sfmproblems

8/2/2019 SFMProblems

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K. HARI KRISHNA MBA TUITIONS, LIVE PROJECTS, NCFM AMFI

CERTIFICATION

M.B.A, M.Com, M.Phil, (Ph.D), (ICWAI) JOB ORIENTED TRAINING IN FINANCE &

ACCOUNTS

Director - Black Swan 91 77 567 568 WITH 100% PLACEMENT ASSISTANCE - 91

77 567 568 PROBABILITY1. What is the probability of getting a head in a single toss of a fair coin.2. What is the probability of obtaining (i) an even number (ii) a number less than

5 (iii) a number 5 in a single throw of a unbiased die.3. Find the probability that a throw of an unbiased die results in (i) an ace

(number 1) (ii) an even number (iii) a multiple of 7.4. A bag contains 3 white, 4 red and 2 green balls. One ball is selected at random

from the bag. Find the probability that the selected ball is (i) white (ii) non white (iii) white or green.

5. What is the chance that a non leap year should have 53 Sundays.6. What is the chance that a leap year selected at random will contain 53

Sundays.7. In a throw of an unbiased dice find the probability of (i) total 7 points (ii) total

8 points8. Two unbiased dice are thrown. Find the probability that the sum of the faces is

not less than 10.9. Two dice are thrown are simultaneously and the points are multiplied

together, find the probability that the product is 4.10. What is the probability of getting 3 white balls in a draw of 3 balls from a box

containing 5 white balls from a box containing 5 white and 4 black balls.ADDITIONAL THEOREM1. One card is drawn from a standard pack of 52 cards. What is the probability

that either king or queen.2. In drawing a card from well shuffled pack find the probability that the card

drawn will be either spade or Arc.3. The probability that a contractor will get a plumbing contract is . And the

probability that he will not get electric contract is 4/9. If the probability ofgetting at least one contract is 5/6, what is the probability that he will get boththe contract?

4. In a college, there are five lecturers. Among them, three are doctorates. If acommittee consisting three lecturers is formed, what is the probability that atleast two of them are doctorates?

5. A bag contains 30 balls numbered from 1 to 30. One ball is drawn at random.Find the probability that the no of the ball drawn will be a multiple of a) 5 or 7

b) 3 or 7MULTIPLICATION THEOREM1. A man wants to marry a girl having qualities, white complexion the

probability of getting such a girl is 1 in 20. Hand some dowry theprobability of getting this is 1 in 50. Westernized manner the probabilityhere is 1 in 100. Find out the probability of his getting married to such a girlwhere the possession of these three attributes are independent.

2. A committee of 4 people is to be appointed from 3 officers of the productiondepartment, 4 officers of the purchase department, two officers of the sales


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77 567 568 department and one chartered accountant. Find the probability of formingcommittee in the following manner.i. There must be one from each category.ii. It should have at least one from the purchase departmentiii. The chartered accountant must be in the committee.

3. There are 5 white and 7 red balls in a box. A ball is drawn and then replaced.What is the probability that a white and a red ball are drawn in that order.i. with replacement of ballsii. without replacement of balls

4. a husband and a wife appear in an interview for two vacancies in the samepost. The probability of husbands selection is 1/9 and that of wife selection is1/5. What is the probability that,i. both of them will be selectedii. only one of them will be selectediii. none of them will be selected

5. Three groups of persons contain 3 boys and 1 girl, 2 boys and 2 girls, 1 boyand 3 girls respectively. One person is selected at random from each group.What is the probability that the group selected consists of 1 boy and 2 girls?

6. The personnel department of a company has records show the following of200 engineers.Age Bachelors Masters Total

Degree degree

Under 30 90 10 100

30 40 20 30 50Above 40 40 10 50If an engineer is selected at random from the company, find the probabilitythata) He has only a bachelors degreeb) He has a masters degree given that he is over 40c) He is under 30 given that he has only a bachelors degree.

7. The data for the promotion status and academic qualification regarding 100Employees of a company is as follows.Promotional status MBA non - MBA Total

Promoted 12 48 60Not promoted 18 22 40Total 30 70 100At random one employee is picked up. What is the probability thatA. He is an MBAB. He is promotedC. He is promoted given that he is an MBAD. He is an MBA promoted given that he is promoted.


