Important MCQ Sampling Quiz – 7

The Online MCQ sampling Quiz is about the Basics of Sampling and Sampling Distributions. It will help you understand the basic concepts of sampling methods and distributions. This Online MCQ Sampling Quiz will help the students to prepare for different exams related to education or jobs. Most of the MCQs on this page cover MCQ 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.

Online MCQs about Sampling and Sampling Distributions with Answers

1. In sampling with replacement, $\sigma_{\overline{X}_1 – \overline{X}_2}$ is equal to

 $\sqrt{\frac{\sigma^2_1}{n_1} + \frac{\sigma_2^2}{n_2} }$

 $\frac{\sigma_1}{n_1} + \frac{\sigma^2}{n_2} $

 $\sqrt{\frac{\sigma_1^2+\sigma^2_2}{n_1+n_2} }$

 $\frac{\sigma^2_1}{n_1} + \frac{\sigma_2^2}{n_2} $

2. If $E(\overline{X})=10$ and $\mu=10$ then bias is equal to

 20

 difficult to tell

 10

 0

3. If $E(s^2)=3$ and $\sigma^2=2$ then bias will be

 1

 2

 5

 3

4. $s^2=\frac{\sum(X-\overline{X})^2}{n-1}$ is called

 true variance

 biased sample variance

 variance of means

 unbiased sample variance

5. In sampling without replacement, $\mu_{s^2}$ is equal to

 $\left(\frac{n-1}{n}\right)\sigma^2$

 $\left(\frac{N}{N-1} \right)\sigma^2$

 $\left(\frac{N-1}{N} \right)\sigma^2$

 $\left(\frac{N}{N-1} \right)\left(\frac{n-1}{n}\right)\sigma^2$

6. If $\overline{X}=10$ and $\mu=12$ then sampling error is

 10

 22

 2

 12

7. In case of sampling with replacement $\sigma_{\hat{p}_1 – \hat{p}_2}$ is equal to

 $\sqrt{p_1q_1+p_2q_2}$

 $\sqrt{\frac{pq}{n}}$

 $\sqrt{\frac{\sigma^2_1}{n_1} + \frac{\sigma^2_2}{n_2}}$

 $\sqrt{\frac{p_1q_1}{n_1} + \frac{p_2q_2}{n_2}}$

8. When sampling is done with replacement, then $\mu_{s^2}$ is equal to

 $\sqrt{\frac{\sigma^2}{n}}$

 $\sigma^2$

 $\left(\frac{n-1}{n}\sigma^2\right)$

 $\frac{\sigma^2}{n}$

9. If $X$ represents the number of units having the specified characteristic and $n$ is the size of the sample then sample proportion $\hat{p}$ is equal to

 $\frac{n}{X}$

 $\frac{X+\sigma}{n}$

 $\frac{X}{n}$

 $\frac{\sigma}{\sqrt{n}}$

10. If $n=25$, $\sigma^2=25$, and $\overline{X}=25$, then standard error of $\overline{X}$ will be

 0

 1

 25

 5

11. When sampling is done with or without replacement, $\mu_{\overline{X}_1-\overline{X}_2}$ is equal to

 $\mu_2-\mu_1$

 $\frac{\mu_1}{n_1} – \frac{\mu_2}{n_2}$

 $\mu_1+\mu_2$

 $\mu_1 – \mu_2$

12. In sampling without replacement, the standard error of sampling distribution of sample proportion $\hat{p}$ is equal to

 $\frac{\sqrt{pq}}{n} \left(\frac{N-n}{N-1} \right)$

 $pq \left(\frac{N-n}{N-1} \right)$

 $\sqrt{\frac{pq}{n} \left(\frac{N-n}{N-1} \right)}$

 $\frac{pq}{n} \left(\frac{N-n}{N-1} \right)$

13. In sampling without replacement, the expected value of $S^2$ is equal to

 $\left( \frac{N}{N-1}\right) \left(\frac{n-1}{n}\right)\sigma^2$

 $\sqrt{\left( \frac{N}{N-1}\right) \left(\frac{n-1}{n}\right)\sigma^2}$

 $\left( \frac{N}{N-1}\right) \left(\frac{n}{n-1}\right)\sigma^2$

 $\left( \frac{N-1}{N}\right) \left(\frac{n-1}{n}\right)\sigma^2$

14. The distribution of the means of samples of size 4, taken from a population with a standard deviation $\sigma$, has a standard deviation of

