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.RMITUNIVERSITY RMIT BUSINESSSCHOOL OF ECONOMICS, FINANCE ANDMARKETING

END OF SEMESTER EXAMINATIONECON 1035: BUSINESS STATISTICSDATE: 2 May 2006 SEMESTER1 2006

15MINUTES3 HOURS

READINGTIME:WRITING TIME:INSTRUCTIONS:1. This paper consists of 2 sections and each section contains 5 sets of questions.

Each section isworth 50% of the marks for this examination.Section A: This section contains 5 sets of Multiple Choice questions.

There is a total of 25 MultipleChoice questions.All MultipleChoice questions carry the same marks.

Section B: This section contains 5 sets of Practical questions.Eachset of Practical questions isworth 10%2. Mark your answers to the Multiple Choice questions in dark pencil or biro on the

Answer Sheet and write your answers to the practical questions in thespace provided in the exam .paper.

3. You must enter your name and your student number on the Answer Sheet andat the bottom of this page.

4. The exam counts for 70% of the total marks available in this subject.5. Use of a calculator which does not store text is permitted. No instruction

manuals or any other books. notes or other relevant materials are permitted.6. The formulae and Probability Tables are given in the 8 page formula sheet.

FAMILY NAME GIVEN NAME STUDENT NUMBER

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SECTION A: ECON 1035 25 MULTIPLE CHOICE QUESTIONS25 Multiple Choice QUestions worth 2 marks each (25 x 2 = 50 marks.)Select the ONE BEST answer. Multiple answers to the same question will bemarked as incorrect.

Circle your multiple choice answers on the answer sheet attached to this paper.Place the entire examination paper, together with the answer sheet, in yourexamination answer script.

Write your name and student number on the answer sheet provided with thisexamination paper.

1. INTRODUCTION AND DESCRIPTIVE STATISTICSQUESTION 1In this subject we discuss statistical terms that managers need to be familiar with. Which of thefollowing statistical definitions is not correct.(a) a random sample is one where the values are chosen in such a way that every value in the

population has an equal chance of being chosen.(b) sampling errors are equal to the standard deviation of the possible values of the sampleestimate of a population summary measure such as the mean or proportion.(c) descriptive statistics is concerned with the collection, presentation and characterization of a

set of data in order to describe the various features of that set of data.(d) regression analysis is used to estimate the relationships between different variables where

these relationships are then used to make forecasts of the values of the variables.(e) the sample frame is the list of items we use when we select a sample.

INFORMATION NEEDED TO ANSWER QUESTIONS 2 TO 6The manager of the customer complaints section of a large homeware manufacturer isinterested in the total amount of time that any employee spends talking to customers in a typical1 hour period. He decides to look at a random sample of n = 72 different one hour periods andnote the time rounded to the nearest minute which one of the staff members spends on thephone during that hour. These values are shown in the table on the top of the next page. Thethe stem-and- lear display for these values is shown below this table.The sum of the values and the sum of the squared values is

nL X . = 1869i=1 I andnL X~ ::; 50641

1 = 1 I

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INFORMATION NEEDED TO ANSWER QUESTIONS 2 TO 6 (continued)

TABLE OF VALUES

13 15 16 17 17 18 19 19 19 19 20 2021 21 21 21 22 22 22 23 23 24 24 2424 25 25 25 25 25 25 25 25 25 25 2626 26 26 27 27 27 27 27 27 27 28 2828 28 29 29 29 29 30 31 31 31 31 3232 32 32 32 32 33 33 34 36 36 36 40

STEM AND LEAF DISPLAY

Branches Leaves10S:

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QUESTION 3

Which of the following statements concerning the measures of central tendency is correct.(The values are rounded to 2 decimal places.)(a) The value of the mean is less than the value of the median and greater than the value of

the mode.(b) The mean value of 25.96 is less than the value of the mode.(c) The median value of 25 has 36 values smaller than it and 36 values larger than it.(d) There are two modal values 25 and 26.(e) None of the aboveQUESTION 4

