# Online Estimation MCQs 1

The Post is about Online Estimation MCQs from Statistical Inference covering the topics of Estimates 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 Online Estimation MCQs Quiz will help the learner to understand the related concepts and enhance their knowledge too. Let us start with the Estimation MCQs Quiz.

Online MCQs about Estimate and Estimation for Preparation of PPSC and FPSC Statistics Lecturer Post

1. What is the maximum expected difference between a population parameter and a sample estimate?

2. If $X_1,X_2,\cdots, X_n$ is the joint density of n random variables, say, $f(X_1, X_2,\cdots, X_n;\theta)$ which is considered to be a function of $\theta$. Then $L(\theta; X_1,X_2,\cdots, X_n)$ is called

3. If $E(\hat{\theta})=\theta$, then $\hat{\theta}$ is said to be

4. Let $X_1,X_2,\cdots,X_n$ be a random sample from a density $f(x|\theta)$, where $\theta$ is a value of the random variable $\Theta$ with known density $g_\Theta(\theta)$. Then the estimator $\tau(\theta)$ with respect to the prior $g_\Theta(\theta)$ is defined as $E[\tau(\theta)|X_1,X_2,\cdots,X_n]$ is called

5. If $f(x_1,x_2,\cdots,x_n;\theta)=g(\hat{\theta};\theta)h(x_1,x_2,\cdots,x_n)$, then $\hat{\theta}$ is

6. In statistical inference, the best asymptotically normal estimator is denoted by

7. Let $Z_1,Z_2,\cdots,Z_n$ be independently and identically distributed random variables, satisfying $E[|Z_t|]<\infty$. Let N be an integer-valued random variable whose value n depends only on the values of the first n $Z_i$s. Suppose $E(N)<\infty$, then $E(Z_1+Z_2+\cdots+Z_n)=E( N)E(Z_i)$ is called

8. If $Var(T_2) < Var(T_1)$, then $T_2$ is

9. Which of the following assumptions are required to show the consistency, unbiasedness, and efficiency of the OLS estimator?

1. $E(\mu_t)=0$
2. $Var(\mu_t)=\sigma^2$
3. $Cov(\mu_t,\mu_{t-j})=0;t\neq t-j$
4. $\mu_t \sim N(0,\sigma^2)$

10. If the conditional distribution of $X_1, X_2,\cdots,X_n$ given $S=s$, does not depend on $\theta$, for any value of $S=s$, the statistics $S=s(X_1,X_2,\cdots,X_n)$ is called

11. For two estimators $T_1=t_1(X_1,X_2,\cdots,X_n)$ and $T_2=t_2(X_1,X_2,\cdots,X_n)$ then estimator $t_1$ is defined to be $R_{{t_1}(\theta)}\leq R_{{t_2}(\theta)}$ for all $\theta$ in $\Theta$

12. A test is said to be the most powerful test of size $\alpha$, if

13. Let $L(\theta;X_1,X_2,\cdots,X_n)$ be the likelihood function for a sample $X_1,X_2,\cdots, X_n$ having joint density $f(x_1,x_2,\cdots,x_n;\theta)$ where ? belong to parameter space. Then a test defined as $\lambda=\lambda_n=\lambda(x_1,x_2,\cdots,x_n)=\frac{Sup_{\theta\varepsilon \Theta_0}L(\theta;x_1,x_2,\cdots,x_n)}{Sup_{\theta\varepsilon \Theta}L(\theta;x_1,x_2,\cdots,x_n)}$

14. What are the main components of a confidence interval?

15. Let $X_1,X_2,\cdots,X_n$ be a random sample from the density $f(x;\theta)$, where $\theta$ may be vector. If the conditional distribution of $X_1,X_2,\cdots,X_n$ given $S=s$ does not depend on $\theta$ for any value of $s$ of $S$, then statistic is called.

