LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

M.Com DEGREE EXAMINATION – COMMERCE

AT 21

FIRST SEMESTER – NOV 2006

CO 1810 – ADVANCED BUSINESS STATISTICS-I

 

 

Date & Time : 02-11-2006/1.00-4.00     Dept. No.                                                          Max. : 100 Marks

 

 

SECTION – A

Answer ALL the questions                                                                (10 x 2 = 20 marks)

 

1. Give the formula for Geometric mean.
2. Define Skewness
3. State the three axioms of probability.
4. Give the expression for expectation in the case of random variables X.
5. State any two properties of normal distribution.
6. Define null hypothesis
7. Define probability of Type-I error
8. Give the test statistic for testing equality of two means when n>30?
9. Explain the non-parametric test
10. Define probability

SECTION – B

Answer any FIVE questions                                                              (5 x 8 = 40 marks)

11.Calculate arithmetic mean from the following data

Marks scored:              0-10     10-20   20-30   30-40   40-50   50-60

No. of students:            5          10         25        30        20       10

 

12. A perfect dice is tossed twice. Find the probability of getting (i) a total of 9 (ii) a total is

multiple of 3 (iii) a total of 5 (iv) a multiple of 6.

 

13. Two boxes contain 12 white and 18 black and 15 white and 25 black balls respectively. One

box was taken at random and a ball was taken from the same.  It is a black ball.  What is the

probability that it is from the first box?

 

14. A random variable x has the following probability function.

X         0          1          2          3          4          5          6          7

P(x)     0          k          2k        2k        3k        k²            2k²    7k²+k

• Find k (ii) P(x<6) (iii) P (x ³6).

15. Five coins are tossed 3,200 times, find the frequencies of the distribution of heads and tails

and tabulate the results in a binomial.

 

 

 

16. A college conducts both day and night classes intended to be identical. A sample of 100 day

students yields examination results as   = 72,  , and a sample of 200 night students

as = 73.9 and   Are the two means statistically equal at 10% level?

 

17. Two sets of ten students selected at random from a college were taken: one set was given

memory test as they were and the other was given the memory test after two weeks of

training and the scores are given below:

Set A:	10	8	7	9	8	10	9	6	7	8
Set B:	12	8	8	10	8	11	9	8	9	9

Do you think there is nay significant effect due to training? (null and alternative

hypothesis should be stated (Given t = 2.10 at df =18, a = 0.05).

 

18. 200 digits are chosen at random from a set of tables. The frequencies of the digits are as

follows:

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

 

Frequency:      18        19        23        21        16        25        22        20        21        15

Use x² test to assess the correctness of the hypothesis that the digits were distributed in

equal numbers in the tables from which they were chosen. (df @ 5% x² =16.92)

 

SECTION – C

Answer any TWO questions                                                             (2×20=20 marks)

 

19. a) Three urns contain respectively 3 green and 2 white balls, 5 green and 6 white balls and 2 green and 4 white balls. One ball is drawn from each urn.  Find the expected number of white balls drawn out.                                                             (12 marks)

 

1. b) Two cards are drawn at random with replacement from a box which contains four

cards numbered 1, 1, 2 and 2.  Let X denote the sum  if the numbers shown on the

two cards.  Find the distribution of X.  Also find E(X) and var (X).       (8 marks)

 

20. a) After correcting the proofs of the first 50 pages of a book, it is found that on the

average there are 3 errors per 5 pages.  Use Poisson probabilities and estimate the

number of pages with 0,1,2,3 errors in the whole book of 1000 pages (e^-6 = 5488).

(12 marks)

 

 

20. b) Three samples below have been obtained from normal populations with equal variances.

Test the hypothesis at 5% level that the population means are equal.

 

8   10   7   14   11

7   5   10   9   9

12   9   13   12   14

 

The table value of Fat 5% level  = 17 is 3.88. (use One Way ANOVA)            (8 Marks)

 

21 .a) Find the equation of regression lines for the following data.

