Best Sampling Quiz – 4

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The sampling Quiz in this post covers the MCQs related to Sampling and Sampling Distributions, Probability Sampling and Non-Probability Sampling, Mean and Standard Deviation of Sample, Sample size, Sampling error, Sample bias, Sample Selection, etc.

Sampling Quiz is about Basics of Sampling and Sampling Distributions. It will help you to understand the basic concepts related to sampling methods and sampling distributions. This test will also help you to prepare yourself for different exams related to education or jobs.

1. If we obtain a point estimate $\overline{X}$ for a population mean $\mu$, the difference between $\overline{X}$ and $\mu$ is called

 
 
 
 

2. A sample is a subset of

 
 
 
 

3. A clothing manufacturer wants to learn more about why their consumers have purchased the brand’s products. How should this manufacturer conduct their survey?

 
 
 
 

4. What is a standard error?

 
 
 
 

5. A list of all the units of the population is called

 
 
 
 

6. Any calculation on the sample data is called

 
 
 
 

7. A distribution formed by all possible values of a statistic is called

 
 
 
 

8. The difference between a statistic and the parameter is called

 
 
 
 

9. To make a voter list in Pakistan we need

 
 
 
 

10. The standard deviation of the sampling distribution of a statistic is called

 
 
 
 

11. The probability distribution of a statistic is called

 
 
 
 

12. The study of population is called

 
 
 
 

13. In probability sampling, the probability of selecting an item from the population is known and is

 
 
 
 

14. A company is trying to learn more about their customer base. They would like to survey to understand why their customers chose their brand. How should the company survey its customers?

 
 
 
 

15. A data professional is analyzing data about a population of aspen trees. They take repeated random samples of 10 trees from the population and compute the mean height for each sample. Which of the following statements best describes the sampling distribution of the mean?

 
 
 
 

16. In sampling with replacement, an element can be chosen

 
 
 
 

17. A high school principal is estimating the total number of students that will attend an upcoming event. She assumes that the older students are unlikely to attend and decides to only survey the first-year students. What issue will the principal face when calculating her estimation?

 
 
 
 

18. Sampling-based on equal probability is called

 
 
 
 

19. A population about which we want to get some information is called

 
 
 
 

20. Any measure of the population is called

 
 
 
 


Online Sampling Quiz with Answers

  • A sample is a subset of
  • A list of all the units of the population is called
  • Any calculation on the sample data is called
  • Any measure of the population is called
  • The difference between a statistic and the parameter is called
  • The probability distribution of a statistic is called
  • The standard deviation of the sampling distribution of a statistic is called
  • If we obtain a point estimate $\overline{X}$ for a population mean $\mu$, the difference between $\overline{X}$ and $\mu$ is called
  • A distribution formed by all possible values of a statistic is called
  • In probability sampling, the probability of selecting an item from the population is known and is
  • A population about which we want to get some information is called
  • The study of population is called
  • To make a voter list in Pakistan we need
  • Sampling-based on equal probability is called
  • In sampling with replacement, an element can be chosen
  • A company is trying to learn more about their customer base. They would like to survey to understand why their customers chose their brand. How should the company survey its customers?
  • A high school principal is estimating the total number of students that will attend an upcoming event. She assumes that the older students are unlikely to attend and decides to only survey the first-year students. What issue will the principal face when calculating her estimation?
  • A clothing manufacturer wants to learn more about why their consumers have purchased the brand’s products. How should this manufacturer conduct their survey?
  • What is a standard error?
  • A data professional is analyzing data about a population of aspen trees. They take repeated random samples of 10 trees from the population and compute the mean height for each sample. Which of the following statements best describes the sampling distribution of the mean?
Sampling and Sampling Distribution Quiz

The sampling Quiz is about the Basics of Sampling and Sampling Distributions. It will help you to understand the basic concepts related to sampling methods and sampling distributions. This test will also help you to prepare yourself for different exams related to education or jobs.