For this sample of n = 72 values which of the following set of values for the 5 key measures i.e.the minimum value, the value of the first quartile, the value of the median, the value of the thirdquartile and the maximum value is correct.(a) 13, 22,26, 30,40(b) 3, 18, 26, 30, 40(e ) 13. 22, 25.96, 29,40(d) 13, 18,25,30,40(e) None of the aboveQUESTION 5

Suppose we use the value of the mean along with the values of the 5 key measures i.e. theminimum value, the value of the first quartile, the value of the median, the value of the thirdquartile and the maximum value to decide whether this set of values is symmetrical or skewed.Which of the following statements is not correct.(a) as the mean and median have values which differ from each other by less than 0.1 we

would say that the values for the time spent on the telephone have a distribution which isclose to but not exactly a symmetrical distribution

(b) while the mean and median exceed the mode which implies that the values are positivelyskewed the mean is less than the median which implies that the values are negativelyskewed.(c) as the difference between the smallest value and the first quartile is less than the differencebetween the first quartile and the median these values are negatively skewed

(d) while the differences between the smallest value and the first quartile and the largest valueand the third quartile indicate that the values are positively skewed the differences betweenthe first quartile and the median and the third quartile and the median lndlcate these valuesare symmetrical.

(e) None of the above


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QUESTION 6

Consider the 72 values in the sample. We use the formula for the unbiased estimate of thevariance and the unbiased estimate of the standard deviation and round the values to 2 decimalplaces. Which of the fol lowing statements is correct(a) The variance is between 29 and 29.52.(b) The standard deviation is more than 5.5.(c) The variance is less than the range.(d) The variance is more than two times the value of the Interquartile range.(e) None of the above

2. PROBABILITY TI~EORY AND PROBABILITY DISTRIBUTIONSINFORMATION NEEDED TO ANSWER QUESTIONS 7 AND 8The area manager for Crazy Karen's mobile phone company is interested in studying thefactors which influence the amount of time which students spend using their mobile phones.She examines a random sample of n = 50 usage records for students and divides them into twogroups namely heavy users (H) and light users (L). Other studies have shown that mobilephone usage is affected by gender. She notes whether each of the records is for a Female (F)or for a Male (M). The results she obtains are shown in the following contingency table.

Mobile Phone UsageGender (L) Ugh~ (H) Heavy Total

(F) Female 24 16 40(M) Male 6 4 10

Total 30 20 50QUESTION 7Which of the following statements about the relevant probabilities is correct.(a) As more Females are Light users the probability that a female is a Light user will be greater

than the probability that a male will be a light user.(b) The joint probability that a person is a Male and a Ught user is P{M AND L) = 0.12.(c) The probability that a person is a male is P(M) = 0.25.(d) The probability that a person is a Heavy User is P(H) = 0.08,(e) None of the above

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QUEST IO N 8T o de te rm in e w he the r ge nde r affects m obile phon e usa ge the are a m an age r looks a t thep erce nta ge s a nd the p ro ba bilitie s w e ca n o bta in from th e co ntin ge ncy ta ble . W hich of thefollo win g s ta te me nts con ce rn in g the re la tion ship b etw ee n g en de r a nd m ob ile p ho ne us ageis n ot correct.(a ) A s the jo in t probability of being Fe male an d a H ea vy user is equal to the product of the ir

s epa ra te p rob abilitie s i.e . P (F AND H ) = P(F) . P (H ) = 0.32 we can say that gender is notre la te d to m ob ile ph on e u sa ge .

(b) Whe n w e ca lcula te the perce ntage s w e w ould use the row s be cause it is ge nd er tha t affe ctsm ob ile ph on e us age ra th er tha n m obile ph on e u sa ge w hich a ffe cts g en de r.

(c) G en de r a nd m ob ile ph on e u sa ge a re in de pe nd en t be ca us e a ny con dition al p ro ba bilitie ssuch as P(H I F} a re th e s am e a s the o rigin al pro ba bility P (H }.

