LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

B.Sc. B.Com., DEGREE EXAMINATION – ECO. & COMM.

FOURTH SEMESTER – APRIL 2012

# ST 4205/4200/3202/3200 – ADVANCED STATISTICAL METHODS

Date : 19-04-2012              Dept. No.                                        Max. : 100 Marks

Time : 1:00 – 4:00

SECTION – A

Answer ALL the questions:                                                                                     (10 X 2 = 20)

1. Write the formula for Yule’s Coefficient of partial association between A and B with C.
2. What are the methods of association?
3. State the addition theorem for two events.
4. Define random variable.
5. What is the difference between small sample and large sample test.
6. Define type – II error.
7. Write down the formula for F-test.
8. Explain Error sum of squares.
9. What are the various types of control charts?
10. Give the control limits for R chart.

SECTION – B

Answer any FIVE of the following:                                                                        (5 X 8 = 40)

1. Out of 5 lakh literates in a particular district of India, the number of criminals was 2000. Out       of 50 lakh illiterates in a particular in the same district, number of criminals was 80,000. On       the basis of these figures, do you find any association between illiteracy and criminality?

1. For two attributes A and B, we have:

(AB)= 16, (A) = 36, (αβ) = 10, N = 70. Calculate Yule’s coefficient of association and          Colligation

1. From the table given below, test whether the colour of son’s eyes is associated with that of father’s eyes by using chi-squares test at 5% level.

 Eyes Colour in Sons Eyes Colour in Fathers Not light Light Not light 230 148 Light 151 471

1. Explain the method of analysis of variance for One way classification.

1. The following data refers to visual defects found during the inspection of the first 10 samples of size 50

Each from a lot of two-wheelers manufactured by an automobile company:

 Sample No. 1 2 3 4 5 6 7 8 9 10 No. of Defectives 4 3 2 3 4 4 4 1 3 2

Draw the control chart for fraction defectives and state your conclusion.

1. The following table shows the distribution of number of faulty units produced in a single       shift in a factory. The data is for 400 shifts.

 No. of faults 0 1 2 3 4 No. of shifts 138 161 69 27 5

( value of e-1=0.3679)

Fit a Poisson distribution to the given data.

1. There are 4 boys and 2 girls in room-I and 5 boys and 3 girls in room-II. A girl from one of       the two rooms laughed loudly. What is the probability that the girl who laughed was from       room-I and room-II.
2. The height of ten children selected at random from a given locality had a mean 63.2 cms and variance 6.25 cms. Test at 5% level of significance the hypothesis that the children of the       given locality are on the average less than 65 cms in all.

SECTION – C

Answer any TWO of the following:                                                                     (2 X 20 = 40)

1. a) Find the value of ’ K’ and also find Mean and Variance.
 X 0 1 2 3 P(X) 1/8 3/8 K 1/8

1. b) State and prove Multiplication theorem of probability.
2. a) In a random sample of 500 persons from town A, 200 are found to be consumers of          wheat. In a sample of 400 from town B, 220 are found to be consumers of wheat. Do         these data reveal a significant difference between town A and town B as far as the          proportion of wheat consumers is concerned?
3. b) The following data show weekly sales before and after recognition of the sales organization.

 Sales before 14 18 13 19 15 14 16 18 Sales after 21 18 17 23 21 18 22 22

Test whether there is any significant difference in sales before and after recognition of the

Sample company.

1. a) The following are the number of defects noted in the final inspection of 20 bales of woolen cloth:

3, 1, 2, 4, 2, 1, 3 ,5, 2 ,1, 5 , 9, 5, 6, 7, 3, 4, 2, 1,6.

Draw C-chart and state whether the process is under control or not.

1. b) Draw the control chart for Mean and comment on the state of control from the given             data:
 Sample number Observations   1              2                3 1 50 55 52 2 51 50 53 3 50 53 48 4 48 53 50 5 46 50 44 6 55 51 56

1. The following table gives the yield on 20 sample plot under four varieties of seeds:

 A B C D 20 18 25 24 21 20 28 30 23 17 22 28 16 15 28 25 20 25 32 28

Perform a One-way ANOVA, using 5% level of significance.

