Q1. a) What is ANOVA? Explain with the help of a suitable example.
b) Two batches of 12 animals each are given test of inoculation. One batch was inoculated and the other was not. The number 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?
Dead
Surviving
Total
Inoculated
2
10
12
Not-inoculated
8
4
12
Total
10
14
24
Q2. a) 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 in the consignment.
b) A stud manufacturer wants to determine the inner diameter of a certain grade of tire. Ideally, the diameter would be 15mm.The data
are as follows:
15, 16, 15, 14, 13, 15, 16, 14
(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 stud.
Q3. a) A lot containing 7 components is sampled by a quality inspectror, 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
(10)
(10)
(10)
(08)
(12)
recorded. They were given a month special coaching and a second test was given to them in the batne 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.
Marks in Test I
70
68
56
75
80
90
68
75
56
58
Marks in Test II
68
70
52
73
75
78
80
92
54
55
Q4. a) In a certain factory turning out blades, there is a small chance 1/500 for any blade to be defective. The blades are supplied in packets of 10. Use the Poisson distribution to calculate the approximate number of packets containing no defective, one defective, two defective blades in a consignment of 10000 packets. (Given e-0.02 = 0.9802).
b) In a certain assembly plant, three machines, B1 B2 and B3 is a make 30%,45% and 25%, respectively of the products. It is known from past experience that 2%, 3% and 2% of 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.
Q5. a) Find the equation of the least square line from the following data and estimate the production in 1982.
Year (X)
1974
75
76
77
78
79
80
81
Production (Y)
(in tons)
12
14
26
42
40
50
52
53
b) The diameters of can tops produced by a machine are normally distributed with standard deviation of 0.01 cms. At what mean diameter the machine be set so that not more than 5% of the can tops produced by the machine have diameters 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.60. Find (i) the number of persons having incomes between Rs.400 and 550, (ii) the lowest income of the richest 500.
b) Present an overview of SPSS package along with its features, applications, advantages and limitations.
Q7. Write short notes on the following
a) Exponential distribution
b) Central limit theorem
c) Deign of Experiments
d) Null Hypothesis