Important Sampling Quiz with Answers 9

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The Online sampling Quiz with Answers is about the Basics of Sampling and Sampling Distributions. It will help you understand the basic concepts of sampling methods and distributions. This Sampling Quiz will help the students prepare for different exams related to education or jobs. Most of the MCQs on this page cover MCQ Sampling Quiz with Answers, Probability Sampling and Non-Probability Sampling, Mean and Standard Deviation of Sample, Sample size, Sampling error, Sample bias, Sample Selection, etc.

Sampling Quiz with Answers

Multiple Choice Questions about Sampling and Sampling Distributions

1. The average of cluster means is the unbiased estimator of a population mean when

 
 
 
 

2. Cluster sampling, stratified sampling, and systematic sampling are types of

 
 
 
 

3. Which of the following would usually require the largest sample size because of its efficiency?

 
 
 
 

4. Which ONE of the following is the main problem with using non-probability sampling techniques?

 
 
 
 

5. In cluster sampling, elements of selected clusters are classified as

 
 
 
 

6. When Hartley-Ross proposed the unbiased ratio estimator?

 
 
 
 

7. Sampling in qualitative research is similar to which type of sampling in quantitative research?

 
 
 
 

8. In systematic sampling, when $N=18$ with $n=3$ what will be the value of $k$?

 
 
 
 

9. There are 50 students in a class. A data analyst wants to know if a majority of students like the instructor. They decided to survey the 15 students who earned an A in the class because these students were paying attention to the instructor. Which of the following statements best describes this sample?

 
 
 
 

10. The human resources department at company XYZ has 42 workers in int. To find out some information about the group as a whole, we want to take a sample of 7 of those workers to interview. If we have an ordered list of workers numbered 1 through 42, and we start at worker number 3, which worker would be included in our sample?

 
 
 
 

11. All of the following are true about cluster sampling except

 
 
 
 

12. In which of the following non-random sampling techniques does the researcher ask the research participants to identify other potential research participants?

 
 
 
 

13. The auxiliary variable is also called

 
 
 
 

14. In a double sampling plan, if the number of defects are in between the two numbers C1 and C2 then

 
 
 
 

15. If a statistician randomly samples 50 observations in each population category then his sample will be ———-.

 
 
 
 

16. A procedure in which the number of elements in a stratum is not proportional to the number of elements in populations is classified as

 
 
 
 

17. Which of the following sampling methods is the best way to select a group of people for a study if you are interested in making statements about the larger population?

 
 
 
 

18. The listing of elements in a population with identifiable numbers is classified as

 
 
 
 

19. If we took the 500 people attending a school in a city, divided them by gender, and then took a random sample of males and a random sampling of females, the variable on which we divide the population is called the

 
 
 
 

20. In systematic sampling, the value of $k$ is classified as

 
 
 
 

Sampling Quiz With Answers

  • A procedure in which the number of elements in a stratum is not proportional to the number of elements in populations is classified as
  • Cluster sampling, stratified sampling, and systematic sampling are types of
  • The listing of elements in a population with identifiable numbers is classified as
  • There are 50 students in a class. A data analyst wants to know if a majority of students like the instructor. They decided to survey the 15 students who earned an A in the class because these students were paying attention to the instructor. Which of the following statements best describes this sample?
  • When Hartley-Ross proposed the unbiased ratio estimator?
  • Which of the following sampling methods is the best way to select a group of people for a study if you are interested in making statements about the larger population?
  • The auxiliary variable is also called
  • The average of cluster means is the unbiased estimator of a population mean when
  • In cluster sampling, elements of selected clusters are classified as
  • Sampling in qualitative research is similar to which type of sampling in quantitative research?
  • Which of the following would usually require the largest sample size because of its efficiency?
  • All of the following are true about cluster sampling except
  • The human resources department at company XYZ has 42 workers in int. To find out some information about the group as a whole, we want to take a sample of 7 of those workers to interview. If we have an ordered list of workers numbered 1 through 42, and we start at worker number 3, which worker would be included in our sample?
  • If a statistician randomly samples 50 observations in each population category then his sample will be ———-.
  • In which of the following non-random sampling techniques does the researcher ask the research participants to identify other potential research participants?
  • In systematic sampling, when $N=18$ with $n=3$ what will be the value of $k$?
  • In systematic sampling, the value of $k$ is classified as
  • If we took the 500 people attending a school in a city, divided them by gender, and then took a random sample of males and a random sampling of females, the variable on which we divide the population is called the
  • In a double sampling plan, if the number of defects is in between the two numbers C1 and C2 then
  • Which ONE of the following is the main problem with using non-probability sampling techniques?
Sampling Quiz with Answers

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Type I and Type II Errors Examples

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The post covers the Type I and Type II Errors examples.