(d) G end er a nd m obile phone usa ge are in de pe nde nt beca use as pel 1M ) = pel) = 0.6.(e ) N on e of the a boveQUEST IO N 9S uppose the a re a m ana ger at C ra zy K are ns is in tere ste d in the num be r of high va lue phon ecalls l.e. ca lls cost ing $10 or m ore , w hich stude nt custom ers m ake . A ve ry la rge stud y ha sshow n tha t the proba bility that an y ca ll m ad e by a stude nt custom er w ill be a high value ca llis p = 0.2.The m anager chooses a random sam ple of n = 6 c alls . W I,ic h o f th e fo llo win g s ta temen tscon ce rn in g th e n um be r of h ig h va lu e .ca lls (x) in th is sam ple of 6 calls is not correct.(a ) F or the n um be r of high va lu e ca lls to h ave a B in om ia l pro ba bility d istrib utio n th e p ro aba bilityof a high va lue ca ll m ust be the sam e for a ll 6 ca lls.(b) If the sam ple is chosen in such a way that tha t the outcom e for on e ca ll a ffe cts the

proba bility of a nothe r call be in g a high va lue call the n the n um ber of high va lue calls w ill noth a ve a B in om i al p robability d is tr ib ut io n.

(c) If w e refer to each of the 6 ca lls as a tria l then the tw o poss ible outcom es of each tria l a re asuccess or high va lue call and a fa ilure or call w hich is not a high va lue ca ll.

(d) As the va lue of the probability of success p is not close to 0 .5 and the value of n p is notlarge then the low er va lues of x (the possible num bers of high value ca lls) such as 0 , 1and 2 w ill have higher probabilities than larger va lues of x such as 5 and 6.

(e ) N one of the a bove.Q UESTIO N 10S uppose the a re a m an age r at C ra zy K aren s de cid es tha t the n um be r of high value ca lls (x)in her sam ple of n = 6 ca lls ha s a B in om ia l p ro ba bility d istrib utio n w ith p = 0.2. She w ants toknow the probability tha t 1 or m ore of the 6 calls is a high va lue ca ll. W hich of the follow ingpo ssib le va lu es fo r this p ro ba bility is corre ct. (A ll va lue s a re ro un de d to 2 d ecim al p la ce s.)(a) 0.74( b) 0 .9 9(c) 0.26(d) 0.20(e ) N on e of the above


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3. STATISTICAL INFERENCE IINFORMATION NEEDED TO ANSWER QUESTIONS 11 TO 15The manager of a health center is concerned with the time that emergency patientsmust wait before a doctor can see them. He thinks that the possible values of thesewaiting times have a Normal distribution with a population mean of Il = 15 minutes and apopulation standard deviation of (j = 5 minutes.QUESTION 11What is the probability that an emergency patient will have to wait for 11 minutes or more(a) 0.2119(b) 0.7881(c) 0.2881(d) 0.7119(e) None of the above.QUESTION 12The manager is worried about the percentage of emergency patients who have to wait for verylong times before they can see a doctor. The waiting time for which we can say that 15% ofemergency patients must wait longer than this number of minutes is (values are rounded to 2decimal places.)(a) 16.04 minutes(b) 16.95 minutes(c) 5.2 minutes(d) 20.2 minutes(e) None of the above.

QUESTION 13Suppose the manager decides to examine a random sample of n = 16 patients andcalculate the value of the sample mean of their waiting times. Which of the followingstatements about the possible values of the sample mean time (X) that patients waitbefore they can see a doctor is correct.(a) The probability of obtaining an X value of 11 minutes or more is less than the

probability that an individual patient will have to wait 11 minutes or more.(b) We cannot say what the mean or standard deviation of the possible X values is

because the sample size is too small.(c) The mean of the possible X values is ~ L X = 15 and the standard deviation of the

possible X values is 0')( = 5.(d) The mean of the possible X values is ~x = 15 and the standard deviation of the

possible X values is O ' x = 1.25.(e) None of the above

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QUESTION 14

Suppose that the manager thinks that the population mean J . I . has changed from 15. Usingthis sample of n = 16 waiting times he finds that the sample mean is x : = 17. If we assumethat the population standard deviation is (1= 5 then which of the following intervals of valuesis the correct 95% interval estimate of the population mean ~l.(a) 15 2.45(b) 17 2.45(c) 17 2.056(d) 17 9.8(e) None of the aboveQUESTION 15

