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)
- Write the formula for Yule’s Coefficient of partial association between A and B with C.
- What are the methods of association?
- State the addition theorem for two events.
- Define random variable.
- What is the difference between small sample and large sample test.
- Define type – II error.
- Write down the formula for F-test.
- Explain Error sum of squares.
- What are the various types of control charts?
- Give the control limits for R chart.
SECTION – B
Answer any FIVE of the following: (5 X 8 = 40)
- 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?
- For two attributes A and B, we have:
(AB)= 16, (A) = 36, (αβ) = 10, N = 70. Calculate Yule’s coefficient of association and Colligation
- 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 |
- Explain the method of analysis of variance for One way classification.
- 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.
- 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.
- 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.
- 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)
- 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 |
- b) State and prove Multiplication theorem of probability.
- 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?
- 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.
- 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.
- 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 |
- 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.