MS 08 - Quantitative Analysis for Managerial Applications

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ASSIGNMENTS

Course Code                                      :               MS 08

Course Title                                       :               Quantitative Analysis for Managerial Applications

Assignment No.                               :               MS-08/TMA/SEM-I/2014

Coverage                                             :               All Blocks

Note : Attempt all the questions and submit this assignment on or before 30th April, 2014 to the coordinator of your study center.

1.            The distribution of Intelligence Quotient (I.Q.) scores measured for 100 students in a test is as follows:

I.Q.*                                      40-50     50-60     60-70     70-80                       80-90   90-100

Number of Students                        10           20            20                          15                             15         20

* The data is recorded with origin as 40, i.e. students with I.Q. between 80 and 90 are included in the first interval. The intervals included the upper class value but not the lower.

Find: Arithmetic Mean, Median, First and Third Quartiles, 90th percentile and 6th Decile.         

Answer:To find mean:

To find Median

2.            A candidate is selected for interview for 3 posts. For the first post, there are 3 candidates, for the second, 4 and for the third post there are 2 candidates. What is the probability that the candidate is selected for at least one post?

Answer:there are 3 candidates for job 1 and 4 candidates for job 2 and 2 candidates for job 3.

We can look at the total possible combinations for all 3 jobs.

Those possible combinations would be 3 * 4 * 2 = 24.

We can call the candidates for job 1: candidate 1a, 1b, 1c.

We can call the candidates for job 2: candidate 2a, 2b, 2c, 2d.

We can call the candidates for job

3.            The lifetimes of a colour TV picture tube is normally distributed, with a mean of 8 yrs and a standard deviation of 2 years.

(i)           What is the probability that a picture tube will last more than 10 yrs?

(ii)          If the firm guarantees the picture tube for 4 yrs, what percentage of the tubes sold will have to be replaced?

Answer:Mean of 8 yrs and a standard deviation of 2 years.

(i)Using TI: The syntax is normalcdf(smaller, larger, µ, σ).

4.            Make a list of formulae for all confidence intervals, sample size determination and tests of hypothesis that you have read in your study material.

Answer:Sample size determination is the act of choosing the number of observations or replicates to include in a statistical sample. The sample size is an important feature of any empirical study in which the goal is to make inferences about a population from a sample. In practice, the sample size used in a study is determined based on the expense of data collection, and the need to have sufficient statistical power. In complicated studies there

5.            What is a time – series? Discuss four components of a time – series. Why is it generally assumed that the impact of these components is multiplicative? 

Answer:Time series decomposition is a familiar component of courses and texts on the forecasting of business and economic data. In its standard form, classical time series decomposition assumes that a series of interest comprises of three underlying components which combine to produce the data under investigation. These three components are the trend-cycle, the seasonal component and the irregular component. Typically, these components are denoted as Tt, St and Et respectively, with the series of interest denoted as Yt. An initial

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