Estimation Theory MBA 1st Year Semester Long Question Answer Study Notes 3 Mock Papers For Self-Assessment Unit-Wise Division Of The Content Knowledge Boosters To Illuminate The Learning Solved Case Studies For Practice Theory Of Estimation, Point Estimation, Interval Estimation. Hypothesis Testing Null And Altenative Hypothesis; Type I And Type Errors; Testing Of Hypothesis; Large Sample Test, Small Sample Test, (T,F,Z Test And Chi-Square Test) Notes.
LONG ANSWER QUESTIONS
Estimation Theory MBA 1st Year Semester Long Question Answer Study Notes | Index
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Q.1. Explain in detall types of estimation theory with confidence interval.
In statistics, estimation refers to the process by which one makes inferences about a population, based on information obtained from a sample.
Point Estimate vs Interval Estimate
Statisticians use sample statistics to estimate population parameters. For example, sample means are used to estimate population means; sample proportions, to estimate population proportions.
An estimate of a population parameter may be expressed in two ways:
1. Point Estimate: A point estimate of a population parameter is a single value of a statistic. For example, the sample mean X is a point estimate of the population meanu. Similarly, the sample proportion p is a point estimate of the population proportion P.
2. Interval Estimate: An interval estimate is defined by two numbers, between which a population parameter is said to lie. For example, a < x < b is an interval estimate of the
population mean u. It indicates that the population mean is greater than a but less than b.
Statisticians use a confidence interval to express the precision and uncertainty associated with a particular sampling method. A confidence interval consists of three parts.
1. A confidence level,
2. A statistic,
3. A margin of error.
The confidence level describes the uncertainty of a sampling method. The statistic and the margin of error define an interval estimate that describes the precision of the method. The interval estimate of a confidence interval is defined by the sample statistic + margin of error.
For example, suppose we compute an interval estimate of a population parameter. We might describe this interval estimate as a 95% confidence interval. This means that if we used the same sampling method to select different sample population parameter would fall within a range defined by the sample statistic#margin of error 95% of the time.
Confidence intervals are preferred to point estimates because confidence intervals indicate: (a) the precision of the estimate and (b) the uncertainty of the estimate.
1. Confidence Level
The probability part of a confidence interval is called a confidence level. The confidence level describes the likehood that a particular sampling method will produce a confidence interval that includes the true population parameter.
Here is how to interpret a confidence level. Suppose we collected all possible samples from a given population, and computed confidence intervals for each sample. Some confidence intervals would include the true population parameter: others would not. A 95% confidence level means that 95% of the intervals contain the true population parameter lain the true population parameter: a 90% confidence level means that 90% of the intervals contain the population parameter; and so on.
A sample statistics is used to construct a confidence interval. It includes sample mean, sample proportion that are used to estimate a population parameter.
3. Margin of Error
in a confidence interval, the range of values above and below the sample statistic is called the margin of error.
For example, suppose the local newspaper conducts an election survey and reports that the independent candidate will receive 30% of the vote. The newspaper states that the survey had a 5% margin of error and a confidence level of 95%. These findings result in the following confidence interval: We are 95% confident that the independent candidate will receive between 25% and 35% of the vote.
Note: Many public opinion surveys report interval estimates, but not confidence intervals. They provide the margin of error, but not the confidence level.
Q.2. What is test of significance? Discuss its procedures.(2007-08)
Ans. Test of Significance: A very important aspect of sampling theory is the study of the test of significance, which enables us to decide on the basis of the sample result if:
1. The deviation between the observed sample statistic and the hypothesis parameter value.
2. The deviation between two sample statistics is significant or due to change or the fluctuation of sampling.
Since, for large ‘n almost all the distributions, e.g. binomial, poisson, negative binomial, hyper-geometric, ‘e’,’F’,xetc. can be approximated very closely by a normal probability curve, we use the normal test of significance for large samples. Some of the well known test of significance to study such difference in small samples are t-test and Fisher’s transformation.
Procedure for Testing of Significance
Step 1. Null Hypothesis: Set-up the null hypothesis H.
Step 2. Alternative Hypothesis: Set-up the alternative hypothesis H. (Here, we should decide whether we have to use two tailed test or a single tailed test, i.e. right tailed test).
Step 3. Level of Significance: Choose the appropriate level of significance (a) depending on the reliability of the estimates and permissible risks, this is to be decided before sample is drawn, i.e. a is fixed in advance. (Usually we take a = 0.05 or 0.01).
Step 4. Test Statistic or Test Criteria: Compute the test statistic,S.Et)
5. Conclusion: We compare the computed value of Z in step 5 with the significant (criteria) value of Za at level of significance ‘a’.
Q.3. Describe the various steps involved in testing a statistical hypothesis.
Or Explain the procedure that is followed in testing of a statistical hypothesis.
Or What is the major purpose of hypothesis testing? Explain the various steps Involved in hypothe testing.
Ans. Hypothesis Testing: A hypothesis is a statement about the population parameter. Hypothesis testing/significance testing is a procedure that helps us to decide whether the hypothesised population. Parameter value is to be accepted or rejected by making use of the information obtained from th sample.
‘A hypomnesis in statistics is simply a quantitative statement about a population.’
‘Islands in the uncharted seas of thought are to be used as bases for consolidation and recuperation as we advance into the unknown.’