MS - 8 Quantitative Analysis for Managerial Applications

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ASSIGNMENT

Course Code :	MS - 8
Course Title :	Quantitative Analysis for Managerial Applications
Assignment Code :	MS-8/SEM - II /2014
Coverage :	All Blocks

Note: Attempt all the questions and submit this assignment on or before 31st October, 2014 to the coordinator of your study centre.

Q. 1 what are quartiles, deciles, and percentiles? State the general equation of computing the ith quartile, jth decile, and kth percentile.

Ans.  Quartileà  In descriptive statistics, the quartiles of a set of values are the three points that divide the data set into four equal groups, each representing a fourth of the population being sampled. A quartile is a type of quantile.

In epidemiology, sociology and finance, the quartiles of a population are the four subpopulations defined by classifying individuals according to whether the value concerned falls into one of the four ranges defined by the three values discussed above. Thus an individual item might be described as being "in the upper quartile".

Q. 2 In a railway reservation office, two clerks are engaged in checking reservation forms. On an average, the first clerk (A1) checks 55 per cent of the forms, while the second (A2) checks the remaining. While A1 has an error rate of 0.03 that of A2 is 0.02. A reservation form is selected at random from the total number of forms checked during a day and is discovered to have an error. Find the probabilities that it was checked by A1, and A2, respectively.

Ans.  Probability that a form is checked by A1 = 0.55      and by A2 = 0.45

Error rate of A1 = 0.03          A1 checks 97 forms out of a 100 correctly.
Error rate of A2 = 0.02          A2 cheks 98 forms out of a 100 corectly.

Probability that a form is checked by A1 and also correctly: 0.55 * 0.97 = 0.5335
Probability that a form is checked by A1 and wrongly : 0.55 * 0.03 = 0.0165

Q.3 The weekly wages of 2000 workmen are normally distributed with mean wage of Rs 70 and wage standard deviation of Rs 5. Estimate the number of workers whose weekly wage are

a. between Rs 70 and Rs 71

b. between Rs 69 and Rs 73

c. more than Rs 72, and

d. less than Rs 65

Ans. The area under the curve of normal distribution gives the probabilities. I hope you have the z tables or cumulative normal distribution tables or error function tables.

z-tables have mean value = 0 and probability at P(z<= 0) = 0.50
Z Table(z < 1.0) gives the probability for z to be between 0 and 1.0 = P(0 < z <1.0)

Q.4 A research organization claims that the monthly wages of industrial workers in district X exceeds that of those in district Y by more than Rs 150. Two different samples drawn independently from the two districts yielded the following results:

District X:  x₁ bar= 648, s₁² = 120, and n₁ = 100

District Y:  x₂ bar= 495, s₂² = 140, and n₂ = 90

Verify at 0.05 level of significance whether the sample results support the claim of the organization.

Ans. The procedure is explained in the following steps:

1.    Test statistics Z= (X₁ bar – X₂ bar)/( s₁²/N₁ + s₂²/N₂)

                            

                         =(648-495)/

Q. 5 what do you mean by decomposition of a time series? State the essential characteristics of the additive and multiplicative models of time series analysis.

Ans.  The following are the two models commonly used for the decomposition of a

time series into its components.

Additive model

Multiplicative model

Most of the time series relating to economic and business phenomenon

Conform to the multiplication model. In practice, additive model is rarely

Used.

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