 $\sigma$

 $\frac{\sigma^2}{2}$

 $\frac{\sigma}{2}$

 $\frac{\sigma}{4}$

15. $S^2=\frac{\sum (X-\overline{X})^2}{n}$ is called

 unbiased sample variance

 biased sample standard deviation

 population variance

 biased sample variance

16. When sampling is done without replacement $\sigma_{\overline{X}}$ is equal to

 $\frac{\sigma^2}{\sqrt{n}}$

 $\frac{\sigma}{\sqrt{n}} \sqrt{\frac{N-n}{N-1}}$

 $\frac{\sigma^2}{n}$

 $\frac{\sigma}{n} \sqrt{\frac{N-n}{N-1}}$

17. If $X$ represents the number of units having the specified characteristic and $N$ is the size of the population, then population proportion $p$ is equal to

 $\frac{X}{N}$

 $\frac{\sigma^2}{N}$

 $\frac{X}{n}$

 $\frac{N}{X}$

18. In case of sampling with replacement, $E(S^2)$ is equal to

 $\left(\frac{n}{n-1}\right)\sigma^2$

 $\left(\frac{N}{N-1}\right)\sigma^2$

 $\left( \frac{n-1}{n}\right)\sigma^2$

 $\frac{\sigma^2}{n}$

19. The standard deviation of the distribution of sample means is equal to

 $\frac{\sqrt{n}}{\sigma}$

 $\frac{\sigma}{\sqrt{n}}$

 $\frac{\sigma^2}{\sqrt{n}}$

 $\frac{\sigma}{n}$

20. When sampling is done with or without replacement, $E(\hat{p}_1 – \hat{p}_2)$ is equal to

 $\hat{p}_1 -\hat{p}_2$

 $p_1-p_2$

 $p_1+p_2$

 $p_1p_2$

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Online MCQ Sampling Quiz

• If $E(\overline{X})=10$ and $\mu=10$ then bias is equal to
• If $\overline{X}=10$ and $\mu=12$ then sampling error is
• The standard deviation of the distribution of sample means is equal to
• If $n=25$, $\sigma^2=25$, and $\overline{X}=25$, then standard error of $\overline{X}$ will be
• $S^2=\frac{\sum (X-\overline{X})^2}{n}$ is called
• $s^2=\frac{\sum(X-\overline{X})^2}{n-1}$ is called
• If $E(s^2)=3$ and $\sigma^2=2$ then bias will be
• In sampling without replacement, the standard error of sampling distribution of sample proportion $\hat{p}$ is equal to
• When sampling is done without replacement $\sigma_{\overline{X}}$ is equal to
• In case of sampling with replacement $\sigma_{\hat{p}1 – \hat{p}_2}$ is equal to
• The distribution of the means of samples of size 4, taken from a population with a standard deviation $\sigma$, has a standard deviation of
• In sampling with replacement, $\sigma{\overline{X}_1 – \overline{X}_2}$ is equal to
• When sampling is done with or without replacement, $E(\hat{p}_1 – \hat{p}_2)$ is equal to
• In case of sampling with replacement, $E(S^2)$ is equal to
• In sampling without replacement, the expected value of $S^2$ is equal to
• When sampling is done with replacement, then $\mu{s^2}$ is equal to
• In sampling without replacement, $\mu_{s^2}$ is equal to
• When sampling is done with or without replacement, $\mu_{\overline{X}_1-\overline{X}_2}$ is equal to
• If $X$ represents the number of units having the specified characteristic and $n$ is the size of the sample then sample proportion $\hat{p}$ is equal to
• If $X$ represents the number of units having the specified characteristic and $N$ is the size of the population, then population proportion $p$ is equal to

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