problem 1) describe the determination of number of classes, class width and construction of frequency distribution to one-dimensional data.
problem 2) find out median to the following data:
Class: 0-5 5-10 10-15 15-20 20-25
Frequency: 3 16 25 18 5
problem 3) What do you mean by scatter diagram? Describe its uses.
problem 4) Compute the co-efficient of correlation to the given data using Spearman’s formula:
Rank given by Judge – 1 : 3 2 6 5 1 4
Rank given by Judge – 2 : 4 3 1 6 2 5
problem 5) If, for the events A and B, P(A) = 0.2, P(B) = 0.3 and P(A∩B) = 0.09, compute P(A∪B) and using which determine P(A∩B^{C}).
problem 6) describe binomial distribution and describe its properties.
problem 7) Describe the terms sampling distribution and standard error with suitable ex.
problem 8) How do you test the significance of hypothetical value of a population proportion? describe.
problem 9)a) Draw frequency polygon to the given data:
Profit (in lakh Rs.) 0-10 10-20 20-30 30-40 40-50 50-60
No. of Firms 5 12 20 16 5 2
b) Investigate the skewness property of the following data.
Age (in years): Below 20 20-25 25-30 30-35 35-40
No. of Employees: 34 78 100 56 22
problem 10)a) Fit a regression line of Y and X using the following data:
x: 23 20 19 21 18 20 17 19
y: 24 19 22 18 20 22 20 17
b) Find out the strength of relationship between x and y from the following data using the co-efficient of determination:
x: 15 20 28 12 40 60 20 80
y: 40 30 50 30 20 10 30 60
problem 11)a) (i) Define Bayes theorem.
(ii) In a bolt factory, machines A,B and C manufacture respectively 32%, 58% and 10% of the total production of the total output of each machine, 5%, 4% and 2% are defective bolts. A bolt is drawn randomly and is found to be defective. Determine the probability that it was manufactured by Machine A?
b) Fit a Poisson distribution to the following data:
x (Value) : 0 1 2 3 4
f (Frequency) : 21 18 7 3 1
problem 12)a) Describe the terms with an illustration: sample, parameter, simple hypothesis, composite hypothesis and two kinds of errors.
b) Describe hypothesis testing problem.
problem 13)a) describe the method of testing the hypothetical value of the mean of a normal population using a small sample. Assume that the population variance is unknown. Applying the procedure test whether the mean of a normal population is 14 at 5% level of significance using the sample drawn from the population:
11 14 13 12 13 12 13 14 11 12
b) From the following data, test whether there is any relationship between sex and preference of colour:
Male Female
Red 20 30
Blue 60 40
Black 10 20