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.A-1)

a)Meaning of statistical survey

A Statistical Survey is a scientific process of collection and analysis of numerical data. Statistical surveys are used to collect information about units in a population and it involves asking questions to individuals. Surveys of human populations are common in government, health, social science and marketing sectors.b)Stages of statistical survey (Listing and Explanation)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.Stagaes of Statistical Survey-Statistical surveys are categorized into two stages- Planning and Execution.

1) Planning a Statistical Survey- The relevance and accuracy of data obtained in a survey depends upon the care exercised in planning. A properly planned investigation can lead to best result with least cost and time.A. Nature of the problem to investigate should be clearly defined in an unambiguous manner.B. Objective of investigation should be stated at the outset objectives could be to:> Obtain certain estimates Establish a theory Verify an existing statement Find relationship between characteristicsA. The scope of investigation has to be made clear. The scope of investigation refers to the area to be covered, identification of units to be studied, nature of characteristics to be observed,accuracy of measurements, analytical methods, time, cost and other resources required.B. Whether to use data collected from primary or secondary source should be determination in advance.C. The organization of investigation I the final step in the process. It encompasses the determination of the number of investigators required, their training, and supervision work needed funds required.

c)Methods for collecting dataCollection of data is the first and most important stage in any statistical survey. The method for collection of data depends upon various factors such as objective, scope, nature of investigation and availability of resources. Direct personal interviews, third party agencies, and questionnaires are some ways through which data is collected.Primary data :Primary data is the one, which is collected by the investigator for the purpose of a specific inquiry or study. Such data is original in character and is generated by a survey conducted by individuals or a research institution or any organisation. For Example: If a researcher is interested to know the impact of a non-meal scheme for school children, he/she has to undertake a survey and collect data on the opinion of parents and children by asking relevant questions. Such a data collected is called primary data. Collection of primary data is done by a suitable method as per the following: 1. Direct personal observation 2. Indirect oral interview 3. Information through agencies 4. Information through mailed questionnaires 5. Information through a schedule filled by investigators.Secondary data: Any information, that is used for the current investigation but is obtained from some data, which has been collected and used by some other agency or person in a separate investigation, or survey, is known as secondary data. They are available in a published or unpublished form. In published form, secondary data is available in research papers, newspapers, magazines, government publication, international publication, and websites.a)Published sources The various sources of published data are: Reports and official publications of international and national organisations as well as central and state governments Publications of several local bodies such as municipal corporations and district boards Financial and economic journals Annual reports of various companies Publications brought out by research agencies and research scholars Some of the journals (both academic and non-academic) are published at regular intervals like yearly, monthly, weekly whereas, other publications are more ad hoc. Internet is a powerful source of secondary data, which can be accessed at any time for any further analysis of the study.

b)Unpublished sources It is not necessary that all statistical contents have to be published. Unpublished data such as records maintained by various government and private offices, studies made by research institutions and scholars can also be used where necessary. Though, use of secondary data is economic in terms of expense, time and manpower requirement, researcher must be careful in choosing such secondary data. Secondary data must possess the following characteristic: 1) Reliability of data: The reliability related to secondary data can be tested by investigating a) Who collected the data? b) What were the sources of data? c) Whether they are collected by a proper method? d) At what time were they collected? f) What level of accuracy was desired? Was it achieved

Q-2)a)Explain the approaches to define probability.Probability is a numerical measure which indicates the chance of occurrence of an event A. It is denoted by P(A). It is the ratio between the favourable outcomes of an event A (m) to the total outcomes of the experiment (n). In other words: P(A)= Where, m is the number of favourable outcomes of an event A and n is the total number of outcomes of the experiment. Probability is a numerical measure which indicates the chance of occurrence.

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?P(A1) = P( that the machine A1 manufacture the bolts) = 25%= 0.25Similarly P(A2) = 35% = 0.35 and P(A3) = 40% = 0.40 Let B be the event that the drawn bolt is defective.P(B/ A1) = P (that the defective bolt from the machine A1)= 5 % = 0.05 Similarly, P(B/ A2) = 4% = 0.04 AndP(B/ A3)= 2% = 0.02We have to find P(A2/ B).Hence by Bayes theorem, we get

P(A2/ B).= (P(A2)P(B/A2))/( ( P(A1) P(B/A1))+ ( P(A2) P(B/A2))+ ( P(A3) P(B/A3)))

=(0.35X0.04)(0.25)(0.05) + (0.35)(0.04) + (0.4)(0.02)= 28/69= 0.4058

Q-3)a)The procedure of testing hypothesis requires a researcher to adopt several steps. Describe in brief all such steps.b)A sample of 400 items is taken from a normal population whose mean as well as variance is 4. If the sample mean is 4.5, can the sample be regarded as a truly random sample?a) Hypothesis testing procedureThere are five steps involved in testing on hypothesis while are as follows:

a)Formulate a Hypothesis: The first step is to set up two hypothesis instead of one in such a way that if one hypothesis is true, the other is false. Alternatively; if one hypothesis is false or rejected then the other is true or accepted.b)Set up a suitable significance level: After formulating the hypothesis, the next steps is to test its validity at a certain level of significance. The confidence with which a null hypothesis is rejected or accepted depends on the significance level used for the purpose.c)Select test criterion: The next steps in hypothesis testing in the selection of an appropriate statistical technique as a test criterion. There are many techniques from which one is to be chosen. For example, when the hypothesis partners to a large of more than 30, the Z test implying normal distribution is used for population mean. If the sample is small (n