After looking at the patients records the manager decides that there is a finite population ofwaiting times for emergency patients of N = 300. This means that the formula that he used inQuestion 14 to calculate the 95% interval estimate of the mean may be incorrect. Which of thefollowing statements is not correct.(a) The value of the finite population correction factor is 0.9746(b) As the ratio n I N = 0.0533> 0.05 we should divide the value of the standard error cr x by

the finite population correction factor value.(c) As the ratio n/N = 0.0533 we need to multiply the standard error of the possible values of

the sample mean by the finite population correction factor.(d) The value of the finite population correction factor is equal to the square root of 0.9498(e) None of the above


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4. S TA TIS TIC AL IN FERENC E IIIN FORMATIO N N EEDED TO ANSWER QUESTIO NS 16 TO 20S uppose the a sset m an age r for a chain of conve nien ce store s is in tere ste d in find ing outw he the r the clea nin g com pan y tha t cle an s their s tores is provid ing a service w hich is a sgood or bette r tha n the curre nt in dustry sta nda rd . A s the va lue of th is cle aning contra ct isbased on the average tim e needed to clean a store she decides to exam ine the averagetim e th at th is cle an in g co ntra ctor ta ke s w he n cle an in g a store . F rom othe r s tu die s sh e fin dstha t the poss ib le va lues of the tim es n eed ed to cle an a store ha ve a popula tion m ean va lueof u = 2 h ou rs . F rom othe r la rg er s tu die s th e a ss et m a na ge r fin ds th at th e po pula tio ns ta nd ard d evia tio n is c = 0.5.A fte r e xam in in g p ay cla im s the a ss et m a na ge r fin ds tha t this cle an in g con tra cto r ta ke slonge r tha n 2 hours to cle an e ach store . S he a pproaches the cle an in g con tra ctor a nd poin tsout that their contra ct w ill not be re ne we d. T he clea nin g con tra ctor a rgues that th is va lue of2 hours is based on overseas da ta w here the stores are m uch sm aller. The la rgerA ustra lian stores n eed m ore tha n 2 hours to clea n.To help d ete rm in e w he the r the se cla im s of the cle aning con tra ctor are or a re not corre ct theasse t m anager decides to se lect a random sam ple of n = 3 6 cle an in g jo bs a nd p erformthem herself. In each case she notes how long it takes to com ple te them . She uses theseva lue s to calculate the va lue of the sa mple m ean (X). This sam ple e vid en ce is used to testth e f ollow in g hypot he s es

(Repla ce th e e xis tin g c le a nin g c on tr ac to r)(D o n ot re pla ce th e e xis tin g cle an in g co ntra cto r)

QUESTION 16If the a sse t m an age r use s a le vel of S ignifica nce of C t. = 0 .0 5 the n w hich of th e follo win gs ta te m en ts is n ot co rre ct(a ) The m ean of the poss ib le va lues of the sam ple m ean (X) is th e p opu la tion m e an ~l.(b) T he possible value s of the sam ple m ea n (X) ca n on ly be N orm ally d is tribu te d w he n the

tim es fo r e ach cle an in g job a re a ls o N orm a lly d is trib ute d.(c) T he varia nce of the poss ible va lue s of the sa mple m ea n (X) is e qua l to the

po pula tio n va ria nce 0 .2 5 d ivid ed by th e s ize o f th e s am ple .(d) The sta nd ard de via tion of the poss ib le va lue s of the sa mple m ean (X), which w ealso ca ll the sta nd ard error, is equal to 0 .0 83 3 (= 0.5/6).

(e) N one of the above


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QUESTION 17Suppose the asset manager finds from this sample of n = 36 values that the sample meancleaning time for each store is X = 2.15 hours. If values are rounded to 4 decimal placeswhich of the following statements concerning the p value in this hypothesis testing problemis correct.(a) The p value of 0.0359 is the probability of obtaining a sample mean X of 2.15 or more

when the null hypothesis is correct and J . 1 = 2.(b) The p value is equal to 0.4641.(c) The p value is twice the probability of obtaining a value for the sample mean X of 2.15 or

more, when the population mean J .1 has the value in the null hypothesis.(d) The p value is the probability of obtaining a value for the sample mean X of 2.15 or more,