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77 567 568 1. The records of 400 examinees are given below.Score BA B.SC B.COM Total

Below 50 90 30 60 18050 60 20 70 70 160Above 60 10 30 20 60Total 120 130 150 400If an examinee is selected at the random from this group of examinees, findthe probability thata. He is a commerce graduate

b. He is a science graduate given that his score is above 60.c. His score is below 50 given that he is a BA2. A restaurant features two types of lunchs special lunch and ordinary

lunch. Sixty percent of its men customers order the special lunch and therest of the men order the ordinary lunch. Ninety percent of its womancustomers order the ordinary lunch and the rest order the special lunch.Seventy percent of its customers are men. In its preparations, what ratiosof special to ordinary lunches should the restaurant plan for? Determinethe probability that the man will order a special lunch.

BAYES THEOREM1. In a bolt factory 3 machines M1,M2,M3 manufactures respectively 25%, 35%

and 40% of the total of the output. 5%, 4%, 2% respectively are defectivebolts. One bolt is drawn at random from the products and is found to bedefective. What is the probability that it is manufactured in Machine 2?

2. Three A, B, C produce 50%, 30% and 20% respectively of the total no ofitems in a factory. The percentage of defective output of these machines are3%, 4%, 5%. An item from production of the factory is selected at randomand is found to be defective. What is the probability it was produced bymachine A?

3. A manufacturing firm produces steel pipes in three plants with dailyproduction volumes of 500, 1000 and 2000 units respectively. According topast experience, it is known that the fraction of defective outputs produced bythe three plants are respectively 0.005, 0.008 and 0.010. if a pipe is selectedfrom the days total production and found to be defective, find out from whichplant the pipe comes?

4. Suppose that there is a chance for a newly constructed building to collapsewhether the design is faulty or not. The chance that the design is faulty is10%. The chance that the building collapse is 95%, if the design is faultyand otherwise it is 45%. It is seen that the building collapsed. What is theprobability that it is due to faulty design?

5. The probability of producing a defective item when the machine is correctlysetup is 0.2 and the probability is 0.5 when it is incorrectly setup. The chanceof correct setup of the machine is 80%. An item is selected at random after itsetup and is found to be defective. What is the probability that the setup was a


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77 567 568 correct set up?

6. There are two identical boxes containing respectively 4 white, 3 red and 3white, 7 red balls. A box is choosen at random and a ball is drawn from it. Ifthe ball is white, what is the probability it is from 1 st box?

7. An organization purchases its requirement of a component from threesuppliers A, B and C who supply 100 units in a box. Historical records ofa company indicates the 5%, 3% and 6% of the components supplied by A,B and C respectively are defectives. The quality control manager randomlypicked up one box and inspected two components from it and found thatboth components are defective. Find the probability that the quality controlmanager has picked up the box supplied by supplier B.

BINOMIAL DISTRIBUTION1. 6 coins are tossed in succession. Find the probability of getting more than 4

heads.2. The probability that an evening college student will graduate is 0.4. determine

the probability that out of five students, one student, two students and at leastone student will be graduate.

3. A bag containing 50 items has five defectives. Indicate the probability of thefollowing if 4 items are drawn with replacementa. Exactly two defective items

b. At least two defective itemsc. At the most two defective items

4. In a market survey it is observed that 30 percent of the consumers prefercolgate tooth paste, when a sample of 10 customers is chosen at random, whatis the probability that,i. At least 3 customers prefer the product.ii. At most 3 customers prefer the product.iii. Expected number of customers preferring the product.iv. The standard deviation of the number of customers preferring the product.

5. A random variable x is binomially distributed with mean & standarddeviation 2.4. find the probability that more than half of the trials aresuccess.

6. 8 coins are tossed at a time 256 times. No of heads observed at each throw is

recorded and the results are given below. Find the expected frequency. Whatis the theoretical value of mean and standard deviation.No of Heads:

At a throw0 1 2 3 4 5 6 7 8Frequency:2 6 30 52 67 56 32 10 1

7. Four coins tossed 150 times and the following results were obtained.X: 0 1 2 3 4f 12 50 54 30 4Fit a binomial distribution under the assumption that the coins are unbiased.


