# Pak Study® Library

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### SECTION – A

1. Attempt any SIX parts: 6
i) What do you mean by CLUSTER SAMPLING?
ii) Explain the Difference between CENSUS and SAMPLING.
iii) Write the Two Plause Points of SAMPLING.
iv) When we say that Estimator is to be Unbiased?
v) Write any Four Properties of t-DISTRIBUTION.
vi) What is meant by 1 – á, Explain it?
vii) What is meant by ONE-TAILED TEST?
viii) Discuss the Difference between CHI-SQUARE DISTRIBUTION and t-DISTRIBUTION.
ix) When the F-Distribution tends to normal?
SECTION – B
2. a) Draw with the help of random numbers, a random sample of size 10 from a binomial distribution with
parameters P = 0.4 and n = 5. b) Suppose a population of N = 9 is Stratified into 3 Strata with the following measurements. 3
Stratum – I = 2, 3, 4 Stratum-II = 3, 6 Stratum-III = 1, 2, 3. If two measurements are drawn from each
stratum for the sample, List these samples and compute the mean for each sample. 5
1. a) A finite population consists of the values 6,6,9,15,6 and 18. Calculate the samples means for all possible samples of size 3, that can be drawn from this population, without replacement. Make thesampling distribution of sample means, Find the mean and variance of obtained distribution. 5

2. b) A population of 1,1,1,3,4,5,6,6,6 and 7 is given. Find the mean and variance of the sampling distribution of mean for a sample of size 5 selected at random with replacement. 3
1. a) The masses of 300 students at a university are normally distribution with mean 68.0Kg and standard deviation 3.0 Kg. If 80 samples of each of size 25 are obtained whose mean is i) between 66.8 and 68.3 Kg. ii) less than 66.4 Kg. Determine the number of samples for each case. 4

2. b) 65% of all male voters and 35% of all female voters favour a particular candidate. A sample of 100 male voters and sample of 100 female voters will be polled. What is probability that at east 10% more male voters than female voters will favour this candidate? 4
1. a) Suppose I choose a random sample of three observations from a population by ranking obtain the values 2, 5, 3. From these values I estimate the center of the population by ranking the observations and taking the middle one. What estimator I am using and what is my estimate? 4

b) Find a 99% confidence interval for the mean of a normal distribution with ó = 2.5 and if the sample of size 7 gave the values 9, 16,10,14,13 and 14. What would be the confidence interval if ó was unknown? 4

(Continued Overleaf)

6. a) In a random sample of 1000 houses in a certain city 618 own colour TV Sets. Is this sufficient evidence

to conclude that 2/3 of the houses in this city have Colour TV Sets? Use á = 0.02. 4 b) It has been found from experience that the mean breaking strength of a particular brand of thread is

9.63 N with a standard deviation of 1.04N. Recently a sample of 36 pieces of thread showed a mean breaking strength of 8.93N. Can we conclude at 5% and 6% level of significance that thread has become inferior? 4

7. a) A manufacturer claims that the average life of his light bulbs is 2000 hours. A random sample of 64

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bulbs is tested and the life of X hours is recorded. The results are; Óx = 127808 and Ó(x -x )2 = 9694.6. Test the hypothesis at 1% level of significance that the manufacturer is over estimating the length of life of his bulbs. Assume that the distribution of life of bulbs is normal. 4

b) The means of simple sample of 500 and 400 are 11.9 and 10.9 respectively. Can the samples be regarded as drawn from a population of standard deviation 5? 4

8. a) A training instructor claims that has training methods are so efficient that the variance of the time requires by his trainees to complete a job does not exceed 30 seconds. If a random sample of 21 traineesyielded a variance of 33 seconds, do you think this evidence supported the instructor’s claim? 4

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b) If the sum of squared deviations Ó(x -x )2 is 2.45 and the sample size is n = 20. Find a 98% confidence interval for the population standard deviation ó. 4

***B.A/B.Sc-II (10/A) – xiii ***

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