X	25	28	35	32	36	36	29	38	34	32
y	43	46	49	41	36	32	31	30	33	39

 

(12marks)

 

1. b) Two salesmen A and B are working in a certain district. From a sample survey

conducted by the Head office, the following results were obtained.  State whether

there is any significant difference in the average sales between the two salesmen:

	A	B
No. of sales Average sales (in Rs.) Standard Deviation (in Rs.)	20 170 20	18 205 25

(8 marks)

 

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LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

RO 38

M.Com. DEGREE EXAMINATION – COMMERCE

FIRST SEMESTER – APRIL 2008

    CO 1810 – ADVANCED BUSINESS STATISTICS-I

 

 

 

Date : 05/05/2008            Dept. No.                                        Max. : 100 Marks

Time : 1:00 – 4:00

PART A

Answer all questions:                                                                                           (10 x 2 = 20)

1. Define Harmonic mean?
2. Give formula for β1?
3. Explain Type I error?
4. Frame equation x on y?
5. What do you mean by Pascal’s Triangle?
6. Discuss the Addition theorem?
7. Give any two properties of Bionomical distribution?
8. Differentiate large samples from small samples?
9. What is ANOVA?
10. Analyse the term sign test?

PART B                   

Answer any five questions:                                                                             (5 x 8 = 40)

1. Explain the BAYES’ Theorem?
2. Discuss the role of poission distribution?
3. For a random sample of 10 persons, fed on diet A, the increased weight in pounds in a certain period were:

For  another random sample of 12 persons, fed on diet B, the increase in the same period  were:

Test whether the diets A and B differ significantly as regards their effect on increase in weight.

Given the following:

1. A sample analysis of examination results of 500 students was made. It was found that 220 students had failed, 170 had secured a third class, 90 were placed in second class and 20 got a first class. Are these figures commensurate with the general examination result which is the ratio of 4: 3: 2: 1 for the various categories respectively (the table value of  for 3 d.f. at 5% level of significance is 7.81)?
2. From the following data, obtained from a sample of 1000 persons, calculate the standard error of the mean.

If the average of the population was Rs. 42, what conclusion can you arrive at about the reliability of the sample?

1. A bag contains 4 white and 6 black balls. Two balls are drawn at random. What is the probability that (a) both are white, (b) both are black, (c) one white and one black?

 

1. Find the Median for the following frequency distribution.

 

1. Use the sign test to see if there is a difference between the number of days until collection of an account receivable before and after a new collection policy. Use the 0.05 significance level.

Before:   30   28   34   35   40   42   33   38   34   45   28   27   25   41   36

After:     32   29   33   32   37   43   40   41   37   44   27   33   30   38   36

 

PART C

Answer any two questions:                                                                   (2 x 20 = 40)

 

1. a. A book has 700 pages. The number of pages with various numbers of misprints is recorded below. At 5% significant level are the misprints distributed according to Poisson law?

(14 marks)

6. A problem in statistics is given to five students A, B, C, D and E. Their chances of solving it are 1/2, 1/3, 1/4, 1/5, and 1/6. What is the probability that the problem will be solved?

(6 marks)

1. a. Assume the mean height of soldiers to be 68.22 inches with a variance of 10.8 inches. How many soldiers in a regiment of 1,000 would you expect is be over six feet tall?                                                                                                                                                                                                                             (6 marks)

1. The yield of four strains of Grallipoli wheat planted in five randomized blocks in kgs per plot is given below:

Strains	Blocks
		1	2	3	4	5
	A	32	34	34	35	36
	B	33	33	36	37	34
	C	30	35	35	32	35
	D	29	22	30	28	28

Test for differences between blocks and differences between strains. Subtract 30 from numbers  (4, 12) TV of F = 5.91.(3, 12) TVof F = 8.74.           (14 marks)

1. If 10% of the screws produced by an automatic machine are defective, find the probability that of 20 screws selected at random, there are

• Exactly two defectives
• At the most three defectives
• At least two defectives; and
• between one and three defectives (inclusive)

Find also the mean, variance and skewness of the number of defective screws. (use binomial          distribution)

 

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LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

QB 19

M.Com. DEGREE EXAMINATION – COMMERCE

FIRST SEMESTER – November 2008

    CO 1810 – ADVANCED BUSINESS STATISTICS-I

 

 

 

Date : 11-11-08                 Dept. No.                                        Max. : 100 Marks

Time : 1:00 – 4:00

SECTION: A

Answer All Questions:                                                                                       (10 x 2 = 20)

• What precautions would you take before using secondary data?
• What is a Questionnaire? How does it differ from a Blank Form?
• Give mean 25, Mode 24, the median would be————?
• If β2 = 3, the distribution called—————-?

