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Statistics: Planning and Executing Effective Questionnaires and Sampling Techniques, Exercises of Statistics

Aliah UniversityStatistics

Answers to frequently asked questions about planning effective questionnaires, defining various sampling techniques, and understanding statistical concepts such as acceptance and rejection regions, null and alternative hypotheses, and quartiles. Topics covered include simple and stratified sampling, stem and leaf method, and the relationship between arithmetic mean, geometric mean, and harmonic mean.

Typology: Exercises

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Question:
How we can plan right QUESTIONNAIRES for the intended audince.
Answer:
COLLECTION THROUGH QUESTIONNAIRES: This method is considered as the standard method for routine business and
administrative inquiries. Questions should be few, brief, very simple, and easy for all respondents to answer, clearly worded a
nd not
offensive to certain respondents.
Question:
Define random sampling.
Answer: In random sampling, all items have some chance of selection that can be calculated. Five common random sampling techniques ar
e:
simple random sampling, systematic sampling, stratified sampling, cluster sampling, and multi-stage sampling
Question:
sampling frame and sampling units.
Answer: The list or map that identifies every unit within the target population is the sampling frame. Such a map or list is needed so th
at
every individual member of the population can be identified unambiguously. The individual members of the target population wh
ose
characteristics are to be measured are the sampling units.
Question:
What is Ogive and polygon.
Answer: In statistics, an ogive is the curve of a cumulative distribution function. polygon and ogive are same.
Question:
What is simple random and stratified sampling.
Answer: Simple random sampling: With simple random sampling, each item in a population has an equal chance
of inclusion in the sample.
Stratified sampling: In stratified sampling, the population is divided into groups called strata. A sample is then drawn from
within
these strata. Some examples of strata commonly used by the ABS are States, Age and Sex. Other
ability or marital status.
Question:
Define cluster sampling.
Answer: Cluster sampling divides the population into groups, or clusters. A number of clusters are selected randomly to represent the
population, and then all units within selected clusters are included in the sample.
Question:
ACCEPTANCE AND REJECTION REGIONS.
Answer: ACCEPTANCE AND REJECTION REGIONS: All possible values which a test-
statistic may assume can be divided into two
mutually exclusive groups
: One group consisting of values which appear to be consistent with the null hypothesis (i.e. values which
appear to support the null hypothesis), and the other having values which lead to the rejection of the null hypothesis The fi
rst group
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Question: How we can plan right QUESTIONNAIRES for the intended audince. Answer: COLLECTION THROUGH QUESTIONNAIRES: This method is considered as the standard method for routine business and administrative inquiries. Questions should be few, brief, very simple, and easy for all respondents to answer, clearly worded a nd not offensive to certain respondents. Question: Define random sampling. Answer: In random sampling, all items have some chance of selection that can be calculated. Five common random sampling techniques ar e: simple random sampling, systematic sampling, stratified sampling, cluster sampling, and multi-stage sampling Question: sampling frame and sampling units. Answer: The list or map that identifies every unit within the target population is the sampling frame. Such a map or list is needed so th at every individual member of the population can be identified unambiguously. The individual members of the target population wh ose characteristics are to be measured are the sampling units. Question: What is Ogive and polygon. Answer: In statistics, an ogive is the curve of a cumulative distribution function. polygon and ogive are same. Question: What is simple random and stratified sampling. Answer: Simple random sampling: With simple random sampling, each item in a population has an equal chance of inclusion in the sample. Stratified sampling: In stratified sampling, the population is divided into groups called strata. A sample is then drawn from within these strata. Some examples of strata commonly used by the ABS are States, Age and Sex. Other strata may be religion, academic ability or marital status. Question: Define cluster sampling. Answer: Cluster sampling divides the population into groups, or clusters. A number of clusters are selected randomly to represent the population, and then all units within selected clusters are included in the sample. Question: ACCEPTANCE AND REJECTION REGIONS. Answer: ACCEPTANCE AND REJECTION REGIONS: All possible values which a test- statistic may assume can be divided into two mutually exclusive groups : One group consisting of values which appear to be consistent with the null hypothesis (i.e. values which appear to support the null hypothesis), and the other having values which lead to the rejection of the null hypothesis The fi rst group

is called the acceptance region and the second set of values is known as the rejection region for a test. The rejection region is also called the critical region. Question: Null & Alternative hypothesis: Answer: Null hypothesis: The hypothesis tentatively assumed t rue in the hypothesis testing procedure. or A null hypothesis, generally denoted by the symbol H0,is any hypothesis which is to be tested for possible rejection or nullification under the assumption that it is true. Alternative hypothesis: The hypothesis concluded to be true if the null hypothesis is rejected. It is denoted by H1. Question: What is stem and leaf method? Answer: Stem and leaf display is the method of summarizing data in such a way that no information in the data is lost. Question: Relation between A.M,G.M and H.M. Answer: Relation between arithmetic mean, geometric mean and harmonic mean is given below: Arithmetic Mean > Geometric Mean >Harmonic Mean I.e. for a data arithmetic mean is greater than geometric mean and harmonic mean. An d geometric mean is greater than harmonic mean. Question: Quartiles & their Uses. Answer: Quartile: The values which divide the distribution into four equal parts are called quartiles. Quartiles divide the data into four equal-sized and non-overlappin g parts. One fourth of the data lies below the Q1 (first quartile). Half of the data lies below Q2 (second quartile) similarly, three quarters of the data lies below Q3 (third quartile) Q2 (second quartile) is also known as median. Use of quartiles: In ord er to describe a data set without listing all the data, we have measures of location such as the mean and median, measures of spread such as the range and standard deviation. Quartiles are also used to describe the data in combination with other measures. For example they are used in five number summary of the data. The five number summary, i.e., the minimum, Q1, Q (median), Q3, and maximum, give a good indication of where data lie. The five number summary is sometimes represented graphically as a (box-and-)whisker plot. Question: What is Discrete Random Variable? Answer: Discrete Variable: A variable that is made up of distinct and separate units or categories and is, most of the times, counted only in whole numbers. Or Discrete Random Variable: A dis crete random variable is one that can take only a discrete set of integers or whole numbers. For discrete variables values are obtained by counting process. For example, if we toss three dice together, a nd let X denote the number of heads, then the random variable X consists of the values 0, 1, 2, and 3. Obviously, in this example, X is a discrete random variable A discrete random variable represents count data such as the number of persons in a family, the numb er of rooms in a house, the number of deaths in an accident, the income of an individual, etc.