Hypothesis testing helps us to determine whether the results are statistically significant or occurred by chance. Hypothesis testing is based on probability, therefore, there is always a chance of making the wrong decision about the null hypothesis (a hypothesis about population). It means that there are two types of errors (Type I and Type II errors) that can be made when drawing a conclusion or decision.

Errors in Statistical Decision-Making

To understand the errors in statistical decision-making, we first need to see the step-by-step process of hypothesis testing:

  1. State the null hypothesis and the alternative hypothesis.
  2. Choose a level of significance (also called type-I error).
  3. Compute the required test statistics
  4. Find the critical value or p-value
  5. Reject or fail to reject the null hypothesis.

When you decide to reject or fail to reject the null hypothesis, there are four possible outcomes–two represent correct choices, and two represent errors. You can:
• Reject the null hypothesis when it is actually true (Type-I error)
• Reject the null hypothesis when it is actually false (Correct)
• Fail to reject the null hypothesis when it is actually true (Correct)
• Fail to reject the null hypothesis when it is actually false (Type-II error)

These four possibilities can be presented in the truth table.

Type I and Type II Errors Examples

Type I and Type II Errors Examples: Clinical Trial

To understand Type I and Type II errors, consider the example from clinical trials. In clinical trials, Hypothesis tests are often used to determine whether a new medicine leads to better outcomes in patients. Imagine you are a data professional and working in a pharmaceutical company. The company invents a new medicine to treat the common cold. The company tests a random sample of 200 people with cold symptoms. Without medicine, the typical person experiences cold symptoms for 7.5 days. The average recovery time for people who take the medicine is 6.2 days.

You conduct a hypothesis test to determine if the effect of the medicine on recovery time is statistically significant, or due to chance.

In this case:

  • Your null hypothesis ($H_0$) is that the medicine has no effect.
  • Your alternative hypothesis ($H_a$) is that the medicine is effective.

Type I Error

A Type-I error (also known as a false positive) occurs when a true null hypothesis is rejected. In other words, one can conclude that the result is statistically significant when in fact the results occurred by chance. To understand this, let in your clinical trial, the results indicate that the null hypothesis is true, which means that the medicine has no effect. In case, you make a Type-I error and reject the null hypothesis, it means that you incorrectly conclude that the medicine relieves cold symptoms while the medicine was (actually) ineffective.

The probability of making a Type I error is represented by $\alpha$ (the level of significance. Typically, a 0.05 (or 5%) significance level is used. A significance level of 5% means you are willing to accept a 5% chance you are wrong when you reject the null hypothesis.

Reduce the risk of Type I error

To reduce your chances of making Type I errors, it is advised to choose a lower significance level. For example, one can choose the significance level of 1% instead of the standard 5%. It will reduce the chances of making a Type I error from 5% to 1%.

Type II Error

A Type II error occurs when we fail to reject a null hypothesis when it is false. In other words, one may conclude that the result occurred by chance, however, in fact, it didn’t. For example, in a clinical study, if the null hypothesis is false, it means that the medicine is effective. In case you make a Type II Error and fail to reject the null hypothesis, it means that you incorrectly conclude that the medicine is ineffective while in reality, the medicine relieves cold symptoms.

The probability of making a Type II error is represented by $\beta$ and it is related to the power of a hypothesis test (power = $1- \beta$). Power refers to the likelihood that a test can correctly detect a real effect when there is one.

Note that reducing the risk of making a Type I error means that it is more likely to make a Type II error or false negative.

Reduce your risk of making Type II Error

One can reduce the risk of making a Type II error by ensuring that the test has enough power. In data work, power is usually set at 0.80 or 80%. The higher the statistical power, the lower the probability of making a Type II error. To increase power, you can increase your sample size or your significance level.

Potential Risks of Type I and Type II Errors

As a data professional, it is important to be aware of the potential risks involved in making the two types of errors.

  • A Type I error means rejecting a true null hypothesis. In general, making a Type I error often leads to implementing changes that are unnecessary and ineffective, and which waste valuable time and resources.
    For example, if you make a Type I error in your clinical trial, the new medicine will be considered effective even though it is ineffective. Based on this incorrect conclusion, ineffective medication may be prescribed to a large number of people. While other treatment options may be rejected in favor of the new medicine.
  • A Type II error means failing to reject a false null hypothesis. In general, making a Type II error may result in missed opportunities for positive change and innovation. A lack of innovation can be costly for people and organizations.
    For example, if you make a Type II error in your clinical trial, the new medicine will be considered ineffective even though it’s effective. This means that a useful medication may not reach a large number of people who could benefit from it.

