mba stat as tics sikkim manipal assignment- set 2

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    Set-2

    1. What do you mean by Statistical Survey?Differentiate between Questionnaire and

    Schedule?

    Ans 1. Definition of statistical survey

    A Statistical survey is a scientific process of collection and analysis ofnumerical data. Statistical surveys are used to collect numericalinformation about units in a population. Surveys involve askingquestions to individuals. Surveys of human populations are common ingovernment, 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. Thequestionnaires are filled with questions pertaining to the investigation. They are sent to the respondents with a covering letter solicitingcooperation from the respondents (respondents are the people whorespond to questions in the questionnaire). The respondents are askedto give correct information and to mail the questionnaire back. Theobjectives of investigation are explained in the covering letter together

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    with assurance for keeping information provided by the respondents asconfidential.

    Good questionnaire construction is an important contributing factor tothe success of a survey. When questionnaires are properly framed and

    constructed, they become important tools by which statements can bemade about specific people or entire populations.

    This method is generally adopted by research workers and otherofficial and non-official agencies. This method is used to cover largeareas of investigation. It is more economical and free frominvestigators bias. However, it results in many non-responsesituations. The respondent may be illiterate. The respondent may alsoprovide 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 thatare biased, then the survey would be useless. An important method forchecking and making sure whether a questionnaire is accuratelycapturing the intended information is to pre-test among a smallersubset of target respondents.

    Success of questionnaire method of collection of data depends mainlyon proper drafting of the questionnaire. You have to keep the followingpoints 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 questionnaireshould not disturb the privacy of the respondents. The task of completion of questionnaire should not have much writingwork. Necessary instructions and glossary should be given in coveringletter. Questions involving technological jargons and mathematicalcalculations should be avoided.

    The completed questionnaire should be kept confidential and usedonly 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 thequestionnaire. A questionnaire can have Contingency questions, Matrixquestions, Closed ended questions and Open ended questions. Letshave a look at each one in detail

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    Contingency questions are questions that are answered only if therespondent gives a particular response to a previous question. Thisavoids 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 thetop and a list of questions are placed down the side. This is used toefficiently occupy page space and respondents time.

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

    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 fromwhich 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 to10, with 10 implying the most preferred appearance and 1 implyingthe least preferred appearance). Scaled questions are mostly questionsrelated to attitudes. A Likert scale provides a number of attitudestatements. The respondent has to say how much they agree ordisagree with each one.

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    Open ended questions are those questions for which the respondentsupplies 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 incompletestory.

    Picture completion In these, respondents fill in an emptyconversation balloon.

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

    Information through schedule filled by investigators

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

    A schedule is suitable for an extensive area of investigation throughinvestigators personal contact. The problem of non-response isminimised.

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

    Difference between Questionnaire and Schedule is as follows:

    S.No.

    Basis Questionnaire Schedule

    1. Liabilityfor fillingup

    Informant is liable forfilling it up.

    Enumerator fills it upafter getting answersfrom informants.

    2. Means of It is sent to the Enumerators

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    Information

    informants by post. themselves take upschedules and contactthe informants.

    3. PersonalRelations

    hip

    Investigator does nothave a personal contact

    with the informants.

    Both investigator andinformants have

    personal contactthrough schedule.

    4. Nature ofInformation

    Sometimes incompleteas there is lack ofpersonal contact.

    Complete information isreceived because of thepersonal contactbetween theinvestigator andinformants.

    5. Scope ofEnquiry

    The use of Questionnaireis suitable where theinformants are literate.

    Schedule can be usedfor both literate as wellas illiterate persons.

    6. Economical

    Information by mailedquestionnaire method iseconomical.

    It is comparatively acostly method as mostof the enumerators arepaid.

    7. Reliability The information collectedthrough it is less reliableas informants cannotgive correct answers tosome of the questions.

    It is reliable method asthe enumerators canget correct answersafter clarifying thequestions to theinformants.

    8. Delay There is delay in the

    receipt of information bythis method.

    The information is

    quickly collected by theenumerators.

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

    Items Expenditure

    Food 4300Clothing 1200Education 700Rent 2000Others 600

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    Depict the data shown in the table using Pie chart.

    Ans 2.

    Items Food Clothing Education Others Rent

    Expenditure 4300 1200 700 600 2000

    PIE CHART

    4300

    1200

    700

    600

    2000

    Food

    Clothing

    Education

    Others

    Rent

    Q3. Average weight of 100 screws in box A is 10.4 gms. Itis mixed with 150 screws of box B. Average weight ofmixed screws is 10.9 gms. Find the average weight of screwsof box B?

    Ans 3. 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 XBNA + NB

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

    XB = 11.23 gms.

    4. (a) Discuss the rules of Probability.

    (b) What is meant by Conditional Probability?