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77 567 568 8. The screws produced by a certain machine were checked by examining

centers of 7. The following shows the distribution of 128 samples according tothe no of defective items they contained.No. of Defectives: 0 1 2 3 4 5 6 7No. of Samples: 7 6 19 35 30 23 7 1Fit a binomial distribution and find the expected frequencies if the chance ofmachine being defective is . Find the mean and variance.

9. Fit a binomial distribution.X: 0 1 2 3 4 5 6 7Y 7 6 19 35 30 23 7 1

10. Fit a binomial distribution to the following data.X: 0 1 2 3 4Y: 28 62 46 10 4

POISSON DISTRIBUTION1. Assuming that on an average 2% of the output in a factory manufacturing

certain bolts is defective and that 200 units are in package. What is theprobability thati. None is defectiveii. At most 3 defectives bolts may be found in that package.

2. The probability that an individual suffers a bad reaction from an injection of a

given serum is 0.001. determine the probability that out of 2000 individuals,i. Exactlyii. More than 2 andiii. Between 4 and 6 individuals will suffer a bad reaction.

3. A book contains 125 misprints distributed at random throughout its 125 pages.What is the probability that a page observed at random contains at least 2misprints.

4. A random x follows a poisson distribution with parameter 3. Find theprobability that x assumes the valuesi. 0, 1, 2ii. Less than 3iii. At least 3

5. In an office between 4&5 PM the average no of incoming phone callsper minute in the switch board is 1.8. find the probability that during oneparticular minute there will bei. No phone call at allii. Exactly 2 phone calls

6. Suppose that a manufactured product has two defectives per unit of productinspected. Using Poisson distribution calculate the probabilities of finding aproduct without any defect, 3 defects and 4 defects.


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77 567 568 7. Fit a Poisson distribution to the following data and calculate the theoretical

frequencies.No of deaths: 0 1 2 3 4Frequencies: 122 60 15 2 1

8. The distribution of typing mistakes committed by a typist is as follows.Assuming a poisson model, find out the expected frequencies.Mistakes/page: 0 1 2 3 4 5No of pages: 142 156 69 27 5 1

9. In ana accounting department of a bank 100 accountants are selected atrandom and examined for errors. The following results has been obtained.Number of Errors: 0 1 2 3 4 5 6

Number of Accounts: 35 40 19 2 0 2 2Does the data verify that the errors are distributed according to the poissonprobability law?

10. The following table shows the number of customers returning the products ina marketing territory.Number of Returns: 0 1 2 3 4 5 6Number of Stores: 4 14 23 23 18 9 9Fit a Poisson distribution.

NORMAL DISTRIBUTION1. A sample of 100 dry battery cells are tested to find out the length of life produced

the following results. =12 hrs. S.D. = 3 hrs. assuming that the data are normally

distributed what percentage of battery cells are expected to havea. More than 15 hrs

b. Less than 6 hrsc. Between 10 and 14 hrs.

2. The mean and standard deviation of the wages of 6000 workers engaged in a factoryare Rs. 1200 and 400 respectively. Assuming the distribution to be normal estimatea. Percentage of workers getting wages above Rs.1600

b. No of workers getting wages between Rs.600 and Rs.900.c. No of workers getting wages between Rs.1100 and Rs.1500.

3. The daily wages of 1000 workmen are normally distributed around a mean of Rs.70and with a standard deviation of Rs.5. estimate the no of workers where daily wageswill be

a. More than 75b. More than 80c. Less than 63d. Between 70&72e. Between 69&72

4. The weekly wages of 1000 workmen are normally distributed, whose mean is Rs. 800and the standard deviation is Rs. 50. Estimate the number of workers whose weeklywages will be,i. Between Rs.800 and Rs.900ii. Less than Rs.750


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77 567 568 iii. Between Rs.700 and Rs.750iv. More than Rs.900

5. The service time of a critical component used in a system is used to follow a normaldistribution with a mean of 14500 hours and a standard deviation of 2100 hours.Estimate the probability that the component has a service time of,i. Below 13500 hoursii. Between 12500 hours and 15000 hoursiii. More than 15500 hours and below 16000 hours

6. Assume that the mean height of soldiers in a regiment of one thousand is 68 andthe standard deviation of 2.5. if the height of the soldiers in this regiment followsnormal distribution find.i. Number of soldiers above 72ii. Number of soldiers between 71 and 73iii. Number of soldiers above 65iv. Number of soldiers below 67.