when the population mean ~L has the value of 2.15.(e) None of the aboveQUESTION 18The asset manager decides that if she uses a sample size of n = 36 the size of the samplingerror may be too large. She decides to select a value for n in such a way that she can be 95%confident that the sampling error i.e. the distance between X and J . l . is 0.2 or less. If we knowthat o = 0.5 which of the following statements is correct(a) The current sample size is larger than the sample size she requires.(b) The sample size she needs is 49.(c) Her sample size of 36 is the correct sample size.(d) The current sample size is less than the sample size she requires.(e) None of the above.QUESTION 19Which of the following descriptions of what happens when the manager makes a Type II Errorwhen testing the given hypotheses is correct(a) She wrongly accepts Ho and keeps the existing cleaners.(b) She wrongly rejects Ho and hires new cleaners when she should not.(c) She wrongly accepts Ho and does not keep the existing cleaners when she should.(d) She wrongly rejects Ho and does not keep the old cleaners when she should.(e) None of the above.QUESTION 20If the manager is equally concerned with the consequences associated with the Type I Errorand the Type II Error in this problem. Which of the following actions is the correct action.(a) Use a 2 tail test so that she will be twice as sure that she is not making a Type I Error.(b) Use a small level of significance such as a. = 0.01.(c) Set up the decision rule so that the probability of making a Type II Error is twice the

probability of making a Type I Error.(d) Use a larger value of a. such as 0.15 or 0.20.(e) None of the above.


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5. SIMPLE LINEAR REGRESSION AND CORRELATIONINFORMATION NEEDED TO ANSWER QUESTIONS 21 TO 25The manager of the customer complaints section of a large homeware manufacturer isinterested in finding the relationship between the total amount of time that any employeespends talking to customers in a typical 1 hour period (y) and the number of calls that he orshe answers in that 1 hour period (X). He decides to look at a random sample of n = 72different one hour periods and note both the time spent talking on the phone (Y), (rounded tothe nearest minute) and the number of calls that the staff member answers. For thisparticular sample of n = 72 values he obtains the following set of 5 values

n nLXi = 816 and L X ~ = 97081 = 1 i=1 1n nL Y . = 1869 and L Y . 2 = 506411 = 1 I 1=1 I

n2 : X . Y . = 22098i= 1 I I

N.B. WHEN YOU PERFORM ANY CALCULATIONS FOR THESE QUESTIONS YOUNEED ONLY USE VALUES THAT ARE ROUNDED TO 4 DECIMAL PLACES.

QUESTION 21Which of the following sets of values, (which are rounded to 3 decimal places) shows thecorrect values of the 3 terms (A or SSXY,rB or SSX and C or SST) that we use whenperforming calculations in regression problems.(a) A = 916, B = 460 and C = 2124.875.(b) A = 460, B = 916 and C = = -2124.875.(c) A = -916, B = -460 and C = 2124.875(d) A = = 2124.875, B = 460 and C = 916.(e) None of the aboveQUESTION 22

Which of the following statements concerning the estimated value of the slope of the simplelinear regression line (these values are rounded to 3 decimal places.) is correct(a) The estimated slope of 1.99 shows the impact of the time spent on the telephone

on the number of calls received.(b) The estimated slope is greater than 3.5.(c) The estimated slope is greater than the estimated intercept.(d) The estimated slope of 1.99 shows the impact of the number of calls on the time

spent on the telephone.(e) None of the above


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QUESTION 23

The analyst now calculates the correlation coefficient (r) for these two variables.Which of the following statements is correct.(a) The r value of ,0.8584 shows that there is a strong positive relationship between

these two variables(b) The r value of 0.9265 indicates that there is no relationship between these two

variables.(c) The r value of 0.8584 indicates that there is a strong relationship between these

two variables but we do not know if this relationship is positive or negative.(d) The r value of 0.9265 indicates that there is a strong positive relationship between

these two variables ..(e) None of the aboveQUESTION 24Which of the following statements about the standard error of the estimate Syx is correct,(The values have been rounded to 3 decimal places.)(a) As there is a SyX value greater than 1.0 there must be is a significant positive relationship

