Estimates and Estimation

Post about Estimates and Estimation that include point estimation, interval estimation, level of significance, Properties of estimators, and real-life examples about estimate and estimation.

Statistical Inference: An Introduction

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Introduction to Statistical Inference

Inference means conclusion. When we discuss statistical inference, it is the branch of Statistics that deals with the methods to make conclusions (inferences) about a population (called reference population or target population), based on sample information. The statistical inference is also known as inferential statistics. As we know, there are two branches of Statistics: descriptive and inferential.

Statistical inference is a cornerstone of many fields of life. It allows the researchers to make informed decisions based on data, even when they can not study the entire population of interest. The statistical inference has two fields of study:

Statistical Inference

Estimation

Estimation is the procedure by which we obtain an estimate of the true but unknown value of a population parameter by using the sample information that is taken from that population. For example, we can find the mean of a population by computing the mean of a sample drawn from that population.

Estimator

The estimator is a statistic (Rule or formula) whose calculated values are used to estimate (a wise guess from data information) is used to estimate a population parameter $\theta$.

Estimate

An estimate is a particular realization of an estimator $\hat{\theta}$. It is the notation of a sample statistic.

Types of Estimators

An estimator can be classified either as a point estimate or an interval estimate.

Point Estimate

A point estimate is a single number that can be regarded as the most plausible value of the $\theta$ (notation for a population parameter).

Interval Estimate

An interval estimate is a set of values indicating confidence that the interval will contain the true value of the population parameter $\theta$.

Testing of Hypothesis

Testing of Hypothesis is a procedure that enables us to decide, based on information obtained by sampling procedure whether to accept or reject a specific statement or hypothesis regarding the value of a parameter in a Statistical problem.

Note that since we rely on samples, there is always some chance our inferences are not perfect. Statistical inference acknowledges this by incorporating concepts like probability and confidence intervals. These help us quantify the uncertainty in our estimates and test results.

Important Considerations about Testing of Hypothesis

  • Hypothesis testing does not prove anything; it provides evidence for or against a claim.
  • There is always a chance of making errors (Type I or Type II).
  • The results are specific to the chosen sample and significance level.

FAQs about Statistical Inference

  1. Define the term estimation.
  2. Define the term estimate.
  3. Define the term estimator.
  4. Write a short note on statistical inference.
  5. What is statistical hypothesis testing?
  6. What is the estimation in statistics?
  7. What are the types of estimations?
  8. Write about point estimation and intervention estimation.

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Best Estimation Online Quiz

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MCQs from Statistical Inference covering the topics of Estimation and Hypothesis Testing for the preparation of exams and different statistical job tests in Government/ Semi-Government or Private Organization sectors. This Estimation online quiz will also help get admission to different colleges and Universities. The Estimation Online Quiz will help the learner to understand the related concepts and enhance their knowledge.

Estimation Online Quiz with Answers

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Statistical inference is a branch of statistics in which we conclude (make wise decisions) about the population parameter by making use of sample information. To draw wise decisions, one can use estimation and hypothesis testing techniques based on extracted information from descriptive statistics. Statistical inference can be further divided into the Estimation of parameters and testing of the hypothesis.

Statistical estimation is the foundation of learning about a population by analyzing a sample. It’s essentially making educated guesses about population characteristics (parameters) based on the data we collect (samples).

Estimation Online Quiz

Estimation is a way of finding the unknown value of the population parameter from the sample information by using an estimator (a statistical formula) to estimate the parameter. One can estimate the population parameter by using two approaches (I) Point Estimation and (ii) Interval Estimation.

In point Estimation, a single numerical value is computed for each parameter, while in interval estimation a set of values (interval) for the parameter is constructed. The width of the confidence interval depends on the sample size and confidence coefficient. However, it can be decreased by increasing the sample size. The estimator is a formula used to estimate the population parameter by making use of sample information.