7. In a business 3.5% of the days account for a daily collection of Rs.25000 or more.On 40% of the days, the daily collection of Rs.13000 or below. Estimate the averagedaily collection and standard deviation of this business. Assume the daily collectionfollows a normal distribution.

8. The distribution of daily sales revenue in a super market is found to follow a normaldistribution. It is found that on an average 10% of the days account for daily revenueof Rs.28000 or more. 30% of the days, the daily revenue is Rs.12000 or below.Estimate the average daily revenue and standard deviation.

TESTING OF HYPOTHESIS

Z TEST

1. A random sample of 900 members is found to have mean of 4.45 cm. Can it be

reasonably recorded sample from a large population whose mean is 5cm and

variance 4 cm.

2. A random sample of 200 tins of vanaspathi has mean weight 4.97 kgs andstandard deviation 0.2 kgs. Test at 1% level of significance, that the tins have 5

kgs vanaspathi.

3. A random sample of 100 rods drawn from a lot of rods has mean length 32.7 cms.

And standard deviation 1.3 cms. Can it be concluded that the lot has mean 32

cms?


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77 567 568 4. The mean life of sample of 100 electric bulbs produced by a company is found to

be 1570 hrs. with standard deviation of 120 hrs. if is the mean life time of all

the bulbs produced by a company, test the hypothesis that = 1600.

5. The mean and standard deviation of heights of 100 randomly selected boys are

163 cms and 3 cms, respectively. The mean and standard deviation of heights

of 80 randomly selected girls are 161 cms and 2 cms, respectively. Can it be

concluded at 1% level of significance that boys and girls are equally tall?

6. The means of two large samples of sizes 1000 & 2000 are 67.5 and 68

respectively. Test the equality of means of two populations with standard

deviation 2.5.

7. The standard deviation of length of fibre manufactured by process A is 0.5 cms,

and standard deviation of length of fibre manufactured by process B is 0.6 cms.

A sample of 40 randomly selected fibres from process A has mean length 16.7.

a sample of 60 randomly selected fibres from process B has mean length 16.4

cms. Test whether process A and process B differ with regard to length of fibre

manufactured by them.8. Intelligence test of two groups of boys and girls gives the following results.

G: mean = 84 S.D = 10 n = 121

B: mean = 81 S.D = 12 n = 81

Is the difference between standard deviations significant?

9. In a sample of 400 parts manufactured by a factory the number of defective parts

was found to be 30. The company however claimed that only 5% of their products

are defective. Is claim tenable?

10. Past experience shows that among bore wells dug by a firm, 78% are successful.

The firm digs 65 bore wells in a district. Among them 58 were successful. Can we

conclude that these figures agree with the past experience? ( test at 5 %)

11. The manufacture of a spot remover claims that his product removes at least 90%

of all spots. What can be concluded about the claim if the spot remover removes

only 174 spots out of 200 spots chosen at random from spots on cloth from dry


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77 567 568 cleaning unit.

12. In a random selection of 85 workers of a factory, 18 were unmarried. Can we

conclude that 20% workers of the factory unmarried?

13. In a certain district 450 persons were considered as regular consumer of tea out

of a sample of 1000. In another district 400 were regular consumers of tea out of

a sample of 800. Do this facts reveal a significance difference between the two

districts as per as drinking habits are considered. (use 5% level)

14. Among 80 electric bulbs manufactured by process A, three were defective.

Among 130 electric bulbs manufactured by process B, two were defectives. Test

whether the proportion of defectives in the two process differ.

15. The proportion of substandard crackers among 400 crackers manufactured by firm

A is 0.12. the proportion among 500 crackers manufactured by firm B is 0.08. test

at 1% level of significance that the proportion is the same among the products of

the two firms.

16. Two suppliers A & B supply an item to a company. Supplier A claimed that he

supplies 3% defectives less than his competitor B. to test his claim the companyselected 400 items from A and found that 35 components are defectives. Where as

300 items from B gave rise to 25 defectives. What can be said about the claim of

supplier A? use = 0.05.

t Test

1. A machine is designed to produce insulating washers for electrical devices

of average thickness of 0.025 cm. a random sample of 10 washers was found

to have a thickness of 0.024 cm with standard deviation of 0.002cm. test the

significance of deviation?

