5 30474 1 n n x x s 2 2 2 method cut short by 02489 1

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(5.5) - 304.74 1 n n ) x ( - x S 2 2 2 method cut - short by 0.2489 1 - 10 2.24 1 n ) x - x ( S 2 Thus, using the sample wholesaler’s cigarettes price mean as an estimator, the point estimation of the golden cigarettes mean is rs.5.50. Both the buyer as well as seller accepts the use of this point estimate as a basis for fixing the price. The point estimate can save time and expense to the producer of cigarettes. Illustration 5 Sensing the downward in demand for a product, the financial manager was consid ering shifting his company’s resources to a new product area. He selected a sample of 10 firms in the textile industry and discovered their earnings (in %) on investment. Find point estimate of the mean and variance of the population from data given below. 18.0 25.0 13.0 21.0 17.0 16.0 12.0 10.0 20.0 Solution Calculation of point estimate of sample mean and its variance X x (x- x ) (x- x ) 2 18.0 25.0 13.0 11.0 21.0 17.0 16.0 12.0 17.0 16.0 16.0 16.0 16.0 16.0 16.0 16.0 16.0 16.0 2.0 9.0 -3.0 -5.0 1.0 0 -4.0 -6.0 1.0 4 81 9 25 25 1 16 36 1 160.0 198 Sample mean = 160/10 = 16 Sample variance = 198/(10-1) = 198/9 = 22 Sample standard deviation = 22 = 4.69
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82 Thus, the point estimates of mean and of variance of the population from which the sample drawn are 16 and 4.69 respectively. Illustration 6 A random sample of 600 appeals was taken from a large consignment and 66 of them were found to be bad. Find the limits at which the bad appeals lie at 99 per cent confidence level. We are given, n = 600 Number of bad appeals in the consignment, 65 proportions of bad appeals in the consignment: p = (a/n) = 66/ 600 = 0.11 Proportion of good appeals in the consignment, q = 1-a/n = 1.00 0.11 = 0.89 Standard error of proportion of bad appeals in consignment is given by: SE(p) = pq/n = 600 0.89 0.11 = 0.0128 The value of statistic at 99.73 per cent confidence level is 3 which is tested to find the most probable limits within which bad appeals lie: P Z pq/n P 3 pq/n 0.11 3 0.0128 0.11 0.0384 0.1484 and 0.0716 Hence, the bad appeals in the consignment lie between the limits at 14.84 per cent and 7.16 per cent. 8.4. REVISION POINTS 1) Random Sampling, Systematic Sampling, Stratified Sampling, Cluster Sampling, Multi-Stage Sampling and Area Sampling 2) Purpose Sampling, Quota Sampling and convenience sampling 8.5. INTEXT QUESTIONS 1) Explain importance of population and sample in research 2) Briefly explain the advantages and disadvantages of cluster sampling 8.6. SUMMARY By the end of this lesson, you should be able to understand Population, Sample, Sampling technique, Probability sampling and Non probability sampling
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83 8.7. TERMINAL EXERCISES Out of 1200 M.Com, students a sample of 150 selected at random to test the accuracy of solving a problem in Quantitative Methods and 10 did mistake. Assign limits within which the number of students who done the problem wrongly in whole universe of 1200 students at 99 per cent confidence level.
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