There are various techniques for statistical estimation that depends on the type of data and parameter of interest begin estimated. The followings are few techniques for statistical estimation:

  • Mean Estimation: Sample mean is used to estimate the population mean for continuous data.
  • Proportion Estimation: Sample proportion is used to estimate the population proportion for categorical data (e.g., yes/ no response).
  • Regression Analysis: Used to estimate relationships between variables and make predictions about a dependent variable based on an independent variable.
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Statistical estimation is a powerful tool that allows us to:

  • Move beyond the sample: Make generalizations about the population from which the data came.
  • Quantify uncertainty: Acknowledge the inherent variability in using samples and express the margin of error in the estimates.
  • Guide decision-making: Inform choices based on the best available information about the population.

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Important Online Estimation Quiz 7

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Online Estimation Quiz from Statistical Inference covers the topics of Estimation and Hypothesis Testing for the preparation of exams and different statistical job tests in Government/ Semi-Government or Private Organization sectors. These tests are also helpful in getting admission to different colleges and Universities. The online MCQS estimation quiz will help the learner understand the related concepts and enhance their knowledge.

MCQs about statistical inference covering the topics estimation, estimator, point estimate, interval estimate, properties of a good estimator, unbiasedness, efficiency, sufficiency, Large sample, and sample estimation.

1. t-distribution is used when

 
 
 
 

2. The best estimator of population proportion ($\pi$) is:

 
 
 
 

3. If $1-\alpha=0.90$ then value of $Z_{\frac{\alpha}{2}}$ is

 
 
 
 

4. For $\alpha=0.05$, the critical value of $Z_{0.05}$ is equal to

 
 
 
 

5. If $Var(T_2)<Var(T_1)$ then $T_2$ is

 
 
 
 

6. The consistency of an estimator can be checked by comparing

 
 
 
 

7. A large sample contains more than

 
 
 
 

8. For a biased estimator $\hat{\theta}$ of $\theta$, which one of the following is correct.

 
 
 
 

9. In a $Z$-test the number of degrees of freedom is

 
 
 
 

10. By decreasing $\overline{X}$ the length of the confidence interval for $\mu$

 
 
 
 

11. A statistician calculates a 95% confidence interval for $\mu$ when $\sigma$ is known. The confidence interval is Rs 18000 to 22000, and then amount of sample means $\overline{X}$ is:

 
 
 
 

12. A sample is considered a small sample if the size is

 
 
 
 

13. If $\mu=130, \overline{X}=150, \sigma=5$, and $n=10$. What Statistic is appropriate.

 
 
 
 

14. In applying t-test

 
 
 
 

15. A confidence interval will be widened if:

 
 
 
 

16. The width of the confidence interval decreases if the confidence coefficient is

 
 
 
 

17. If the population Standard Deviation is unknown and the sample size is less than 30, then the Confidence Interval for the population mean ($\mu$) is

 
 
 
 

18. Which is NOT the property of a point estimator?

 
 
 
 

19. Criteria to check a point estimator to be good are

 
 
 
 

20. Interval estimation and confidence interval are:

 
 
 
 

Statistical inference is a branch of statistics in which we conclude (make some wise decisions) about the population parameter using sample information. Statistical inference can be further divided into the Estimation of the Population Parameters and the Hypothesis Testing.

Estimation is a way of finding the unknown value of the population parameter from the sample information by using an estimator (a statistical formula) to estimate the parameter. One can estimate the population parameter by using two approaches (I) Point Estimation and (ii) Interval Estimation.

