PROBABILITY AND STATISTICAL METHODS
Q1 . a) How Chi-square test is used as a test of independence? Explain
b) Explain briefly the general procedure of testing the appropriateness of a distribution.
C) A random sample of 700 oranges was taken from a large consignment and 100 found to be defective. Construct the 95% confidence limits for the % number of oranges the consignment.
Q2. A) Two batches of 12 animals each are given test of inoculation. One batch was inoculated and the other was not. The numbers of dead and surviving animals are given in the following table for both cases. Can the inoculation be regarded as effective against the disease at 5% level of significance?
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Dead
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Sun/lying
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Total
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Inoculated
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2
|
10
|
12
|
|
Not-inoculated
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a
|
4
|
12
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Total
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10
|
14
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24
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b) A tyre manufacturer wants to determine the inner diameter of a certain grade of tyre. Ideally, the diameter would be 570mm.
The data are as follows:
572. 572: 573, 568 569, 575, 555, 570
i) Find the sample mean and median,
(ii) Find the sample variance, standard deviation and range
(iii) Using the calculated statistics in parts (I) and
(ii), comment on the quality of tyres.
Q3 a) A lot containing 7 components is sampled by a quality inspector, the lot contains 4 good components and 3 defective components. A sample of 3 is taken by the inspector. Find the expected value of the number of good components in this sample.
b) Ten school boys were given a test in Statistics and their scores were recorded. They were given a month special coaching and a second test was given to them in the same subject at the end of the coaching period. Test if the marks given below give evidence to the fact that the students are benefited by coaching.
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Marks in
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70
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68
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56
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75
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80
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90
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68
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75
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56
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58
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Test I
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Marks in
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68
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70
|
52
|
73
|
75
|
78
|
80
|
92
|
54
|
55
|
|
Test II
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4. a) In a certain assembly plant, three machines, B. B2 and B3 make 30%, 45% and 25%, respectively of the products. It is known from past experience that 2%, 3% and 2% of the products made by each machine respectively are defective. Now, suppose that a finished product is randomly selected. What is the probability that it was made by machine B3.
b) Present an overview of SPSS package along with its features, applications, advantages and limitations.
Q5. a) A process engineer is investing the effect of process operating temperature X on product yield Y. The study results in the following data.
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X
|
100
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110
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120
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130
|
140
|
150
|
160
|
170
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180
|
190
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V
|
45
|
51
|
54
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61
|
65
|
70
|
74
|
78
|
85
|
8
|
Find the equation of the least square line which will enable to predict yield on the basis of temperature. Find also the degree of relationship between the temperature and the yield
b) The diameters of can tops produced by a machine are normally distributed with standard deviation of 0.01 erns. At what mean diameter the machine be set so that not more than 5% of the can tops produced by the machine have diameter's exceeding 3 cms.
Q6. a) The incomes of a group of 10,000 persons were found to be normally distributed with mean Rs.520 and standard deviation Rs. o. Find (i) the number of persons having incomes between Rs, 400 and 550, (ii) the lowest income of the richest 500.
b) What is forecasting? Explain any one method of forecasting.
c) Write about short cut method to calculate standard error of estimates.
Q7. Write short notes on the following
I) Design of Experiments
ii) Binomial distribution
iii) Regression analysis
iv) Central limit theorem