SAMPLE MBA SOLVED ASSIGNMENT

JAN JUNE 2017 MS-08

Course Code MS - 08 Course Title Quantitative Analysis for Managerial

Applications Assignment Code MS-08/TMA/SEM - I/2017 Assignment Coverage All Blocks

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School of Management Studies

INDIRA GANDHI NATIONAL OPEN UNIVERSITY MAIDAN GARHI, NEW DELHI – 110 068

1. The net incomes of a sample of large importers of antiques were organized into the following table:

(a) What is the table called?

The table is called --------------------------------------------- table. (b) Based on the distribution, what is the estimate of the arithmetic mean net income?

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(c) Based on the distribution, what is the estimate of the standard deviation?

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2. The employees of Cartwright Manufacturing are awarded efficiency ratings based on such factors as monthly output, attitude, and attendance. The distribution of the ratings follows the normal probability distribution. The mean is 400, the standard deviation 50.

(a) What is the area under the normal curve between 400 and 482? Write this area in probability notation.

(b) What is the area under the normal curve for ratings greater than 482? Write this area in probability notation.

Or

(c) Show the facets of this problem in a chart.

3. Advertisements by Star Fitness Center claim that completing its course will result in losing weight. A random sample of eight recent participants showed the following weights before and after completing the course. At the .01 significance level, can we conclude that the students lost weight?

(a) State the null hypothesis and the alternate hypothesis.

(b) What is the critical value of t?

(c) What is the computed value of t?

(d) Interpret the result. What is the p-value?

-------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------- (e) What assumption needs to be made about the distribution of the differences? -------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------- --------------------------------------------------------------------------------------------------------------

4. What is time series analysis? Decompose a time series into its various components and describe them. One definition of a time series is that of a collection of quantitative observations that are evenly spaced in time and measured

successively. Examples of time series ---------------------------------------------------------------------------------------

--------------------------------------------------------------------------------------yearly sales figures. Time series

analysis is generally used when there are ------------------------------------------------------------------------------------

-----------------------------------------------------------------------------------------. Goals of time series analysis:

1. Descriptive: Identify ---------------------------------------- and seasonal variation

2. Explanation: understanding -------------------------------------- the data

3. Forecasting: prediction of ------------------------------------------ patterns

4. Intervention analysis: how ----------------------------------------- time series?

5. Quality control: deviations ------------------------------------------ a problem

Time series are analyzed in -------------------------------------------------------------------------------------------------

----------------------------------------------------------------------------to be developed that explains the data in such a

way that prediction, monitoring, or control can occur. Examples include prediction/forecasting, which is widely used in

economics and business. ----------------------------------------------------------------------------------------------------

-------------------------------------------------------------------------, and industry.

It is assumed that a time series data set --------------------------------------------------------------------------------------

---------------------------------------------------------------------------------------averages or regression analysis is

often used. Seasonality is a trend that repeats itself systematically over time. A second assumption is that the data exhibits

enough of a random process so that it is hard to -----------------------------------------------------------------------------

------------------------------------------------------------------------------------------------potential patterns have to do

with lingering effects of earlier observations or earlier random errors.

There are numerous software programs that ---------------------------------------------------------------------------------

--------------------------------------------------------------------------------------------packages that can perform time

series analyses. Excel can be used if linear regression analysis is all that is required (that is, if all you want to find out is the

magnitude of the most obvious trend). A word of ----------------------------------------------------------------------------

-------------------------------------------------------------------------------------------------of independence of errors.

Type I error rates will increase substantially when autocorrelation is present. Also, inherent patterns in the data may dampen

or enhance the effect ------------------------------------------------------------------------ for within the analysis.

Observations made over time can be either discrete or continuous. Both types of observations can be equally spaced,

unequally spaced, or have missing data. Discrete measurements can be recorded at any time interval, but are most often taken

at evenly spaced intervals. Continuous --------------------------------------------------------------------------------------

---------------------------------------------------------------------------------------of a natural phenomenon such as air

temperature, or a process such as velocity of an airplane.

Time series are very complex because each ---------------------------------------------------------------------------------

--------------------------------------------------------------------------------------------from one observation to another.

These influences are called autocorrelation—dependent relationships between successive observations of the same variable.

The challenge of time series analysis is to extract the autocorrelation elements of the data, either to understand the trend itself

or to model the underlying mechanisms.

Time series reflect the stochastic nature of ----------------------------------------------------------------------------------

-------------------------------------------------------------------------------------------independent. Another non-normal

aspect of time series observations is that they are often not evenly spaced in time due to instrument failure, or simply due to

variation in the number of days in a month.

There are two main approaches used to --------------------------------------------------------------------------------------

---------------------------------------------------------------------------------------time domain is most often used for

stochastic observations. One common technique is the Box-Jenkins ARIMA method, which can be used for univariate (a

single data set) or multivariate (comparing two or ---------------------------------------------------------------------------

--------------------------------------------------------------------------------------------------the data. Below, I will

demonstrate a Box-Jenkins ARIMA time domain analysis of a single data set.

