ 10. The probability of raia today is 0.2. The probebility of rain tommorrow is also 0.2. The probability of rain on both days is 0.1. What is the probablity that it will rain tommopow if it rains todav? a) 0.2 b) 0.1 d) 1 e) none of the above 11. A normal random variabte, c, han sp unkown meaD ,, and va^rienceo2 :4. 9. You are given that tbe equation- V :2.3 - 0.8s is the least-squares line of bestfit for a re8ression of y on c, lf s!: aazr, the correlatiron coefficient, r, between c and y is a) 0.6 b) -0.8 \ ") -o I d) not computabte \-/ d) 7 e) none of tbe above d) 8.6 e) none of the above

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