**IGNOU BCA SOLVED ASSIGNMENT 2017-18BCS-040 Statistics Techniques**

**QUESTIONS SOLVED IN ASSIGNMENT:**

1. In a study on the Per capita Income for a particular year in a city, the following weekly

observations were made.

Per Capita Income (Rs.) -(1K=1000)

14K-15K 15K-16K 16K-17K 17K-18K 18K-19K 19K-20K

Number of Weeks 5 10 20 9 6 2

Draw a histogram and a frequency polygon on the same scale

2. Do you find any correlation between ages and playing habits of the students, whose distribution

according to age groups is given in the following table

Age of groups(Years) 15-16 16-17 17-18 18-19 19-20 20-21

Number of Students 200 270 340 360 400 300

Number of Regular players 150 152 170 180 180 120

3. Data are given below shows statistics viz. standard deviation & average marks secured by

students, in the examination of subject A and B

SUBJECT A SUBJECT B

MEAN MARKS 36 85

STANDARD DEVIATION 11 8

Assuming the Coefficient of correlation between A and B = ±0.66

Perform the following tasks:

i) Determine the two equations of regression

ii) Calculate the expected marks in A corresponding to 75 marks obtained in B.

4. Calculate 2-sigma and 3-sigma upper and lower control limits for means of samples 4 and

prepare a control chart for a drilling machine, which bores holes with a mean deviation of

0.5230 cm and a standard deviation of 0.0032 cm.

5. Construct 5- yearly moving averages from the following data

YEAR 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012

SALE 105 107 109 112 114 116 118 121 123 124 125 127 129

6. In 120 throws of a single dice, following distribution of faces (F0) was observed.

FACES 1 2 3 4 5 6 TOTAL

F0 30 25 18 10 22 15 120

From the given data, verify that the hypothesis “dice is biased” is acceptable or not.

7. a) If X is a Poisson variate and p(X = 3)> p(X = 2) then find the minimum value of mean.

b) Ten individuals are chosen at random, from a normal population and their weights (in kg) are found

to be

63, 63, 66, 67, 68, 69, 70, 70, 71 and 71. In the light of this data set, test the claim that the

mean weight in population is 66 kg at 5% level of significance.

8. From a population of 20,000 observations, a sample of 500 observations is selected. Calculate

the standard error of sample mean if the population standard deviation equals 20.

9. A random sample of 700 units from a large consignment showed that 200 were damaged. Find

95% confidence interval for the proportion of damaged unit in the consignment.

10. Two floppies are selected at random without replacement from a box containing 7 good and 3

defective floppies. Let A be the event that the first floppy drawn is defective, and let B be the

event that the second floppy drawn is defective.

(i) Find the conditional probabilities P(B/A) and P(B/AC)

(ii) Show that P(B) = P(B/A). P(A) + P(B/AC) P(AC) = P(A).

(iii) Where Ac = complement of event A.

14. Explain the following with the help ofan example :

(a) Goodness of fit test

(b) Test of Independence

(c) Criteria for a good estimator

(d) Time Series analysis and its categories

(e) t – distribution

(f) F – distribution

(g) CHI – SQUARE distribution

15. Differentiate between the following (any two) :

(a) Linear systematic sampling & circular systematic sampling.

(b) Z – Test & T – Test

(c) Correlation and Regression

16. List the advantages and disadvantages of using a sampling approach instead of a census approach for studying the characteristics of data.. Explain any two of the following sampling approaches:

(a) Cluster sampling

(b) Stratified sampling

(c) Systematic sampling

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