Analysis in the frequency domain is -----------------------------------------------------------------------------------------

------------------------------------------------------------------------------------technique is Fast Fourier Transform

(FFT). Mathematically, frequency domain ----------------------------------------------------------------------------------

-------------------------------------------------------------------------------------------analysis is more difficult to

understand, so time domain analysis is generally used outside of the sciences.

Time Series Decomposition

Time series decomposition ---------------------------------------. There are three components that are typically of interest:

Tt, a deterministic, non ----------------------------------------------------------------------------------------------------------------

------------------------------------ to being a linear trend, though higher-degree polynomials are also used.

St, a deterministic seasonal -----------------------------------------------------------------------------------------

------------------------------------------------------------------------------------years. It is often considered to

be a nuisance component, and seasonal adjustment is a process for eliminating it.

It, a stochastic irregular --------------------------------------------------------------------------------------------

---------------------------------------------------------------------------------reason, it is often thought to

contain information about the business cycle, and is usually the most interesting component.

There are three functional forms ------------------------------------------- its trend, seasonal, and irregular components:

Additive decomposition, where

yt=Tt+St+It.

This is the classical decomposition. It is -------------------------------------------------------------------------------------

----------------------------------------------------------------------------------------component, the seasonal and

irregular components are assumed to fluctuate around zero.

Multiplicative decomposition, where

yt=TtStIt.

This decomposition is appropriate -----------------------------------------------------------------------------------------------------------------------------------------------------------------------------the trend component, the seasonal and irregular components are assumed to fluctuate around one.

Log-additive decomposition, where logyt=Tt+St+It.

This is an alternative to the -----------------------------------------------------------------------------------------------------------------------------------------------------------------------------time series contains many small observations. For identifiability from the trend component, the seasonal and irregular components are assumed to fluctuate around zero.

You can estimate the -----------------------------------------------------------------------------------------------------------------------------------------------------------------------------component is estimated as

ˆIt=yt−ˆTt−ˆSt

using -----------------------------------------------, and

ˆIt=yt(ˆTtˆSt

)

using -----------------------------------------------------------.

The series

yt−ˆTt

(or yt/ˆTt using --------------------------------------------------------------- a detrended series.

Similarly, the series yt−ˆ---------------------------------- a deseasonalized series.

Example- An example of using -------------------------------------------- production forecast

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5. What is a random variable? How is it used to define a probability distribution? Make the probability distribution of “scores facing up” in a throw of two dice. Random variables can be any outcomes from some chance process, like how many heads will occur in a series of 20 flips. We calculate probabilities of random variables and calculate expected value for different types of random variables. When the value of a variable is the outcome of a statistical experiment , that variable is a random variable. An example will make this clear. -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------the number of Heads that result

from this experiment. The variable X can take on the values 0, 1, or 2. In this example, X is a random variable; because its value is determined by the outcome of a statistical experiment. A random variable is a variable -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------as discrete, which are variables that have specific values, or continuous, which are variables that can have any values within a continuous range. Consider an experiment where a ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- (from no heads in three successive coin tosses, to all heads). No other value is possible for X. An example of a -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------of 25 people.

How random ----------------------------------------------------------- distribution-

A random variable is defined as a function that associates a real number (the probability value) to an outcome of an experiment.

In other words, a random variable is a -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------to refer to different situations. Random variables make working with probabilities much neater and easier.

A random variable in probability is ---------------------------------------- used to ascribe a value to the random variable.

For examples, given that you flip -------------------------------------------------------------------- given by the following:

There are four possible ----------------------------------------------------------------------------------- and T stands for tails.

The ---------------------------------------------------------- following:

To find the --------------------------------------------------------- question as:

which means that ------------------------------------------------------- to some real number x.

In the above example, we can say:

Let X be a random variable ------------------------------------------------. Find the probability the you obtain two heads.

So now we've been told --------------------------------------------------------------------------- information as:

Since we already have --------------------------------------------------------------- heads, so we find the probability as:

we ------------------------------------------------------------- the above as:

From this example, you should ------------------------------------------------------------------------------ in a given sample space.

There are two --------------------------------------------------------------------------------- random variables.

Discrete Random Variables

The word discrete means separate and individual. Thus discrete random variables are those that take on integer values only. They never include fractions or decimals.

A quick example is the sample space of any number of coin flips, the outcomes will always be integer values, and you'll never have half heads or quarter tails. Such a random variable is referred to as discrete. Discrete random variables give rise to discrete probability distributions.

Continuous Random Variable

Continuous is the opposite of -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------probability distributions.

Random Variables and Probability Distributions

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Discrete Probability Distributions --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------

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Distribution Functions for Random Variables

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Distribution Functions for Discrete Random Variables

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Continuous Random Variables --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------

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Make the probability distribution of “scores facing up” in a throw of two dice 1-

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2- ---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------

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