MB0040 – STATISTICS FOR MANAGEMENT

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ASSIGNMENT

 

 

 

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.

 

Q.1 A statistical survey is a scientific process of collection and analysis of numerical data.

Explain the stages of statistical survey. Describe the various methods for collecting data

in a statistical survey.

 

Answer : Meaning of statistical survey :

 

A statistical survey is a scientific process of collection and analysis of numerical data. Statistical survey are use to collect numerical information about units in population. Surveys involve asking questions to individuals. Surveys of human populations are common in government, health, social science and marketing sectors.

 

Stages of statistical survey (Listing and Explanation) :

 

 

 

 

Q.2 Analysis of daily wages of workers in two organisations A and B yielded the following

results: 

	Org A	Org B
No of worker	10	20
Average daily wages(rs.)	30	15
variance	25	100

 

Obtain the average daily wages and the standard deviation of wages of all workers in the

two organisations taken together. Which organisation is more equitable in regard to

wages?

 

Ans:  Let  x1 , x2 , n1, n2, σ1 , σ2 respectively denote mean, no. of workers and standard deviation of A and B.

Then : x1 = 30 , x2 = 15, n1 = 10, n2 = 20 , σ1= sqrt (25) = 5 , σ2 = sqrt(100) = 10   (given)

 

So combined mean  X12 = n1x1 +

 

 

Q.3  a. 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.

 

 

 

b. In a bolt factory machines A, B, C manufacture 25, 35 and 40 percent of the total output. Of their total output 5, 4 and 2 percent are defective respectively. A bolt is drawn at random and is found to be defective. What are the probabilities that it was  manufactured by machines A, B and C?

 

Ans : Let Ai (i=1,2,3) be the events of drawing a bolt produced by machine A, B , C respectively. From the data we know that :

P(A1) = 0.25  P(A2) = 0.35  P(A3) = 0.40

 

From the additional information we know that

B = The event of drawing a defective bolt

 

 

 

Q. 4  a. What is a Chi-square test? Point out its applications. Under what conditions is this test

applicable?

 

Ans : 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.

 

 

 

 

 

b. Discuss the types of measurement scales with examples.

 

Answer :

1.Nominal:

 

Nominal scales are naming scales. They represent categories where there is no basis for ordering the categories. Nominal Scale Examples

 

• diagnostic categories
• sex of the participant
• group affiliation

 

2. Ordinal:

 

 

 

 

Q. 5 Explain the Components of Time series.

 

Answer: Meaning of Time series :

 

A time series is a sequence of data points, measured typically at successive points in time spaced at uniform time intervals. Examples of time series are the daily closing value of the Dow Jones Industrial Average and the annual flow volume of the Nile River at Aswan. Time series are very frequently plotted via line charts. Time series are used in statistics, signal processing, pattern recognition, econometrics, mathematical finance, weather forecasting, earthquake prediction, electroencephalography, control engineering,

 

 

Q.6 a. What is analysis of variance? What are the assumptions of the technique?

 

Ans : 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. Doing multiple

 

 

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.

 

 

Formulas/Calculation/Solution to the problem

7

 

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