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RAN-2257
S.Y.B.A. (External) Examination
March / April - 2019
Statistics (Higher) Paper - III (3)
Time: 3 Hours | Total Marks: 100
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Instructions:
Q-1 a) What is the difference between Population census and Sample census? (8)
b) State limitations of sample. (5)
c) How many samples of size 2 can be taken from the population 51, 53, 55, 54, 52? And for these sample show that sample mean is an unbiased estimator of population mean. (7)
OR
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a) What is Simple random sampling? Explain the method to select it. (10)
b) One population is distributed in two strata. Their numbers of observations are respectively 20 and 30. Sample of first sample : 12, 15, 18, 23 Sample of second sample : 16, 20, 24, 25, 30 Obtain mean of stratified random sample. (10)
Q-2 a) Explain analysis of variance method for one way classification. (8)
b) Four workers alternately work on four machines. During a particular tenure the number of defective goods which each worker has produced are shown below. (12)
| Machine | W1 | W2 | W3 | W4 |
|---|---|---|---|---|
| M1 | 10 | 15 | 7 | 12 |
| M2 | 12 | 20 | 10 | 16 |
| M3 | 14 | 7 | 9 | 10 |
| M4 | 8 | 16 | 20 | 8 |
Test the difference between work done by the workers and difference between the machines using analysis of variance.
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OR
a) Explain analysis of variance method for two way classification. (8)
b) The following table gives yield of three types of crop plant in four plots. (12)
| Types of crop | Plot No. I | Plot No. II | Plot No. III | Plot No. IV |
|---|---|---|---|---|
| A | 6 | 8 | 5 | 3 |
| B | 7 | 9 | 10 | 8 |
| C | 3 | 5 | 6 | 8 |
Carry out an analysis to test the significance of the difference in the three types of yields.
Q-3 a) What is trend? Explain method of moving averages to find trend. (8)
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b) Obtain the leaner trend by method of least square to the following data. (12)
| Year | 1970 | 1971 | 1972 | 1973 | 1974 | 1975 | 1976 |
|---|---|---|---|---|---|---|---|
| Production (in thousands) | 80 | 90 | 92 | 83 | 94 | 99 | 92 |
OR
a) What is time series? Explain various components of Time Series. (8)
b) Obtain seasonal fluctuations by method of seasonal moving averages. (12)
| Year | Q1 | Q2 | Q3 | Q4 |
|---|---|---|---|---|
| 1990 | 50 | 45 | 48 | 53 |
| 1991 | 52 | 47 | 49 | 41 |
| 1992 | 51 | 45 | 48 | 52 |
| 1993 | 55 | 46 | 46 | 51 |
Q-4 a) What is statistical quality control? Explain the types of variation in quality. (8)
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b) From the following data, construct X and R chart. State your decision about the production process. (12)
n=5, A2=0.58, D3=0, D4=2.12
| X | 43 | 49 | 37 | 44 | 45 | 37 | 51 | 46 | 43 | 47 |
|---|---|---|---|---|---|---|---|---|---|---|
| R | 5 | 6 | 5 | 7 | 7 | 4 | 8 | 6 | 4 | 6 |
OR
a) Explain the construction of p -chart and state its usefulness. (8)
b) A company manufactures 10 motor cycles and following number of defects per unit is obtained as follows. (12)
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2, 5, 5, 5, 1.5, 1, 7, 5, 6
Draw C — chart. State your conclusions.
Q-5 a) Write short notes. (8)
(1) O.C.Curve
(2) AOQ and AOQL
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b) Draw O.C. curve for the following single sampling plan (12)
N=2000, n=200, C=2
OR
Q-5 Answer any three of the following. (20)
(1) State the various units and publications of Indian statistical organization.
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(2) State the various methods to collect the official statistics, Write its limitations.
(3) Write short note on Indian Official Statistical Institute.
(4) Describe the merits and demerits of Indian Official Statistics.
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