# Pak Study® Library

Forum

### Section – A

1. Attempt any FIVE parts: 5 i) Name the Basic Principles of EXPERIMENTAL DESIGN. ii) What is S.E of ESTIMATE? iii) Define RATES and RATIOS. iv) What is AGE SPECIFIC BIRTH RATE? v) What is EXPERIMENTAL ERROR?

vi) Define CHI SQUARE DISTRIBUTION. vii) What is WILCOXON SIGNED RANK TEST?

### Section – B

2. a) Discuss the Procedure of Analysis of VARIANCE in CR Design. 3

b) The following statistic are obtained from the data for the number of packages of 5 popular brands of Cigarettes A, B, C, D, E sold by a super market on 8 randomly selected days. 5

 Brand A B C D E Sample Mean -Xj 30 26 42 37 33 Sample Biased Variance S 2 j 93.5 77.75 76.5 75.5 50

Perform Analysis of variance and determine whether or not the 5 brands sell, on the average, the same number of Cigarettes at this super market.

1. a) Derive the Partition of degree of freedom for Analysis of variance in two way classification. 3 b) Carry out Analysis of Variance for the following Latin Square Design. Let á=0.05 5

1. a) We wish to conduct a field experiment to test the yielding ability of 6 varieties of wheat and have available area of land for 30 plots. Give the lay out for Randomised Complete Block Design. 3

2. b) Complete the following analysis of variance table and test whether the treatments differsignificantly at 5% level of significance. 5
2. a) Find the least value of ã in a sample of 18 pairs from a bivariate normal population that is significant at 5% level of significance. 5 b) How many pairs of observations must be included in a sample in order that an observed

 V1 2.3 V2 3 V3 3.3 V4 2.5 V2 3.1 V3 4.1 V4 2.4 V1 2.4 V3 4.3 V4 2.5 V1 2.1 V2 2.9 V4 2.6 V1 2 V2 2.4 V3 4.4
 Source d.f S. S M. S Blocks 5 700 ---- Treatments ---- ---- ---- Error ---- ---- 12.2 Total 23 1200 ----

correlation co-efficient of value 0.47 shall have a calculated value of t greater than 2.12. 3 (Continued Overleaf)

6. a) The following data represents the number of hours that a rechargeable hedge trimmer operates before a recharge is required. 1.5, 2.2, 0.9, 1.3, 2.0, 1.6, 1.8, 1.5, 2.0, 1.2 and 1.7. Use sign test to test the hypothesis at 5% level of significance that this particular trimmer operates, on the average, 1.8 hours before requiring a charge. 4

b) Given below are the scores given by two groups of trainees. 4

Group I 31 28 42 36 29 51 34 25 44 33 49
Group II 27 45 30 53 41 39 48 43 26 37

Use a Mann-Whitney Test to test if the scores for the two groups differ significantly.

7. a) Five pennies were tossed 1000 times and number of heads were observed as given below. Fit a

binomial distribution and determine the goodness of fit test. Use á = 0.05. 4

b) The proportion of individuals Possessing the four blood types should be in the proportion

q2 : P2 + 2Pq : r2 + 2qr : 2Pr, where P + q + r = 1. Given the observed frequencies 180, 360, 132,

98, test the compatibility with P = 0.4, q = 0.4 and r = 0.2. Use á = .05 4

8. a) Compute Gross and Net Reproduction Rates for the following data. 4

Age Group (Year) Female PoP (000) Female Births Probability of Survival
15 – 19 1558 18,900 0.914
20 – 24 1112 71,100 0.899
25 – 29 1595 96,900 0.884
30 – 34 1629 64,200 0.868
35 – 39 1627 34,900 0.852
40 – 44 1522 10,800 0.834
45 – 49 1401 800 0.813

b) Calculate the Crude and Standardised death rates of the local population from the following data using direct method.

Age Group (Years) Standard Population No. of deaths in Standard Population Local Population No. of deaths in Local Population
0 – 10 600 18 400 16
10 – 20 1000 5 1500 6
20 – 60 3000 24 2400 24
60 and Over 400 20 700 21

***B.A/B.Sc-II (10/A) – xliii ***

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