MB0040 Set2

Name:

Roll No:

Learning Centre:

Subject: MB0040 – STATISTICS FOR MANAGEMENT

Assignment No: Set 2

Date of Submission at the Learning Centre:

1 | P a g e

MB0040 Set2

Q1. What do you mean by Statistical Survey? Differentiate between “Questionnaire” and “Schedule”.

Answer:

1. Definition of statistical survey

A Statistical survey is a scientific process of collection and analysis of numerical data. Statistical surveys are used to collect numerical information about units in a 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

Statistical surveys are categorised into two stages –

Planning and

Execution.

The figure below shows the two broad stages of Statistical survey.

Fig.1: Stages of Statistical Survey

Information is collected through mailed questionnaires

Often, information is collected through questionnaires. The questionnaires are filled with questions pertaining to the investigation. They are sent to the respondents with a covering letter soliciting cooperation from the respondents (respondents are the people who respond to questions in the questionnaire). The respondents are asked to give correct information and to mail the questionnaire back. The objectives of investigation are explained in the covering letter together with assurance for keeping information provided by the respondents as confidential.

2 | P a g e

MB0040 Set2

Good questionnaire construction is an important contributing factor to the success of a survey. When questionnaires are properly framed and constructed, they become important tools by which statements can be made about specific people or entire populations.

This method is generally adopted by research workers and other official and non-official agencies. This method is used to cover large areas of investigation. It is more economical and free from investigator’s bias. However, it results in many “non-response” situations. The respondent may be illiterate. The respondent may also provide wrong information due to wrong interpretation of questions.

If the questionnaire consists of invalid questions, or questions in incorrect order, or questions in inappropriate format, or questions that are biased, then the survey would be useless. An important method for checking and making sure whether a questionnaire is accurately capturing the intended information is to pre-test among a smaller subset of target respondents.

Success of questionnaire method of collection of data depends mainly on proper drafting of the questionnaire. You have to keep the following points in mind while preparing a questionnaire:

The respondent should not take much time in completing the questionnaire. It should be small and not lengthy.· The questions asked should be well structured and unambiguous.· The questions asked should be in proper logical sequence.· Questions should be unbiased. The questions in the questionnaire should not disturb the privacy of the respondents.· The task of completion of questionnaire should not have much writing work. · Necessary instructions and glossary should be given in covering letter.· Questions involving technological jargons and mathematical calculations should be avoided.· The completed questionnaire should be kept confidential and used only for the purpose of the survey as mentioned in the investigation.· There should not be any scope for misinterpretation in the questions.

There are different types of questions that can be used in the questionnaire. A questionnaire can have Contingency questions, Matrix questions, Closed ended questions and Open ended questions. Let’s have a look at each one in detail

Contingency questions are questions that are answered only if the respondent gives a particular response to a previous question. This avoids asking people questions that do not apply to them

Matrix questions are questions which are placed one under the other, forming a matrix. The response categories are placed along the top and a list of questions are placed down the side. This is used to efficiently occupy page space and respondents’ time.

Closed ended questions are those where the respondents’ answers are limited to a fixed set of responses. Usually scales are closed ended.

3 | P a g e

MB0040 Set2

There are various types of closed ended questions.

Yes/no questions – here the respondents answer with “yes” or “no”. Some of the examples are:

Multiple choices – here the respondents have several options from which to choose. For example:

Scaled questions – here the responses are graded on a continuum (For example, rating the appearance of a product on a scale from 1 to 10, with 10 implying the most preferred appearance and 1 implying the least preferred appearance). Scaled questions are mostly questions related to attitudes. A Likert scale provides a number of attitude statements. The respondent has to say how much they agree or disagree with each one.

Open ended questions are those questions for which the respondent supplies their own answer without any fixed set of possible responses. Examples of types of open ended questions include:

Sentence completion – In these, respondents complete an incomplete sentence.

Story completion – In these, respondents complete an incomplete story.

Picture completion – In these, respondents fill in an empty conversation balloon.

Thematic Apperception Test – In these, respondents explain a picture or make up a story about what they think is happening in the picture.

4 | P a g e

MB0040 Set2

Information through schedule filled by investigators

Information can be collected through schedules filled by investigators through personal contact. In order to get reliable information, the investigator should be well trained, tactful, unbiased and hard working.

A schedule is suitable for an extensive area of investigation through investigator’s personal contact. The problem of non-response is minimised.

There is a difference between a schedule and a questionnaire. A schedule is a form that the investigator fills himself through surveying the units or individuals. A questionnaire is a form sent (usually mailed) by an investigator to respondents. The respondent has to fill it and then send it back to the investigator.