Computer MCQs

R and Data Analysis

Probability and Non-Probability Sampling (2021)

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The fundamental methods of Probability and non-probability sampling are used for selecting a sample from a population in research studies. They differ in how they approach the selection process and the resulting generalizability of the findings. The non-probability sampling methods are valuable for initial research stages or specific situations, but for strong statistical inferences and generalizability, probability sampling is preferred.

In probability sampling, each unit of the population has a known (non-zero) probability of being included in the sample, and samples are selected randomly by using some random selection method. That’s why probability sampling may also be called random sampling. In probability sampling, the reliability of the estimates can be determined. In probability sampling, samples are selected without any interest. The advantage of probability sampling is that it provides a valid estimate of sampling error. Probability sampling is widely used in various areas such as industry, agriculture, business sciences, etc.

Important types of probability sampling are

  • Simple Random Sampling
  • Stratified Random Sampling
  • Systematic Sampling
  • Cluster Sampling
Sample and Sampling

Non-probability sampling

In this sampling technique samples are selected by personal judgment due to this personal judgment in the selection of sample bias may include which makes the result unrepresentative. This sampling technique may also be called non-random sampling. The disadvantage of non-probability is that the reliability of the estimates cannot be determined.

The Non-Probability Samplings are:

  • Purposive sampling
  • Quota sampling
  • Judgment sampling
  • Snowball sampling
  • Convenience sampling

Differences between Probability and Non-Probability Sampling

The difference between these two is that non-probability sampling does not involve random selection of objects while in probability sampling objects are selected by using some random selection method. In other words, it means that non-probability samples aren’t representative of the population, but it is not necessary. However, it may mean that non-probability samples cannot depend upon the rationale of probability theory.

In general, researchers may prefer probabilistic or random sampling methods over a non-probabilistic sampling method, and consider them to be more accurate and rigorous.  However, in applied social sciences, for researchers, there may be circumstances where it is not possible to obtain sampling using some probability sampling methods. Even practical or theoretical it may not be sensible to do random sampling. Therefore a wide range of non-probability sampling methods may be considered, in these circumstances.

Probability and Non-Probability Sampling

The choice between probability and non-probability sampling depends on the research question, resources available, and the desired level of generalizability.

  • Use probability sampling when the generalizability of findings to the population is crucial, and resources allow for random selection.
  • Use non-probability sampling when: You need a quick and easy way to gather initial insights, explore a topic, or a complete sampling frame is unavailable. However, be cautious about generalizing the results.
ApplicationNon-Probability SamplingProbability Sampling
GoalInitial insights, specific situationsGeneralizable Finding
Selection MethodConvenience, judgement basedRandom
GeneralizabilityLimitedHigh
ExamplePilot studies, focus groups, market research, case studiesPublic opinion polls, medical research
https://itfeature.com

Read More about Sampling Basics

R and Data Analysis

Test Preparation MCQs

Estimation Statistics MCQs 3

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Estimation Statistics MCQs Quiz covers the topics of Estimate and Estimation 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 Estimation Statistics MCQs Quiz will help the learner to understand the related concepts and enhance their knowledge too.

Please go to Estimation Statistics MCQs 3 to view the test

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.

Estimation, point estimate and Interval Estimate

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.

Estimation Statistics

Online Estimation Statistics MCQs

  • The process of making estimates about the population parameter from a sample is called
  • There are two main branches of statistical inference, namely
  • Estimation can be classified into
  • A formula or rule used for estimating the parameter of interest is called:
  • ‘Statistic’ is an estimator and its computer values are called:
  • The estimate is the observed value of an:
  • The process of using sample data to estimate the values of unknown population parameters is called
  • The numerical value which we determine from the sample for a population parameter is called
  • A single value used to estimate a population value is called:
  • A set (range) of values calculated from the sample data and is likely to contain the true value of the parameter with some probability is called:
  • A range (set) of values within which the population parameter is expected to occur is called:
  • The end points of a confidence interval are called:
  • The probability associated with confidence interval is called
  • The estimator is said to be ________ if the mean of the estimator is not equal to the mean of the population parameter.
  • If $\hat{\theta}$ is the estimator of the parameter $\theta$, then $\hat{\theta}$ is called unbiased if:
  • The value of a statistic tends towards the value of the population as the sample size increases. What is it said to be?
  • For computing the confidence interval about a single population variance, the following test will be used
  • The end points of a confidence interval are called
  • The difference between the two end points of a confidence interval is called
  • The estimate is the observed value of an
Estimation Statistics MCQs

