MB0040 - STATISTICS FOR MANAGEMENT

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ASSIGNMENT

DRIVE	FALL 2015
PROGRAM	MBADS / MBAHCSN3 / MBAN2 / PGDBAN2 / MBAFLEX
SEMESTER	I
SUBJECT CODE & NAME	MB0040 - STATISTICS FOR MANAGEMENT
BK ID	B1731
CREDITS	4
MARKS	60

Note: Answer all questions. Kindly note that answers for 10 marks questions should be approximately of 400 words. Each question is followed by evaluation scheme.

Note: Answer all questions. Kindly note that answers for 10 marks questions should be approximately of 400 words. Each question is followed by evaluation scheme.

Q1.Statistics plays a vital role in almost every facet of human life. Describe the functions of Statistics. Explain the applications of statistics.

Answer: Statistics :

A type of mathematical analysis involving the use of quantified representations, models and summaries for a given set of empirical data or real world observations. Statistical analysis involves the process of collecting and analyzing data and then summarizing the data into a numerical form. Statistics is a general term used to summarize a process that an analyst, mathematician or statistician can use to characterize a data set. If the data set is based on a sample of a larger population, then the analyst can

Q2.

a) Explain the approaches to define probability.

Answer: In some areas, such as mathematics or logic, results of some process can be known with certainty (e.g., 2+3=5). Most real life situations, however, involve variability and uncertainty. For example, it is uncertain whether it will rain tomorrow; the price of a given stock a week from today is uncertain Note_1 ; the number of claims that a car insurance policy holder will make over a one-year period

b) State the addition and multiplication rules of probability giving an example of each case.

Answer: Addition rule of probability and an example:

If two events A and B are mutually exclusive then

P(A ∪B) = P(A) +P(B)

This is the simplified version of the Addition Law. However, when A and B are not mutually

exclusive, A ∩B _= ∅, it can be shown that a more general law applies:

P(A ∪B) = P(A) +P(B)−P(A ∩B)

Of course if A ∩ B = ∅ then, since P(∅) = 0 this general expression reduces to the simpler

version.

Example:A bag contains 20 marbles, 3 are

Q3. a) The procedure of testing hypothesis requires a researcher to adopt several steps. Describe in brief all such steps.

Answer. Meaning of hypothesis can be defined in two ways:

1.It is a supposition or explanation (theory) that is provisionally accepted in order to interpret certain events or phenomena, and to provide guidance for further investigation. A hypothesis may be proven correct or wrong, and must be capable of refutation. If it remains unrefuted by facts, it is said to be verified or corroborated.

2.Statistics:It is an assumption about certain characteristics of a population. If it specifies values for every parameter of a population, it is called a simple hypothesis; if not, a composite hypothesis. If it attempts to nullify the difference between two sample means (by suggesting that the difference is of no statistical significance), it is called a null hypothesis.

b) Explain the components of time series.

Answer. Components of Time series:

The four components of time series are:

1. Secular trend

2. Seasonal variation

3. Cyclical variation

4. Irregular variation

1. Secular trend:

Q4. a. What is a Chi-square test? Point out its applications. Under what conditions is this test applicable?

Answer : Chi-square test:

A chi-squared test, also referred to as chi-square test or χ² test, is any statistical hypothesis test in which the sampling distribution of the test statistic is a chi-squared distribution when the null hypothesis is true. Also considered a chi-squared test is a test in which this is asymptotically true, meaning that the sampling distribution (if the null hypothesis is true) can be made to approximate a chi-squared distribution as closely as desired by making the sample size large enough.

Applications:

Q5.Business forecasting acquires an important place in every field of the economy. Explain the objectives and theories of Business forecasting.

Answer: : Business forecasting :

Business Forecasting is an estimate or prediction of future developments in business such as sales, expenditures, and profits. Given the wide swings in economic activity and the drastic effects these fluctuations can have on profit margins, it is not surprising that business forecasting has emerged as one of the most important aspects of corporate planning. Forecasting has become an invaluable tool for businesspeople to anticipate economic trends and prepare themselves either to benefit from or to counteract them.

Q6 a. What is analysis of variance? What are the assumptions of the technique?

Answer : Analysis of variance :

Analysis of variance (ANOVA) is a collection of statistical models used to analyse the differences between group means and their associated procedures (such as “variation” among and between groups). In ANOVA setting, the observed variance in a particular variable is partitioned into components attributable to different sources of variation. In its simplest form, ANOVA provides a statistical test of whether or not the means of several groups are equal, and therefore generalizes t-test to more than two groups. Doing multiple two-sample t

b. Three samples below have been obtained from normal populations with equal variances. Test the hypothesis at 5% level that the population means are equal.

A	B	C
8	7	12
10	5	9
7	10	13
14	9	12
11	9	14

(The table value of F at 5% level of significance for 1 = 2 and 2 = 12 is 3.88)

Ans: Meaning of Analysis of Variance:

Analysis of variance (ANOVA) is a collection of statistical models used to analyze the differences between group means and their associated procedures (such as "variation" among and between groups). In ANOVA setting, the observed variance in a particular variable is partitioned into components attributable to different sources of variation. In its simplest form, ANOVA provides a statistical test of whether or not the means of several groups are equal, and therefore generalizes t-test to more than two groups.

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