In summary, as a data professional, it helps to be aware of the potential errors built into hypothesis testing and how they can affect the final decisions. Depending on the certain situation, one may choose to minimize the risk of either a Type I or Type II error. Ultimately, it is the responsibility of a data professional to determine which type of error is riskier based on the goals of your analysis.

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Easy Hypothesis Testing Questions MCQs 7

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Online MCQs Hypothesis Testing Questions with Answers. The Hypothesis Testing Quiz is important for the preparation of examinations 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.

Please go to Easy Hypothesis Testing Questions MCQs 7 to view the test

Hypothesis Testing Questions MCQs

The goal of hypothesis testing is to assess the evidence against the null hypothesis (a statement about population also called claimed hypothesis). If the evidence is strong enough (based on the sample information), one can reject the null hypothesis and conclude that the alternative hypothesis is more likely to be true. However, it is important to remember that we never truly “prove” the alternative hypothesis; one can only reject the null hypothesis.

Hypothesis Testing Questions MCQs

  • Statistical inference is divided into two major branches as given below
  • The probability of accepting the true null hypothesis is called
  • The probability of rejecting a true null hypothesis is called
  • If a false hypothesis is accepted, it is called
  • Hypothesis testing and estimation are major classifications of
  • The hypothesis that is tested for the possible purpose of rejection is called
  • In testing of the hypothesis, the sampling distribution of the test statistics is based on the assumption that
  • Which of the following cannot be considered as a hypothesis ($H_0$)
  • The alternative hypothesis may be of the form
  • The null hypothesis always contains some sign of
  • Which of the following is not the composite hypothesis
  • The critical region is the part of the sampling distribution for which the null hypothesis is
  • The null hypothesis ($H_0$) is
  • One-sided and two-sided tests are based on
  • If the alternative hypothesis is of the form $H_1:\theta < \theta_0$ then the test will be
  • If the alternative hypothesis is of the form, $H_1: \theta \ne \theta_0$ then the test will be
  • If the population standard deviation is not known and the sample size is large ($n\ge 30$) then the test statistic to be used is
  • In the t-test, we use
  • For testing of the hypothesis about population proportion, we use
  • The ———— of a test is the maximum probability with which we are willing to a risk of Type-I error.
Hypothesis Testing Questions with Answers

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Important Chi-Square Test MCQs with Answers 4

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The post is about the Chi-Square Test MCQS with Answers. The Chi-square test is used to find the association between attributes. Let us start with the Chi-Square Test MCQs with Answers.

Please go to Important Chi-Square Test MCQs with Answers 4 to view the test

The relationship/ Dependency between the attributes is called association and the measure of degrees of relationship between attributes is called the coefficient of association. The Chi-Square Statistic is used to test the association between the attributes. The Chi-Square Association is defined as

$$\chi^2 = \sum \frac{(of_i – ef_i)^2}{ef_i}\sim \chi^2_{v}$$

where $v$$ denotes the degrees of freedom.

The Chi-Square tests:

  • are appropriate for categorical data, not continuous data (like height or weight).
  • The data needs to be from a random sample and have sufficient sample size for the test to be reliable.
  • The test results in a chi-square statistic and a p-value.

Chi-Square Test MCQs with Answers

  • A characteristic which cannot be measured numerically is called
  • Which of the following is not an example of an attribute
  • The eye colour of students in a girl’s college is an example of
  • Religions of the people of a country is
  • The degree of relationship between two attributes is called
  • In a contingency table with $r$ rows and $c$ columns, the degree of freedom is
  • The $\chi^2$ distribution is
  • If $\chi^2_{calculated}$ is greater than the critical region, then the attributes are
  • In a $3 \times 3$ contingency table, the degrees of freedom is
  • The Spearman’s coefficient of rank correlation always lies between
  • The Yule’s coefficient of association lies between
  • If $(AB) < \frac{(A)(B)}{n}$ then the two attributes $A$ and $B$ are said to be
  • If $(AB) = \frac{(A)(B)}{n}$ the attributes $A$ and $B$ are said to be
  • The coefficient of contingency is measured by
  • If $\chi^2_{calculated} = 0$ then
  • $(\alpha \beta)$ is the frequency of the class of the order
  • If $A$ and $B$ are independent attributes then the coefficient of associate is
  • The value of $\chi^2$ is always
  • In a Chi-Square test of independence, no expected frequencies should be
  • The two attributes are said to be ———–, if for every cell of the contingency table, the observed frequency $O_{ij}$ is equal to the expected frequency $e_{ij}$
Chi-Square Test MCQs with Answers

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