Estimation is a fundamental part of statistics because populations can be very large or even infinite, making it impossible to measure every single member. By using estimation techniques, we can draw conclusions about the bigger picture from a manageable amount of data.

Take another Quiz: Estimation Statistics MCQs

R Programming Language

Breusch Pagan Test for Heteroscedasticity (2021)

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The Breusch Pagan test (named after Trevor Breusch and Adrian Pagan) is used to check for the presence of heteroscedasticity in a linear regression model.

Assume our regression model is $Y_i = \beta_1 + \beta_2 X_{2i} + \mu_i$ i.e we have simple linear regression model, and $E(u_i^2)=\sigma_i^2$, where $\sigma_i^2=f(\alpha_1 + \alpha_2 Z_{2i})$,

That is $\sigma_i^2$ is some function of the non-stochastic variable $Z$’s. The $f()$ allows for both the linear and non-linear forms of the model. The variable $Z$ is the independent variable $X$ or it could represent a group of independent variables other than $X$.

Step to Perform Breusch Pagan test

  1. Estimate the model by OLS and obtain the residuals $\hat{u}_1, \hat{u}_2+\cdots$
  2. Estimate the variance of the residuals i.e. $\hat{\sigma}^2=\frac{\sum e_i^2}{(n-2)}$
  3. Run the regression $\frac{e_i^2}{\hat{\sigma^2}}=\beta_1+\beta_2 Z_i + u_i$ and compute the explained sum of squares (ESS) from this regression
  4. Test the statistical significance of $\frac{ESS}{2}$ by $\chi^2$-test with 1 df at the appropriate level of significance ($\alpha$).
  5. Reject the hypothesis of homoscedasticity in favour of heteroscedasticity if $\frac{ESS}{2} > \chi^2_{(1)}$ at the appropriate level of $\alpha$.
Bruesch-Pagan-Test-of-Heteroscedasticity

Note that the

  • The Breusch Pagan test is valid only if $u_i$’s are normally distributed.
  • For k independent variables, $\frac{ESS}{2}$ has ($\chi^2$) Chi-square distribution with k degree of freedom.
  • If the $u_i$’s (error term) are not normally distributed, the White test is used.

If heteroscedasticity is detected, remedies may include using robust standard errors, transforming the data, or employing weighted least squares estimation to adjust for heteroscedasticity.

The Breusch Pagan test is considered a useful tool for detecting the presence of heteroscedasticity in the regression models. The Breusch Pagan Test helps to ensure the validity of statistical inference and estimation.

A sample of Stata output related to the Breusch-Pagan Test for the detection of heteroscedasticity.

Breusch Pagan Test Stata Output

By analyzing the p-value of the chi-squared test statistic from the second regression, one can decide whether to reject the null hypothesis of homoscedasticity. If the p-value is lower than the chosen level of significance (say, 0.05), one has the evidence of heteroscedasticity.

The following are important points that need to be considered while using Breusch Pagan test of Heteroscedasticity.

  • The Breusch-Pagan test can be sensitive to the normality of the error terms. Therefore, It is advisable to check if the residuals are normally distributed before running the Breusch-Pagan test.
  • There are other tests for heteroscedasticity, but the Breusch-Pagan test is a widely used and relatively straightforward option.
Breusch Pagan Test of Heteroscedasticity

References:

  • Breusch, T.S.; Pagan, A.R. (1979). “Simple test for heteroscedasticity and random coefficient variation”. Econometrica (The Econometric Society) 47 (5): 1287–1294.

See the Numerical Example of the Breusch-Pagan Test for the Detection of Heteroscedasticity

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