between these variables.(b) Because the SyX value is less than 1.96 this shows that there is not a significant positive

relationship between these two variables.(c) The Syx value is between 4 and 5.(d) The SyX value of 2.073 is the standard deviation of the error terms in the regression model.(e) None of the above.QUESTION 25When you test whether the null hypothesis that the value of the slope for the population isequal to against the alternative hypothesis that it is not equal to 0 with C t. " " 0.05, which ofthe following statements is correct(a) As the t statistic has a value of over 20 which is greater than the critical value 1.96 we

will reject the null hypothesis and conclude that there is a significant relationshipbetween these two variables.

(b) As this is a 2-Tail test we must divide the critical value of 2.3646 by 2.(c) While the t statistic has a value which is less than 10 this is still greater than the critical

value which is 1.645.(d) As the t statistic has a value of over 20 which is greater than the critical value 1.96 we

will accept the null hypothesis and conclude that there is not a significant relationshipbetween these two variables.

(e) None of the above.


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.-1"

SECTION B: ECON 1035 5 PRACTICAL QUESTIONS5 Practical Questions worth 10 marks each (5 x 10 = 50 marks.)Enter all your working and answers in the spaces provided under the questions,If you require extra space for your working write on the blank page opposite to theexamination questions.QUESTION 1The finance officer for a firm which imports and distributes Asian groceries is looking at theexpense claims of staff in the marketing section of the firm. She takes a random sample ofn = 64 expense claims. The values she obtains are arranged in ascending order andplaced in the following table

12.76 18.09 18.38 18.7 18.82 19.19 20.68 21.1124.19 27.8 28.18 28.78 29.24 29.25 30.08 30.4930.76 31 31.07 31.84 32.01 32.17 32.63 33.4734.74 34.85 36.25 36.41 36.54 36.69 37.12 37.4937.62 39.21 39.68 40.11 40.17 40.19 40.86 40.8841.17 41.49 41.82 41.87 42.16 42.4 42.56 42.9243.16 43.2 43.43 44.16 44.6 45.45 45.47 45.5345.56 46.05 46.37 46.71 46.83 47.49 48.04 50.86

(a) Find the 3 measures of central tendency Le. the mean, the median, the mode along withthe values of Quartile 1 and Quartile 3. It is suggested that you perform the followingcalculations when you answer this question.Find the mean

She finds that for these values their sum and their sum of squares are as followsnL X . = 2308j , , , 1 I a n d

nL X~ = 88439.978i= 1 I

~ '" - - -" & " -., , ,

.. . _ _ " . . "" _

........................................................................................... ,. .......................................................... 1 .


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QUESTION 1(a) (continued)Find the median

Find the Mode.

Find the first Quartile

....................... ,. ~'" ~.................. I' ." , ' .

Find the third Quartile


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QUESTION 1 (continued)(b) Briefly explain why you think that this set of values is or is not distributed symmetrically. It is

suggested that you perform the following steps when you answer this question.Compare the values of the mean and the median

Compare the values in the 5 number summary i.e, the minimum value, the first quartile, themedian, the third quartile and the maximum value .

... I ~.' " , '''' , '" '" .

, , .

............................................................................................. , . ,o '" " , '0. , '" I ~. ", 0.' ,0, , .' _ '0' '" '" ,0' ,., _

o , " '" '" , .. ~ ' I " ~ .


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QUESTION 1 (continued)(c) Find the sample estimate of the standard deviation and then find the interval of values

which is one standard deviation below the mean and one standard deviation abovethe mean.

(d) Find the proportion of the 64 values which lie in the interval which extends onestandard deviation on either side of the mean, Briefly discuss whether this resultagrees or disagrees with the empirical rule .

... . .~~..~ ~.~ ~ , , .


