Determine the coefficient of association

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Reference no: EM132314834

Descriptive Statistics Assignment -

Note: All questions are compulsory. Answer in your own words.

Q1. State whether the following statements are true or false and also give the reason in support of your answer:

a) If the regression coefficients b_YX and b_XY of a data are 1.6 and 0.4, respectively, then the value of r(X, Y) is 0.8.

b) If each value of X is multiplied by 10 and each value of Y is multiplied by 20, then the modified regression coefficient b_XY would be the half of previous one.

c) If (AB) = 10, (αB) = 15, (Aβ) = 20 and (αβ) = 30 then A and B are associated.

d) If standard deviation of x is 5, standard deviation of y = 2x-3 is 7.

e) If with usual notations for two attributes the inequality (AB) (αβ) < (αB)(Aβ) holds, then - 1 ≤ Q ≤ 1.

Q2. a) Find the missing information from the following data:

	Group I	Group II	Group III	Combined
Number	50	?	90	200
Standard Deviation	6	7	?	7.746
Mean	113	?	115	116

b) If AM and GM of two numbers are 30 and 18, respectively, find the numbers.

Q3. a) For the following distribution, calculate first four central moments using recurrence relations:

Marks:	2.7-7.5	7.5-12.5	12.5-17.5	17.5-22.5	22.5-27.5	27.5-32.5	32.5-37.5
Frequency:	06	13	23	39	19	15	05

Also find the coefficients of skewness and kurtosis.

b) Calculate the first, second and third quartile for the following data:

Class:	0-10	10-20	20-30	30-40	40-50
Frequency:	05	15	30	12	08

Also find the quartile deviation and coefficient of quartile deviation.

Q5 a) A researcher collects the following information for two variables x and y: n = 20, r = 0.5, mean (x) = 15, mean (y) = 20, σ_x = 4 and σ_y = 5

Later it was found that one pair of values (x, y) has been wrongly taken as (16, 30) whereas the correct values were (26, 35). Find the correct value of r(x, y).

b) Calculate the coefficient of rank correlation for the following data:

X:	48	33	40	09	16	16	65	24	16	57
Y:	13	13	24	06	15	04	20	09	06	19

Q6 a) Explain the method of least squares. Fit a straight line Y = a +b X to the following data:

X:	1	3	5	7	9	10
Y:	5	8	12	15	18	22

b) The equations of two regression lines are given as follows:

5x - 15y = 30

10x - 20y = 15

Calculate (i) regression coefficients, b_yx and b_xy; (ii) correlation coefficient r(x, y); (iii) Mean of X and Y; and (iv) Value of σ_y if σ_x = 3.

Q7. (a) In a trivariate distribution: σ₁ = 4, σ₂ = σ₃ = 6, r₁₂ = 0.5, r₂₃ = r₃₁ = 0.8

Find (i) r_23.1, (ii) R_1.23, (iii) b_12.3, b_13.2 and (iv) σ_1.23

ii. Suppose a computer has found for a given set of values of X₁, X₂ and X₃: r₁₂ = 0.90, r₁₃ = 0.30 and r₂₃ = 0.70. Examine whether these computations are error free.

Q8 a) A company is interested in determining the strength of association between the communication time of their employees and the level of stress-related problems observed on job. A study of 120 assembly line workers reveals the following data:

	Stress
	High	Moderate	Low	Total
Under 20 min.	10	10	15	35
20-50 min	15	10	25	50
Over 50 min	15	10	10	35
Total	40	30	50	120

Determine the amount of association between the communication time of their employees and the level of stress using coefficient of contingency and interpret the result.

b) 600 candidates were appeared in an examination. The boys outnumbered girls by 15% of all candidates. Number of passed exceeded the number of failed candidates by 300. Boys failing in the examination numbered 80. Determine the coefficient of association.

Reference no: EM132314834

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