If  β2 >3, the distribution called—————-?

If  β2 <3, the distribution called—————-?

• What is meant by Time Series Analysis?
• The probability that a boy will get a scholarship is 0.9 and that a girl will get 0.8. What is the probability that at least one of them will get the scholarship?
• What is χ2 test? State the uses of χ2
• What are non parametric tests? In what ways are they different from parametric tests?
• Explain Type II error?
• Draw Pascal’s Triangle for five numbers of known values?

SECTION – B

Answer any five only:                                                                                    (5 x 8 = 40)

11) Write short notes on the following terms

• Mutually exclusive events
• Independent and dependent events
• Equally likely events
• Complementary events

12) What is a Control Chart? Show a typical Control Chart. How are Control Charts

for Mean and Range constructed when Standard are given?

13) The following are some of the particulars of the distribution of weight of boys

and girls in a class:

Boys                            Girls

Number                                   100                              50

Mean Weight                          60 Kg                         45 Kg

Variance                                  9                                 4

Find the standard deviation of the combined data.

Which of the two distributions is more variable?

14) The following table relates to the tourist arrivals (in millions) during 1997 to 2003

India:

Years:                         1997    1998    1999    2000    2001    2002    2003

Tourists arrivals:           18        20        23        25        24        28        30

(In millions)

 

Fit a straight line trend by the method of least squares and estimate the number of

tourists that would arrive in the year 2009.

15) A) find out n, p, q when the mean of a binomial distribution is 99 and Standard

Deviation is 9.

24. B) In an intelligent test administered to 1000 students the average score was 42 and standard deviation 24. Find ( a) the number of students exceeding a score of 50, (b) the number of students lying between 30 and 54, and (c) the value of score exceeded by the top 100 students.

16) A) The sales manager of large company conducted a sample survey in states A

and B taking 400 samples in each case. The results were:

 

Average Sales Standard Deviation	Stat A	Stat B
	Rs.2500	Rs.2200
	Rs.400	Rs.550

 

Test whether the average sales is the same in the two states at 1% level.

 

650. B) A sample of ten house owners is drawn and the following values of their incomes are obtained. Mean Rs.6000, standard deviation Rs.650. Test the hypothesis that the average income of house owners of the town is Rs.5500. ( The table value of t for 9 d.f at 5% level = 2.262)

 

• Perform a Two- way ANOVA on the data given below:

	TREATMENT –  I
TREATMENT II		I	II	III
	I	30	26	38
	II	24	29	28
	III	33	24	35
	IV	36	31	30
	V	27	35	33

 

Use the coding method, subtracting 30 from the given numbers.

 

• The nicotine contents of two brands of cigarettes, measured in milligrams, was found to be as follows:

 

Brand A	2.1	4.0	6.3	5.4	4.8	3.7	6.1	3.3
Brand B	4.1	0.6	3.1	2.5	4.0	6.2	1.6	2.2	1.9	5.4

 

Test the hypothesis, at 0.05 level of significance, that the average nicotine contents of the two brands are equal against the alternative that they are unequal by applying Mann-Whitney U test.

 

SECTION – C

Answer any two only:                                                                                        (2 x 20 = 40)

 

• Find out the two regression equations from the following distribution.

 

Sales (Rs.’000)	Profit (in Rs.’000)
	0 – 10	10 – 20	20 – 30	30 – 40
50 – 70	4	3	5	8
70 – 90	6	7	4	9
90 – 110	5	3	5	6
110 – 130	3	2	6	4

 

Calculate, 1) The coefficient of correlation. 2) The profit corresponding to sales of Rs.1, 50,000.

• Ten competitors in a beauty contest are ranked by three judges in the following order:

1st Judge	1	5	4	8	9	6	10	7	3	2
2nd Judge	4	8	7	6	5	9	10	3	2	1
3rd Judge	6	7	8	1	5	10	9	2	3	4

 

 

 

 

 

 

 

Use the rank correlation coefficient to discuss which pair of judges has the nearest approach to common tastes in beauty.

 

• In the accounting department of a bank 100 accounts are selected at random and examined for errors. Suppose the following results have been obtained:

 

No. of  errors	0	1	2	3	4	5	6
No. of accounts	35	40	19	2	0	2	2

 

 

 

 

On the basis of this information can it be concluded that the errors are distributed according to the Poisson probability law? Test the goodness of fit by χ2.