2. In the past a machine has produced washers having a thickness of 0.050


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77 567 568 inches. To determine whether the machine is in proper working order a

sample of 10 washers is chosen for which the mean thickness is 0.053 and the

standard deviation is 0.003 inches. Test the significance?

3. A random sample of size 16 has 53 mean. The sum of squares of deviations

take from the mean is 135. Can this sample be regarded as taken from the

population having the 56 as mean? Obtain 95% confidence limits of the mean

population.

4. The manufacturer of a certain make of electric bulbs claims that his bulbs

have a mean of 25 months with a standard deviation of 5 months. A random

sample of 6 such bulbs gave the following values. Life in months: 24, 26, 30,

20, 20, 18

Can you regard the producers claim to be valid at 1% level of significance.

5. A drug manufacturer has installed a machine to fill automatically an amount

of 15 grams of drug in each pill. A random sample of 15 pills is found to

contain 14.95 grams on the average with a standard deviation of 0.09 gms in

a pill. Test the 5% level of significance if the adjustments to the machine arerequired.

6. Sample of two types of electric bulbs were tested for length of life and the

following data was obtained.

Particulars type 1 type 2

No in sample 8 7

Mean of sample 1134 1024

S.D of sample 35 40

Test at 5% level whether the difference in the sample mean is significant?

7. Sample of two different types of bulbs were tested for length of life and the

following data were obtained.

Particulars type 1 type 2

Sample size 8 7

Sample mean 1234 1136


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77 567 568 S.D 36 40

Is the difference in the mean significant?

8. A physical fitness centre claim that their training programme results in a

weight loss. In order to test the claim 8 persons who undergone the training

programme are randomly selected. The weights are presented below.

Person: 1 2 3 4 5 6 7 8

Weights before: 145 200 160 185 164 175 189 148

Weights after: 143 190 165 183 160 176 176 190

What can be said about the claim at = 5%

9. 10 female respondents are exposed to an advertising campaign about a

fairness cream. The results are given below.

Respondent No: 1 2 3 4 5 6 7 8 9 10

Score before: 35 37 38 36 40 35 30 38 36 38

Score after: 40 38 39 36 44 45 35 37 40

45

Test whether the advertising campaign is successful at = 0.0510. A drug is given to 10 patients and the increment in their blood pleasure were

recorded to be 3, 6, -2, 4, -3, 4, 6, 0, 0, 2. Is it reasonable to believe that the

drug has no effect on change of blood pressure. = 5%

11.A certain stimulus administered to each of 12 patients resulted in the

following changes in blood pressure. 5, 3, -4, -1, 3, 0, -2, 1, 5, 0, 4, 8. Can it

be concluded that the stimulus will in general be accompanied by an increase

in blood pressure?

12. 8 students were given a test in mathematics and after one month coaching they

were given another test of similar nature. The following table gives increase in

their marks in the second test over the first.

Roll no: 1 2 3 4 5 6 7 8

Increase in marks: 4 -2 6 -8 12 5 -7 2

Do the marks indicate that the students have gained from coaching?


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77 567 568 CHI SQUARE TEST ()

1. The following table gives the observed and theoretical distributions

concerning a survey. To find the theoretical frequencies if mean has been

estimated, test whether it is a good fit.

Class Observed Theoretical

0-2 13 162-4 27 254-6 58 426-8 34 388-10 16 2310-12 12 16

2. To an observed frequency distribution, binomial distribution is fitted

after estimating P from the observed data. The observed and theoretical

frequencies are given below. Test whether binomial distribution is a good

fit.

Xi: 0 1 2 3 4 5 6 7 Total

Oi: 3 3 17 31 28 11 1 2 96

Ei: 1 7 19 27 24 13 4 1 96

3. A dice was thrown 90 times with the following results.

Face: 1 2 3 4 5 6

Frequency: 10 12 16 14 18 20

Are this data consistent with the hypothesis that the dice is unbiased?

4. 200 digits chosen at random from a set of tables the frequencies of the

digits are as follows.

Digits: 0 1 2 3 4 5 6 7 8 9

Frequency: 18 19 23 21 16 25 22 20 21 15Use chi square test to assess the correctness of the hypothesis that the

digits are distributed in equal number in tabled from which they were

chosen?