Difference between Questionnaire and Schedule is as follows:

S.No. Basis Questionnaire Schedule

1. Liability for filling up

Informant is liable for filling it up. Enumerator fills it up after getting answers from informants.

2. Means of Information

It is sent to the informants by post. Enumerators themselves take up schedules and contact the informants.

3. Personal Relationship

Investigator does not have a personal contact with the informants.

Both investigator and informants have personal contact through schedule.

4. Nature of Information

Sometimes incomplete as there is lack of personal contact.

Complete information is received because of the personal contact between the investigator and informants.

5. Scope of Enquiry

The use of Questionnaire is suitable where the informants are literate.

Schedule can be used for both literate as well as illiterate persons.

5 | P a g e

MB0040 Set2

6. Economical Information by mailed questionnaire method is economical.

It is comparatively a costly method as most of the enumerators are paid.

7. Reliability The information collected through it is less reliable as informants cannot give correct answers to some of the questions.

It is reliable method as the enumerators can get correct answers after clarifying the questions to the informants.

8. Delay There is delay in the receipt of information by this method.

The information is quickly collected by the enumerators.

Q2. The table shows the data of Expenditure of a family on food, clothing, education, rent and other items.

Items Expenditure

Food 4300

Clothing 1200

Education 700

Rent 2000

Others 600

Depict the data shown in the table using Pie chart.

Answer:

Items Food Clothing Education Others Rent

Expenditure 4300 1200 700 600 2000

6 | P a g e

MB0040 Set2

Q3. Average weight of 100 screws in box „A‟ is 10.4 gms. It is mixed with 150 screws of box „B‟. Average weight of mixed screws is 10.9 gms. Find the average weight of screws of box „B‟.

Answer:

Given: Average Weight in Box ‘A’ [XA] = 10.4 gms.

Number of Screws in Box ‘A’ [NA] = 100.

Number of Screws in Box ‘B’ [NB] =150.

Average Weight of mixed Screws [XAB] =10.9 gms.

[XAB] = NA XA + NB XB

NA + NB

10.9 = (100 X 10.4) + (150 X XB)

100 + 150

XB = 11.23 gms.

7 | P a g e

MB0040 Set2

Q4. (a) Discuss the rules of “Probability”. (b) What is meant by “Conditional Probability”?

Answer:

4(a)Rules of Probability (unit-5) (5.2 and 5.3)

Managers very often come across with situations where they have to take decisions about implementing either course of action A or course of action B or course of action C. Sometimes, they have to take decisions regarding the implementation of both A and B.

For Example: A Sales manager may like to know the probability that he will exceed the target for product A or product B.sometimes,he would like to know the probability that the sales of product A and B will exceed the target.the first type of probability is answered by addition rule.the second type of probability is answered by multiplication rule.

Addition rule:

The addition rule of probability states that:

i)     If ‘A’ and ‘B’ are any two events then the probability of the occurrence of either ‘A’ or ‘B’ is given by:

ii)     If ‘A’ and ‘B’ are two mutually exclusive events then the probability of occurrence of either A or B is given by:

iii)     If A, B and C are any three events then the probability of occurrence of either A or B or C is given by:

In terms of Venn diagram, we can calculate the probability of occurrence of either event ‘A’ or event ‘B’, given that event ‘A’ and event ‘B’ are dependent events. From the figure 5.5, we can calculate the probability of occurrence of either ‘A’ or ‘B’, given that, events ‘A’ and ‘B’ are independent events. From the figure 5.6, we can calculate the probability of occurrence of either ‘A’ or ‘B’ or ‘C’, given that, events ‘A’, ‘B’ and ‘C’ are dependent events.

8 | P a g e

MB0040 Set2

iv)     If A1, A2, A3………, An are ‘n’ mutually exclusive and exhaustive events then the probability of occurrence of at least one of them is given by:

Multiplication rule :

If ‘A’ and ‘B’ are two independent events then the probability of occurrence of ‘A’ and ‘B’ is given by:

4(b) Conditional Probability :

Sometimes we wish to know the probability that the price of a particular petroleum product will rise, given that the finance minister has increased the petrol price. Such probabilities are known as conditional probabilities.

Thus the conditional probability of occurrence of an event ‘A’ given that the event ‘B’ has already occurred is denoted by P (A / B). Here, ‘A’ and ‘B’ are dependent events. Therefore, we have the following rules.

If ‘A’ and ‘B’ are dependent events, then the probability of occurrence of ‘A and B’ is given by:

It follows that:

 

 

9 | P a g e

MB0040 Set2

For any bivariate distribution, there exists two marginal distributions and ‘m + n’ conditional distributions, where ‘m’ and ‘n’ are the number of classifications/characteristics studied on two variables.