Online Estimation Quiz

  • A large sample contains more than
  • A sample is considered a small sample if the size is
  • In applying t-test
  • t-distribution is used when
  • If the population Standard Deviation is unknown and the sample size is less than 30, then the Confidence Interval for the population mean ($\mu$) is
  • If $\mu=130, \overline{X}=150, \sigma=5$, and $n=10$. What Statistic is appropriate?
  • If $1-\alpha=0.90$ then value of $Z_{\frac{\alpha}{2}}$ is
  • For $\alpha=0.05$, the critical value of $Z_{0.05}$ is equal to
  • In a $Z$-test the number of degrees of freedom is
  • The width of the confidence interval decreases if the confidence coefficient is
  • By decreasing $\overline{X}$ the length of the confidence interval for $\mu$
  • A statistician calculates a 95% confidence interval for $\mu$ when $\sigma$ is known. The confidence interval is Rs 18000 to 22000, and then the amount of sample means $\overline{X}$ is:
  • Criteria to check a point estimator to be good are
  • The consistency of an estimator can be checked by comparing
  • If $Var(T_2)<Var(T_1)$ then $T_2$ is
  • For a biased estimator $\hat{\theta}$ of $\theta$, which one of the following is correct?
  • Which is NOT the property of a point estimator?
  • The best estimator of population proportion ($\pi$) is:
  • Interval estimation and confidence interval are:
  • A confidence interval will be widened if:

In point estimation, a single numerical value is computed for each parameter, while in an interval estimation, a set of values (interval) for the parameter is constructed. The width of the confidence interval depends on the sample size and confidence coefficient. However, it can be decreased by increasing the sample size. The estimator is a formula used to estimate the population parameter by making use of sample information.

Online Estimation Quiz

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Important MCQs Estimation 6

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MCQs Estimation Quiz covers the topics of Estimation for the preparation of exams and different statistical job tests in Government/ Semi-Government or Private Organization sectors. These quizzes help get admission to different colleges and Universities. The MCQs Estimation Quiz will help the learner to understand the related concepts and enhance the knowledge too.

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Statistical inference is a branch of statistics in which we conclude (make wise decisions) about the population parameter by making use of sample information. Statistical inference can be further divided into the Estimation of parameters and testing of the hypothesis.

Estimation is a way of finding the unknown value of the population parameter from the sample information by using an estimator (a statistical formula) to estimate the parameter. One can estimate the population parameter by using two approaches (I) Point Estimation and (ii) Interval Estimation.
In point Estimation, a single numerical value is computed for each parameter, while in interval estimation a set of values (interval) for the parameter is constructed. The width of the confidence interval depends on the sample size and confidence coefficient. However, it can be decreased by increasing the sample size. The estimator is a formula used to estimate the population parameter by making use of sample information.

Online MCQs Estimation with Answers

  • Criteria to check a point estimator to be good are
  • By the method of moments, one can estimate:
  • If the sample average $\overline{x}$ is an estimate of the population mean $\mu$, then $\overline{x}$ is:
  • A quantity obtained by applying a certain rule or formula is known as
  • The consistency of an estimator can be checked by comparing
  • For an estimator to be consistent, the unbiasedness of the estimator is
  • Sample median as an estimator of the population mean is always
  • Roa-Blackwell Theorem enables us to obtain minimum variance unbiased estimator through:
  • An estimator $T_n$ is said to be a sufficient statistic for a parameter function $\tau(\theta)$ if it contains all the information which is contained in the:
  • Crammer-Rao inequality is valid in the case of:
  • If $n_1=16$, $n_2=9$ and $\alpha=0.01$, then $t_{\frac{\alpha}{2}}$ will be
  • If $\alpha=0.10$ and $n=15$ then $t_{\frac{\alpha}{2}}$ will be
  • A _ is the specific value of the statistics used to estimate the population parameter.
  • An Estimator $\hat{T}$ is an unbiased estimator of the population parameter $T$ if
  • Since $E(X)=$_______. $X$ is said to be an unbiased estimator of the population mean.
  • The sample proportion $\hat{p}$ is ________ estimator Sampling error decreases by the sample size.
  • __________ is the value of a sample statistic.
  • __________ is an estimate expressed by a single value.
  • The estimation and testing of the hypothesis are the main branches of ________.
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