5. The theory predicts the proportion of the beans in the four groups A,B,C

& D should be 9:3:3:1. In an experiment 1600 beans the numbers in the


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77 567 568 four groups were 882, 313, 287, 118. Does the experimental result support

the theory?

6. The results of a survey to know the educational attainment among 100

persons randomly selected in a locality are given below.

Person/

Education Middle High Middle College Total

Male 10 15 25 50

Female 25 10 15 50

Total 35 25 40 100

Can you say that education depend on persons?

7. Test whether marriage adjustment scores and level of education are dependent at

= 0.05Level of education/ 1-25 26-45 46-70 71-100 Total

Marriage adjustment score

P.G 30 40 75 20 165

U.G 50 60 50 40 200

Others 60 30 20 20 130

Total 140 130 145 80 495

8. A movie producer is bringing out a new movie. In order to make out his

advertising campaign he wants to determine whether the movie will appeal

most to a particular age group or whether it will appeal to equal to all age

groups. The producer takes a random sample from persons attending a

preview of the movie and obtain the following results. Use chi square test

to determine conclusions.


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77 567 568 under

20

20-39 40-59 60 and

over

Total

Likedthemovie 320 80 110 200 710

Un liked the

movie

50 15 70 60 195

In different 30 5 20 40 95

Total 400 100 200 300 1000

9. A milk producers union wishes to test whether the preference pattern of

consumers for its products is dependent on income levels. A random

sample of 500 individuals gives the following data.

Product preferred

Income Product A Product B Product C Total

Low 170 30 80 280

Medium 50 25 60 135

High 20 10 55 85

Can you conclude that the preference pattern are independent of income

levels?

10. Among 79 students, 58 were hard working. Among these hard working

students, 52 passed in the examination. Whereas, among the non-hard

working students, only 5 passed. Apply chi-square test at 1% level of

significance to test whether hard work and pass are independent.

11. A sample of 300 students of under graduate and 300 students of P.G ofa university were asked to give their opinion towards the autonomous

colleges. 190 of U.G and 210 P.G students are favored for autonomous

status. Present the above facts in the form of a frequency table and test at

5% level that opinions of U.G students and P.G students on autonomous

status are independent?


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77 567 568 12. Out of 800 persons 25% were literate and 300 had travelled beyond the

limits of their districts. 40% of literate were among those who had not

travelled. Prepare a 2x2 table and test at 5% level of significance whether

there is any relationship between traveling and literacy?

13. In a survey of 200 boys, of which 75 were intelligent, 40 had skilled

fathers. While 85 of the un intelligent boys had un skilled fathers. Do

this figures support the hypothesis that the skilled fathers have intelligent

boys?

ANOVA - Analysis of Variance (F- TEST )

1. To assess the significance of possible variations in performance in a certain test between

the grammar schools in a city, a common test was given to a number of students taken at

random from the 5th class of four schools concerned. The results are given below. Make

an analysis of variance.

School A School B School C School D

8 12 18 13

10 11 12 9

12 9 16 12

8 14 6 16

1. 4 8 15

2. The following data gives the yields per hectare of a certain variety of paddy in aparticular type of soil treated with manures A,B and C. at 5% level, analyse the results formanure effects. Display your results in ANOVA table.

A 49 50 48 49B 48 48 49 47C 50 50 51 49

3. The price of a certain commodity was ascertained in each of the four towns A,B,C,D in

four quarters of a year. The prices are given below. Are the variations in prices between

different towns and in different quarters significant?

Quarters/Towns A B C D

1 60 50 60 50

2 50 40 65 50


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77 567 568 3 45 35 45 50

4 65 45 60 70

4. A tea company appoints four salesmen A,B,C and D and observes their sales in three

seasons-summer, winter and monsoon. The figures (in lakhs) are given in the following

table:

Seasons salesmen Total

A B C D

Summer 36 36 21 35 128Winter 28 29 31 32 120Monsoon 26 28 29 29 112

Total 90 93 81 96 360Do the salesmen significantly differ in performance?