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LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

THIRD SEMESTER – NOVEMBER 2012

# ST 3105 – INTRODUCTION TO STATISTICS

Date : 07/11/2012             Dept. No.                                        Max. : 100 Marks

Time : 9:00 – 12:00

SECTION – A

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

1. Distinguish between classification and tabulation.
2. What are the different types of diagrams?
3. State any two methods of probability sampling.
4. State merits and demerits of mean
5. Find the median of the following data:

84 , 91, 72 , 68, 87 ,78,

1. Define dispersion. What are the measures of dispersion?
2. The average rainfall of a city from Monday to Saturday is 0.3 inches. Due to heavy rainfall on Sunday the average rainfall of the week increased to 0.5 inches. Find the rainfall on Sunday.
3. What are the properties of correlation coefficient.
4. What are the various components of a time series?
5. State Yule’s coefficient of variation.

SECTION – B

Answer any FIVE questions:                                                                            (5 X 8  =  40 Marks)

1. What are the limitations of statistics?
2. Write short notes of the following:

(a)   Cluster Sampling   (b) Random sampling.

1. The mean of 200 items is 60.Later on it was discovered that one of the observation with value 182 was wrongly taken as 82 . Find the correct mean.

1. Calculate the harmonic mean for the following :
 x 10 12 14 16 18 20 F 7 9 10 4 3 6

1. Compute mean deviation abut median from the following data:
 X 0-10 10-20 20-30 30-40 40-50 50-60 60-70 F 8 12 17 14 9 7 4

1. Calculate Karl Pearson`s coefficient of correlation from the following data:
 Demand (kg) 95 96 98 110 115 125 130 140 Price (Rs.) 25 26 23 27 30 33 35 40

1. Calculate the trend values for the following data using 3 yearly moving average
 Year 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 Sales 26 27 29 32 35 38 35 34 30 32

18.Out of 900 persons, 300 were literates and  400 had travelled beyond the limits of their district.100 of

the literates were among those who had not travelled.  Is there any relationship between literacy and

travelling?

SECTION – C                                   (2 X 20  =  40 Marks)

19.(a) Draw a histogram and frequency polygon on the basis of the following data:

 Mid value 18 25 32 39 46 53 60 Frequency 10 15 32 42 26 12 9

(10)

19.(b) Calculate the mean, median and mode from the following data and verify the empirical  relationship.

 C.I 1-10 11-20 21-30 31-40 41-50 51-60 61-70 71-80 81-90 91-100 F 5 9 12 15 10 9 7 5 6 4

(10)

20.(a) The scores of two players A and B in 12 rounds are given below:

 A 84 87 80 85 88 87 89 98 95 94 92 91 B 87 84 80 90 85 94 96 82 85 84 86 81

(10)

Identify the better player and the more consistent player.                                                       (10)

20.(b) From the following data  compute Bowley’s coefficient of skewness.

 Marks 40 – 50 50 – 60 60 -70 70 – 80 80 – 90 No.of students 20 25 28 23 15

(10)

1. Calculate Skewness and kurtosis for the following distribution and interpret them.
 Marks 0-10 10-20 20-30 30-40 40-50 50-60 Frequency 10 15 20 27 14 12

(20)

22.(a) Fit a straight line trend for the following data by the method of least squares. Also estimate the trend value for  the  Year 2005.

 Year 1996 1997 1998 1999 2000 2001 Production 12 10 14 15 16 20

(10)

22.(b) Calculate the seasonal indices from the following data using the simple average method.

 Year 1stquarter 2ndquarter 3rdquarter 4thquarter 1974 72 68 80 70 1975 76 70 82 74 1976 74 66 84 80 1977 76 74 84 78 1978 78 74 86 82

(10)

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