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QUEST IO N 2(a ) T he fin an ce office r for a firm w hich im ports an d d is tribute s A sia n groce rie s is lookin g a t

the fa ctors w hich a ffe ct the leve l of the e xpe nse cla im s of s ta ff in the m arke tin g se ctionof the firm . She defines expense cla lm s of $40 or m ore as high (H) and cla im s of lessthan $40 dolla rs as not high (NH). She thinks tha t the num ber of high cla im s is affectedby the a moun t o f tim e tha t a sta ff m em ber has w orked for the firm . She ca lls s taff w hohave w orked for the firm for 2 years or m ore long te rm staff (l) and sta ff w ho have beenw ith the firm for less tha n 2 ye ars a re calle d short te rm (S ) sta ff.Us ing a random sam ple of n = 64 e xpe ns e cla im s a nd em plo ym e nt re cord s th e fin an ceoffice r o bta in s th e follo win g co ntin ge ncy ta ble w hich sh ow s th e n um be r o f cla im sassocia ted w ith each com bina tion of the type of expense cla im (H or NH ) and the type ofemployee (L or S ).

Short Te rm (S ) 1540

TYPE OFEMPLOYEE High (H) Not H igh (NH)

TYPE OF EX PENSE CLAIM

920L on g T erm (L) 20

2429 35 64

U sin g th e a bo ve ta ble a ns we r th e fo llo win g qu es tion s(i) Find t he fol low ing p robab il it ie sP(HAND S) ..

P(H AND NH) .. < > ~ ~ ~ - . r

P{LAND NH) .

(ii) Find t he foll ow ing p robab il it ie sP{ll H) .

P(NH IS) , ..


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QUESTION 2 (a) (continued)(iii) Briefly explain why the Type of Employee and the Type of Expense Claim are or

are not independent. 4 ~ ' ~ " ~ , ~ .

(b) After examining a number of expense claims the finance officer finds that many of theforms were filled in incorrectly. By examining a large number of claims she finds that theprobability that an expense claim form is not filled in correctly is p = 0.25. She also findsthat the number of expense claim forms not fi lled in correctly has a Binomial distribution.If she examines n = 8 expense claim forms:,(i) What is the average and the variance of the number of claim forms that are not filled

in correctly?

(ii) What is the probability that 2 or more of the 8 claim forms are not filled in correctly?


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QUESTION 2 (continued)(c) Suppose the finance officer finds that the number of claim forms not filled in correctly does

not have a Binomial distribution. Instead she finds out that on any day the number of claimforms that are not filled in correctly has a Poisson distribution with an average number foreach day of A . = 2.(i) What is the average and the variance of the number of claim forms that are notfilled in correctly on anyone day?

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(ii) What is the probability that on any day 2 or more of the claim forms are not filled incorrectly?

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QUEST IO N 3T he m a na ge r o f a ch ain o f clothin g s tore s w is he s to u se ce rta in s ta tis tica l proce du re sw he n m a kin g th e d ecis io n w he th er to a dve rtis e th rou gh th e lo ca l T V s ta tio n. T his s ta tio nbroa dca sts to all are as w he re the stores a re loca te d. To he lp him w hen he is m aking thede cis ion w hethe r he should ad ve rtise on T V the m ana ger d ecide s to look a t the proportionof the ir re gu la r cus tome rs w ho ca n remem be r se ein g 2 or m ore a dve rtisem en ts fo r clothin gs tore s in th e la st w ee k.(a ) O th er stud ie s ha ve fou nd tha t the p rop ortion of re gu la r clo th in g s hop pe rs w ho ca n

rem em be r see in g 2 or m ore ad vertise men ts for clothing store s in the la st w ee k is p = 0.3.The m anager plans to take a sam ple of n = 3 6 typica l custom ers a nd in ea ch ca se n otew he ther the y re mem ber se ein g 2 or m ore a dve rtise me nts for clothin g stores in the lastw ee k. H e w ill fin d the num be r (x) w ho rem em be r se ein g 2 or m ore a dve rtise me nts forcloth in g store s in the la st w ee k a nd the n he w ill fin d the sa mple proportion (P s) of re gularcustom ers w ho re mem ber see in g 2 or m ore a dve rtise me nts for cloth in g stores in the la stw ee k u sin g the form ula .