5. The following data represent the number of units of production per day turned out by 5

different workers using 4 different types of machines:

Machine type

A B C D

1 44 38 47 36

2 46 40 52 433 34 36 44 32

Workers 4 43 38 46 33

5 38 42 49 39

Test whether the 5 men differ with respect to mean productivity?

6. The following are the details of sales affected by three sales persons in three door-to-door

campaigns.

Sales person sales in door to door campaign

A 8 9 5 10

B 7 6 6 9

C 6 6 7 5

Construct an ANOVA table and find out whether there is any significant difference in the

performance of the sales persons.


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77 567 568

7. The following table gives the weights (in kg) of 12 individuals selected from 4 different

sources situated in 3 different states. At 5% significance level test whether the difference

in weights due to sources or due to states is significant. Perform 2 way ANOVA and

display your results in a table.

States

Sources 1 2 3

A 61 62 63

B 63 64 63

C 68 69 69

D 66 67 68

CORRELATION ANALYSIS

1. Calculate karl pearsons correlation coefficient from the following data and

interpret its value.Roll No. of

Students 1 2 3 4 5Marks in

Accounts 48 35 17 23 47Marks in

Statistics 45 20 40 25 452. Making the use of data summarized below calculate coefficient of correlati on.

Also calculate probable error.Case A B C D E F G HX 10 6 9 10 12 13 11 9Y 9 4 6 9 11 13 8 4

3. Calculate karl pearsons coefficient of correlation from the following data taking100 and 50 as the assumed averages of X and Y respectively.X 104 111 104 114 118 117 105 108 106 100 104 105Y 57 55 47 45 45 50 64 63 66 62 69 61

4. The following data gives the sales and advertisement values. Calculate thecoefficient of correlation from the data by taking 44 and 26 as assumed means andinterpret its values.Sales 57 42 40 38 42 45 42 45 42 44 40 46Advert. 10 26 30 41 29 27 27 19 18 19 31 29


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77 567 568 5. The following table shows the amount of advertising expenses(X) and the sales

(Y) of 10 firms in Rs. 000s. Find the karl pearsons coeeficient of correlation andcomment.X 1.1 1.3 1.4 1.6 1.6 1.5 1.5 1.4 1.3 1.6Y 60 80 70 50 70 65 58 60 75 80

6. Calculate coefficient of correlation from the following data.X 500 1000 1500 2000 2500 3000 3500Y 100 200 300 400 500 600 700

7. From the following data compute the coefficient of correlation between X and Y.X Series Y Series

No. of items 15 15Arithmetic mean 25 18Squares of deviations from mean 136 138Summation of product of deviations of X and Y series from their respectiveArithmetic mean is 122.

8. A computer while calculating correlation coefficient between two variables X andY from 25 pairs of observations obtained the following results.N = 25, x = 125, y = 100, xy = 508, x = 650, y = 460.It was however discovered at the time of checking that two pairs of observationswere not correctly copied. They were taken as (6,4) and (8,6) while the correctvalues are (8,12) and (6,8). Prove that the correct value of the correlationcoefficient should be 2/3.

9. Calculate karl pearsons coefficient of correlation and find out probable error.X: 13-14, 14-15, 15-16, 16-17, 17-18, 18-19, 19-20, 20-21, 21-22Y: 39 40 43 43 36 39 48 44 56

10. The ranks of 10 students in two subjects of accountancy and auditing are as

follows.Accountancy: 3 5 8 4 7 10 2 1 6 9Auditing: 6 4 9 8 1 2 3 10 5 7What is the coefficient of rank correlation?

11. 10 competitors in a beauty contest are ranked by 3 judges in the following order.1st Judge: 1 6 5 10 3 2 4 9 7 82nd Judge: 3 5 8 4 7 10 2 1 6 93rd Judge: 6 4 9 8 1 2 3 10 5 7Use the rank correlation coefficient to determine which pair of judges has thenearest approach to common taste in beauty.

12. Calculate the correlation coefficient from the following data by the spearmansrank correlation method.


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77 567 568 Price of tea: 75 88 95 70 60 80 81 50Price of coffee: 120 134 150 115 110 140 142 100

13. Quotations of index no. of security prices of a certain joint stock company aregiven below.Year: 1 2 3 4 5 6 7Debenture Price: 97.8 99.2 98.8 98.3 98.4 96.7 97.1Share price: 73.2 85.8 78.9 75.8 77.2 87.2 83.8Using rank correlation method determine the relationship between debenture priceand share price.