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

    Managers very often come across with situations where they have totake decisions about implementing either course of action A or courseof 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 hewill exceed the target for product A or product B.sometimes,he wouldlike to know the probability that the sales of product A and B willexceed the target.the first type of probability is answered by additionrule.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 ofoccurrence of either event A or event B, given that event A andevent B are dependent events. From the figure 5.5, we can calculatethe probability of occurrence of either A or B, given that, events Aand B are independent events. From the figure 5.6, we can calculate

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    the probability of occurrence of either A or B or C, given that,events A, B and C are dependent events.

    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:

    5(b) Conditional Probability :

    Sometimes we wish to know the probability that the price of aparticular petroleum product will rise, given that the finance ministerhas increased the petrol price. Such probabilities are known asconditional probabilities.

    Thus the conditional probability of occurrence of an event A giventhat the event B has already occurred is denoted by P (A / B). Here,A and B are dependent events. Therefore, we have the followingrules.

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

    It follows that:

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    For any bivariate distribution, there exists two marginal distributionsandm + n conditional distributions, where m and n are the number of

    classifications/characteristics studied on two variables.

    5. (a) What is meant by Hypothesis Testing? GiveExamples(b) Differentiate between Type-I and Type-II Errors?

    Ans 5 In hypothesis testing, we must state the assumed orhypothesised value of the population parameter before we beginsampling. The assumption we wish to test is called the null hypothesisand is symbolised by Ho.

    The term null hypothesis arises from earlier agricultural and medicalapplications of statistics. In order to test the effectiveness of a new

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    fertilizer or drug, the tested hypothesis (the null hypothesis) was that ithad no effect, that is, there was no difference between treated anduntreated samples. If we use a hypothesised value of a population

    mean in a problem, we would represent it symbolically as H0. This isread The hypothesised value of the population mean.

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

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

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

    H1: > 200 (population mean greater than 200)

    H1: < 200 (population mean less than 200)

    Example

    We want to test the hypothesis that the population meanis equal to 500. We would symbolise it as follows and readit as,

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

    The purpose of hypothesis testing is not to question the computedvalue of the sample statistic but to make a judgment about thedifference between that sample statistic and a hypothesisedpopulation parameter.

    The next step after stating the null and alternative hypotheses is todecide what criterion to be used for deciding whether to accept orreject the null hypothesis. If we assume the hypothesis is correct, thenthe significance level will indicate the percentage of sample means

    that is outside certain limits (In estimation, the confidence levelindicates the percentage of sample means that falls within the definedconfidence limits).

    5(b) Type I error:

    Suppose that making a Type I error (rejecting a null hypothesis when itis true) involves the time and trouble of reworking a batch of chemicals

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    that should have been accepted. At the same time, making a Type IIerror (accepting a null hypothesis when it is false) means taking achance that an entire group of users of this chemical compound will bepoisoned. Obviously, the management of this company will prefer aType I error to a Type II error and, as a result, will set very high levels

    of significance in its testing to get low s.

    Type II error:

    Suppose, on the other hand, that making a Type I error involvesdisassembling an entire engine at the factory, but making a Type IIerror involves relatively inexpensive warranty repairs by the dealers.

    Then the manufacturer is more likely to prefer a Type II error and willset lower significance levels in its testing.

    Q6. From the following table, calculate Laspyres IndexNumber, Paasches Index Number, Fishers Price IndexNumber and Dorbish & Bowleys Index Number taking 2008as the base year?

    Commodity 2008 2009

    Price (Rs) per Kg Quantityin Kg

    Price (Rs) perKg

    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

    Ans 6.

    Commodity

    2008 2009

    P0q0 P1q1 P0q1 P1q0Price(Rs.) perKg (P0)

    Qty inKg(q0)

    Price(Rs.) perKg (P1)

    Qty inKg(q1)

    A 6 50 10 56 300 560 336 500B 2 100 2 120 200 240 240 200C 4 60 6 60 240 360 240 360D 10 30 12 24 300 288 240 360

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    E 8 40 12 36 320 432 288 480Total () 1360 1880 1344 1900

    a) Laspeyers Method= P01= P1q0 X 100

    P0q0

    Laspeyers Index Number= P01= 1900 X 100 = 139.711360

    b) Paasches Method= P01= P1q1 X 100 P0q1

    Paasches Index Number= P01= 1880 X 100 = 139.881344

    c) Dorbish and Bowleys Method= P01= P1q0 + P1q1 P0q0 P0q1 X 100

    2OrL + P

    2Dorbish & Bowleys Index Number= P01= 139.71+139.88 = 139.80

    2

    d) Fishers Method= P01= P1q0 X P1q1 X 100 P0q0 P0q1

    Fishers Price Index Number= P01= 1900 X 1880 X 100 = 139.791360 1344

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