10 | P a g e

MB0040 Set2

Q5. (a) What is meant by “Hypothesis Testing”? Give Examples (b) Differentiate between “Type-I” and “Type-II” Errors

Answer:

5(a) In hypothesis testing, we must state the assumed or hypothesised value of the population parameter before we begin sampling. The assumption we wish to test is called the null hypothesis and is symbolised by ’Ho’.

The term ‘null hypothesis’ arises from earlier agricultural and medical applications of statistics. In order to test the effectiveness of a new fertilizer or drug, the tested hypothesis (the null hypothesis) was that it had no effect, that is, there was no difference between treated and untreated samples. If we use a hypothesised value of a population mean in a problem, we would represent it symbolically as ‘mH0’. This is read – ‘The hypothesised value of the population mean’.

If our sample results fail to support the null hypothesis, we must conclude that something else is true. Whenever we reject the hypothesis, the conclusion we do accept is called the alternative hypothesis and is symbolised H1 (“H sub-one”).

For the null hypothesis H0: m = 200, we will consider three alternative hypothesis as:

H1: m ¹ 200 (population mean is not equal to 200)

H1: m > 200 (population mean greater than 200)

H1: m < 200 (population mean less than 200)

Example

We want to test the hypothesis that the population mean is equal to 500. We would symbolise it as follows and read it as,

The null hypothesis is that the population mean = 500 written as,

The purpose of hypothesis testing is not to question the computed value of the sample statistic but to make a judgment about the difference between that sample statistic and a hypothesised population parameter. The next step after stating the null and alternative hypotheses is to decide what criterion to be

11 | P a g e

MB0040 Set2

used for deciding whether to accept or reject the null hypothesis. If we assume the hypothesis is correct, then the significance level will indicate the percentage of sample means that is outside certain limits (In estimation, the confidence level indicates the percentage of sample means that falls within the defined confidence limits).

 5(b) Type I error:

Suppose that making a Type I error (rejecting a null hypothesis when it is true) involves the time and trouble of reworking a batch of chemicals that should have been accepted. At the same time, making a Type II error (accepting a null hypothesis when it is false) means taking a chance that an entire group of users of this chemical compound will be poisoned. Obviously, the management of this company will prefer a Type I error to a Type II error and, as a result, will set very high levels of significance in its testing to get low b’s.

Type II error:

Suppose, on the other hand, that making a Type I error involves disassembling an entire engine at the factory, but making a Type II error involves relatively inexpensive warranty repairs by the dealers. Then the manufacturer is more likely to prefer a Type II error and will set lower significance levels in its testing.

Q6. From the following table, calculate Laspyres Index Number, Paasches Index Number, Fisher‟s Price Index Number and Dorbish & Bowley‟s Index Number taking 2008 as the base year?

Commodity 2008 2009

Price (Rs) per Kg Quantity in Kg Price (Rs) per Kg

Quantity in Kg

A 6 50 10 56

B 2 100 2 120

C 4 60 6 60

D 10 30 12 24

E 8 40 12 36

12 | P a g e

MB0040 Set2

Answer:

Commodity

2008 2009

P0q0 P1q1 P0q1 P1q0Price (Rs.) per Kg (P0)

Qty in Kg

(q0)

Price (Rs.) per Kg (P1)

Qty in Kg

(q1)

A 6 50 10 56 300 560 336 500

B 2 100 2 120 200 240 240 200

C 4 60 6 60 240 360 240 360

D 10 30 12 24 300 288 240 360

E 8 40 12 36 320 432 288 480

Total (Σ) 1360 1880 1344 1900

a) Laspeyer’s Method= P01= Σ P1q0 X 100

Σ P0q0

Laspeyer’s Index Number= P01= 1900 X 100 = 139.71

1360

b) Paasche’s Method= P01= Σ P1q1 X 100

Σ P0q1

Paasche’s Index Number= P01= 1880 X 100 = 139.88

1344

c) Dorbish and Bowley’s Method= P01= Σ P1q0 + Σ P1q1

13 | P a g e

MB0040 Set2

Σ P0q0 Σ P0q1 X 100

2

Or

L + P

2

Dorbish & Bowley’s Index Number= P01= 139.71+139.88 = 139.80

2

d) Fisher’s Method= P01= √Σ P1q0 X Σ P1q1 X 100

Σ P0q0 Σ P0q1

Fisher’s Price Index Number= P01= √ 1900 X 1880 X 100 = 139.79

1360 1344

************

14 | P a g e