14. Calculate the spearmans rank correlation coefficient in maths and statistics.Maths: 78 25 36 78 62 65 62 79 98 63Statistics: 51 84 91 60 62 68 60 47 53 51

15. Calculate rank correlation coefficient of the following data?Series A: 115 109 112 87 98 120 98 100 98 118Series B: 75 73 85 70 76 82 65 73 68 80

16. Following are the scores of 10 students in a class and their IQ.

Students: 1 2 3 4 5 6 7 8 9 10Scores : 35 40 25 55 85 90 65 55 45 50

IQ : 100 100 110 140 150 130 100 120 140110

17. Coefficient of rank correlation between marks in statistics and maths obtainedby a group of students is 2/3 and the sum of squares of differences in ranks is 55.Calculate the number of observations or value of n?

18. In a bivariate samples the sum of squares of difference between the ranks ofobserved values of two variables is 33. The coefficient of correlation betweenthem is 0.8. calculate no of observations.

REGRESSION ANALYSIS

1. You are given data relating to purchase and sales. obtain the two regression

equations and estimate likely sales when purchase is equal to 100.Purchase: 62 72 98 76 81 56 76 92 88 49Sales : 112 124 131 117 132 96 120 136 97 85

2. The following table shows the ages (X) and BP (Y) of 8 persons obtain tworegression equations and find the expected BP of a person who is 49 years old.X: 52 66 45 36 72 65 47 25


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77 567 568 Y: 62 55 51 25 79 43 60 33

3. In a correlation study the following values are obtained.Particulars X YMean 65 67S.D 2.5 3.5Coefficient ofCorrelation (r) 0.8Find the two regression equations that are associated with the above values.

4. We are given the following data.Particulars X YArithmetic mean 36 85S.D 11 8Coefficient ofCorrelation (r) 0.66Find the two regression equations and estimate the value of X when Y is 75.

5. In a partially established laboratory record of an analysis of correlation data, thefollowing results are only available.Variance of X = 98X 10Y + 66 = 0

40X 18Y = 214Find on the basis of above informationa. The mean values of X and Y.

b. Coefficient of correlation between X and Y.c. Standard deviation of Y

6. For certain X and Y series which are correlated the two lines of regression are5X 6Y + 90 = 0, 15X 8Y 130 = 0. Find the means of two series and thecorrelation coefficient.

7. Two random variables have the regression equations 3X + 2Y 26 = 0, 6X + Y 31 =0. Find the mean values and correlation coefficient between X and Y. if thevariance of X = 25, Find the standard deviation of Y from the date given above.

TIME SERIES ANALYSIS

1. Calculate 3 yearly moving averages of the production figures given below. Also

calculate short term fluctuations.Year: 1985 86 87 88 89 90 91 92 93 94 95 96 97 98 99Production: 15 21 30 36 42 46 50 56 63 70 74 82 90 95 102

2. Using 3 yearly moving averages determine the trend and short term fluctuations.


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77 567 568 Year: 1987 88 89 90 91 92 939 94 95 96ProductionIn tons : 21 22 23 25 24 22 25 26 27 26

3. Find the trend for the following series using 4 yearly moving average.Year: 1994 95 96 97 98 99 00 01 02 03 04Production: 614 615 652 678 681 655 717 719 708 779 757

4. Find the five years weighted moving average with weights 1,2,2,2,1 respectivelyfor measuring the trend of the following time series.Year: 1974 75 76 77 78 79 80 81 82Sales: 2 6 1 5 3 7 2 6 4

5. For the below data calculate 4 yearly weighted moving average with weights1,2,2,1.Year: 1974 75 76 77 78 79 80 81 82Slaes: 2 6 1 5 3 7 2 6 4

6. Calculate the equation of a straight line trend for the following data.Year: 1974 75 76 77 78Sales: 35 56 79 80 40

7. Fit a straight line by the method of least squares and estimate the values for 1984

and 1986.Year (X): 1978 79 80 81 82Y : 80 85 87 93 100

8. Fit a straight line trend by the method of least squares and estimate the productionin 1981.Year: 1985 86 87 88 89 90Production: 15 18 16 18 20 19

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