01.792 No. of Printed Pages: 16 lAST-OIl
BACHELOR'S DEGREE PROGRAMME
Term-End Examination
December, 2015

(APPLICATION ORIENTED COURSE) AST-01 STATISTICAL TECHNIQUES
Time: 2 hours Maximum Marks: 50 (Weightage
Note: Question no. 7 is compulsory. Attempt any four questions from questions no. 1 to 6. Calculidors are not allowed. You may want to use some values given at the end.

1. A manufacturer of pins knows that on an average of his product is defective. He sells pins in boxes of 100 and guarantees that not more than 4 pins will be defective. What is the probability that the box will meet the guaranteed quality?

(ii) will not meet the guaranteed quality? The results of a survey to know the educational attainment among 100 people randomly selected in a locality are given below:

Middle High School College
Male 10 15 25
Female 20 15 15

Test the hypothesis that the level of education depends upon gender. Use level of significance.

2. Compute the appropriate regression equation for the following data:

X Y
(Independent (Dependent
Variable) Variable)
2 18
4 12
5 10
6 8
8 7
11 5

Also find the correlation coefficient between X and Y and infer about the relationship between X and Y.

Assuming that it is true that 2 in 10 industrial accidents are due to fatigue, find the probability that
exactly 2 of 8 industrial accidents will be due to fatigue;

(ii) at least 2 of8 industrial accidents will be due to fatigue.

3. 20% of all students at a university are graduates and 80% are undergraduates. The probability that a graduate student is married is 0.5 and the probability that an undergraduate student is married is 0.1. One student is selected at random. What is the probability that he/she is married

(ii) the student is a graduate if he/she is found to be married?

An editor of a publishing company calculates that it requires 11 months on an average to complete the publication process with a standard deviation of 4 months. He believes that the distribution of publication time is well described by a normal distribution. Determine out of 190 books that he will handle this year, how many will complete the process in less than one year in less than 9 months.

4. The following data represents the sale (Rs. 1,000) per month of 3 brands of a toilet soap allocated among 3 cities

<img src='./qimages/12812-4a.jpg'>

At level of significance, test whether the mean sales of 3 brands are equal.

A sample of 25 items is selected from a very large shipment. It is found to have a mean weight of 310 gm and standard deviation equal to 9gm. State and compute the 95% confidence limits for the population mean weight.

5. Do the forecasting by applying simple exponential smoothing procedure to the following data. Take w 0.15

Year No. of Branches
2001 5
2002 3
2003 3
2004 4
2005 3
2006 6
2007 4

Consider a random sample of two industries from a population of 5 industries having yearly turnover as follows:

Industry Turnover (in lakhs)
1 2000
2 2400
3 1800
4 3000
5 2600

Enumerate all possible samples of size two and show that the sample mean gives an unbiased estimate of population mean.

6. 20 samples each of size 10 were inspected. The number of defectives detected in each of them is given below:


Find the control limits for the number of defectives and establish quality standards for the future. Plot the graph and interpret.


There are 50 fields in a village, sown with wheat and each is divided into 8 plots of equal size. Out of the 50 fields, 5 are selected by SRSWOR method. Again from each selected field, 2 plots are chosen by SRSWOR method. The yield in kg/plot recorded is as given in the following table

Selected Field Plot Plot -II
1 4.16 4.76
2 5.40 3.52
3 4.12 3.73
4 4.38 5.67
5 5.31 2.59

Estimate the average yield of all the 50 plots.

7. Which of the following statements are True and which are False? Justify. 5x2=10 Type II error is same as critical value. For a uniform distribution with

f(x) 0 x 1.5 If A and B are independent events, then

(A n U n U B. There is no difference between parameter and statistic if the sample is drawn from a population with known distribution. Yearly data in a time series are dependent on the effects of seasonal variations.

Some values for use, if required :

<img src='./qimages/12812.jpg'>