Ps = x InB rie fly e xp la in w ha t th e S am plin g D is trib utio n o f th e p os sib le va lue s o f the s am plep ro po rtio n (p s) is in th is s itu atio n.(Y ou should state w ha t the m ea n a nd sta nda rd d eviation of the poss ib le P s va lue s aree qu al to a nd yo u s hou ld a lso n ote w hy th e d is tribu tio n is o r is n ot the N orm a l d istrib utio n.). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . .. .. .. .. ~ '"'' , "" .,........................................ y ,. ~ "

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QUESTION 3 (continued)(b) If you were told that in the sample of n = 36 people the number who can remember seeing 2

or more advertisements for clothing stores in the last week was x = 14, find the sampleproportion Ps and then find the 90% interval estimate of the population proportion p.Briefly explain how we interpret this interval estimate .

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(c) The manager finds out that the size of the population of people who watch this TVstation is N = 2000. If the population proportion of people who can remember seeing 2or more advertisements for clothing stores in the last week is p = 0.3 and we use asample of n = 160, what is the sampling distribution of the possible values of thesample proportion .


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QUESTION 4An analyst for a large property management firm is interested in the average rate of return oninner city student housing units. The firm is interested in investing in this type of property aslong as the average returns are 7% p.a. or more. If the average returns are less than 7% p.a.then the firm will not invest in this type of property. From other larger studies it is known thatthe standard deviation of returns on this type of property is cr= 4%.A random sample of n = 16 units is examined and it is found that these returns have a samplemean of X = 6.4%. The analyst decides to use a level of significance of ct = 0.01 to choosebetween the following hypotheses.

(Invest in student accommodation.)(Do not invest in student accommodation.)

(a) State what assumption you must make before you can use the standard procedure to selectone of the above hypotheses.

(b) Use the standard hypothesis testing procedure to select one of the above hypotheses.

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QUESTION 4(b) (continued)

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(c) Brie fly expla in w hat w e m ea n by a p value.F in d the p v alu e in th is p ro blem .U se the p va lue to choose betw een the tw o hypotheses.

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QUESTION 5The finance officer for a firm which imports and distributes Asian groceries is looking at therelationship between the number of product lines a staff member manages and the value oftheir expense claims. She decides to use Regression analysis to estimate the relationshipbetween the value of expense claims (Y) and the number of product lines a staff membermanages (X). To obtain an estimate of the linear relationship between these tw o variables shetakes a random sample of n = 64 expense claims and in each case she notes the value of theexpense claims and the number of product lines the person who made the expense claim isresponsible for. She then finds that for these two variables the sum of the values and the sumof squared values are as follows.

nL X . = 485 andj=1 InL v . = 2308.8 andi=1 I

nL X2 = 41611=1 Inr y _ 2 = 88439.978i=1 I

n}2XY = 19036.571=1 I I

(a) Calculate the 3 key values, called A, Band C in the formula sheet, which are used inRegression analysis. .4 a 0 ," , '.' ~ 'O .. ~ ~ "

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QUESTION 5 (continued)(b) Find the Sample Regression Function (SRF) from these values.

Briefly explain what the estimated intercept and the estimated slope tell us about therelationship between these variables ... . . .. . . . . . . ," ~, .

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(c) Find both the correlation coefficient r a~d the coefficient of determination lBriefly explain how we interpret these two values.


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QUESTION 5 (continued)(d) Find the 95% Prediction Interval of the level of the expense claim when the number of

product lines a person manages is Xo = 5.

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ECON 1035 - BUSINESS STATISTICSSECTION A - MULTIPLE CHOICE QUESTIONS

FAMILY NAME; GIVEN NAME: ..STUDENT NUMBER: .Indicate your answer to each question in Section B by circling the option you haveselected. Mark one option ONLY.

QUESTIONS POSSIBLE ANSWERS1 a b c d e2 a b c d e3 a b c d e4 a b c d e5 a b c d e6 a b c d e7 a b c d e8 a b c d e9 a b c d e10 a b c d e11 a b c d e12 a b c d e13 a .. b c d e14 a b c d e15 a b c d e16 a b c d e17 a b c d e18 a b c d e19 a b c d e20 a b c d e2 1 a b c d e22 a b c d e23 a b c d e24 a b c d e25 a b c d e

PLEASE ENSURE THAT YOUR NAME AND STUDENT NUMBER IS ON THE SHEET


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