 

 

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      LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

M.Com. DEGREE EXAMINATION – COMMERCE

KP 39

FIRST SEMESTER – April 2009

CO 1810 – ADVANCED BUSINESS STATISTICS-I

 

 

 

Date & Time: 30/04/2009 / 1:00 – 4:00       Dept. No.                                                       Max. : 100 Marks

 

 

SECTION: A

Answer All Questions:                                                                                       10 x 2 = 20

 

• Indicate whether the following are True or False:
  1. A listing of all population units is called a frame.
  2. One of the biggest problems in survey is that of non – response.
• What is a questionnaire?
• What is Skewness?
• Indicate whether the following are True or False:
  1. In a symmetrical distribution, Mean = Median = Mode.
  2. β2 is a measure of Kurtosis.
• What are the components of Time Series?
• Three perfect coins are tossed together. What is the probability of getting at least one head?
• What is meant by theoretical frequency distribution?
• What do you mean by the statistical quality control charts?
• What are non parametric tests?
• Define Type I and Type II errors.

 

SECTION – B

Answer any five only:                                                                              5 x 8 = 40

 

• What is a Control Chart? Show a typical Control Chart. How are Control Charts for Mean and Range constructed when Standard are given?

 

• What are the basic conditions for the application of Chi – Square test?

 

13) Write short notes on the following terms

• Mutually exclusive events
• Independent and dependent events
• Equally likely events
• Complementary events

 

• Ten students are selected at random from a college and their heights are found to be 100, 104, 106, 110, 118, 120,122,124,126 and 128 cms. In the light of these data discuss the assumption that the mean height of the students of the college is 110cm.

The table value of t at 5% level for 8 df is 2.306 and for 9 df is 2.262 and 10 df is 2.228 for a two tailed test.

 

• The following data is collected on two characteristics:

Particulars                   Smokers          Non – Smokers

Literate                             83                           57

Illiterate                            45                           68

Based on this can you say that there is no relation between the habit of smoking and literacy.

 

16) The following table relates to the tourist arrivals (in millions) during 1997 to 2003

India:

Years:                         1997    1998    1999    2000    2001    2002    2003

Tourists arrivals:           18        20        23        25        24        28        30

(In millions)

 

Fit a straight line trend by the method of least squares and estimate the number of

tourists that would arrive in the year 2009.

 

17) The following are some of the particulars of the distribution of weight of boys

and girls in a class:

Boys                            Girls

Number                                   100                              50

Mean Weight                          60 Kg                         45 Kg

Variance                                  9                                 4

Find the standard deviation of the combined data.

Which of the two distributions is more variable?

 

• The following data is relating to the units produced per day by 4 workers in 5 machines of different types. Test whether the four workers differ in terms of mean productivity and test whether the mean productivity is the same for the five different machines. Perform Two Way

Workers	Machine Type
	1	2	3	4	5
1	10	9	8	12	10
2	11	9	8	12	10
3	13	10	9	10	11
4	14	9	8	12	12

 

SECTION – C

Answer any two only:                                                                                  2 x 20 = 40

 

• The following are the numbers of hours which 10 students studied for an examination and the scores they obtained:

No. of hours Studied (x)	8	5	11	13	10	5	18	15	2	8
Score (y)	56	44	79	72	70	54	94	85	33	65

Calculate rank correlation; also test at  0.01 level of significance whether the value obtained is significant.

 

• School children taking coaching in three private schools A,B and C secure the following scores out of 100.

No of Children	1	2	3	4	5	6	7	8	9	10
School – A	33	38	39	48	58	70	61	41	45	49
School – B	32	15	87	32	22	63	56	57	44	—
School – C	55	68	27	88	46	52	76	—	—	—

Test the hypothesis that the students in the three private schools have identical distribution of scores at significance level at 1 %. Apply H test.

 

• The life time of electric bulbs for a random sample of 10 from a large consignment gave the following data:

Item	1	2	3	4	5	6	7	8	9	10
Life in ‘000 hours	4.2	4.6	3.9	4.1	5.2	3.8	3.9	4.3	4.4	5.6

Can we accept the hypothesis that the average life time of bulbs is 4000 hours.

 

 

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