16. Which of the following statements describes an interval estimate?

17. If $Var(\hat{\theta})\rightarrow 0$ as $n \rightarrow 0$, then $\hat{\theta}$ is said to be

18. $Var_\theta (T) \geq \frac{[\tau'(\theta)]^2}{nE[{\frac{\partial}{\partial \theta}log f((X;\theta)}^2]}$, where $T=t(X_1,X_2,\cdots, X_n)$ is an unbiased estimator of $\tau(\theta)$. The above inequality is called

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

20. A set of jointly sufficient statistics is defined to be minimal sufficient if and only if

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.

### Online Estimation MCQs

• If $Var(\hat{\theta})\rightarrow 0$ as $n \rightarrow 0$, then $\hat{\theta}$ is said to be
• If $E(\hat{\theta})=\theta$, then $\hat{\theta}$ is said to be
• If $Var(T_2) < Var(T_1)$, then $T_2$ is
• If $f(x_1,x_2,\cdots,x_n;\theta)=g(\hat{\theta};\theta)h(x_1,x_2,\cdots,x_n)$, then $\hat{\theta}$ is
• Which of the following assumptions are required to show the consistency, unbiasedness, and efficiency of the OLS estimator?
(i) $E(\mu_t)=0$
(ii) $Var(\mu_t)=\sigma^2$
(iii) $Cov(\mu_t,\mu_{t-j})=0;t\neq t-j$
(iv) $\mu_t \sim N(0,\sigma^2)$
• For a biased estimator $\hat{\theta}$ of $\theta$, which one is correct
• A test is said to be the most powerful test of size $\alpha$, if
• In statistical inference, the best asymptotically normal estimator is denoted by
• If the conditional distribution of $X_1, X_2,\cdots,X_n$ given $S=s$, does not depend on $\theta$, for any value of $S=s$, the statistics $S=s(X_1,X_2,\cdots,X_n)$ is called
• A set of jointly sufficient statistics is defined to be minimal sufficient if and only if
• If $X_1, X_2, \cdots, X_n$ is the joint density of $n$ random variables, say, $f(X_1, X_2,\cdots, X_n;\theta)$ which is considered to be a function of $\theta$. Then $L(\theta; X_1,X_2,\cdots, X_n)$ is called
• For two estimators $T_1=t_1(X_1,X_2,\cdots,X_n)$ and $T_2=t_2(X_1,X_2,\cdots,X_n)$ then estimator $t_1$ is defined to be $R_{{t_1}(\theta)}\leq R_{{t_2}(\theta)}$ for all $\theta$ in $\Theta$
• Let $X_1,X_2,\cdots,X_n$ be a random sample from the density $f(x;\theta)$, where $\theta$ may be vector. If the conditional distribution of $X_1,X_2,\cdots,X_n$ given $S=s$ does not depend on $\theta$ for any value of $s$ of $S$, then statistic is called.
• $Var_\theta (T) \geq \frac{[\tau'(\theta)]^2}{nE[{\frac{\partial}{\partial \theta}log f((X;\theta)}^2]}$, where $T=t(X_1,X_2,\cdots, X_n)$ is an unbiased estimator of $\tau(\theta)$. The above inequality is called
• Let $X_1,X_2,\cdots,X_n$ be a random sample from a density $f(x|\theta)$, where $\theta$ is a value of the random variable $\Theta$ with known density $g_\Theta(\theta)$. Then the estimator $\tau(\theta)$ with respect to the prior $g_\Theta(\theta)$ is defined as $E[\tau(\theta)|X_1,X_2,\cdots,X_n]$ is called
• Let $L(\theta;X_1,X_2,\cdots,X_n)$ be the likelihood function for a sample $X_1,X_2,\cdots, X_n$ having joint density $f(x_1,x_2,\cdots,x_n;\theta)$ where ? belong to parameter space. Then a test defined as $\lambda=\lambda_n=\lambda(x_1,x_2,\cdots,x_n)=\frac{Sup_{\theta\varepsilon \Theta_0}L(\theta;x_1,x_2,\cdots,x_n)}{Sup_{\theta\varepsilon \Theta}L(\theta;x_1,x_2,\cdots,x_n)}$
• Let $Z_1,Z_2,\cdots,Z_n$ be independently and identically distributed random variables, satisfying $E[|Z_t|]<\infty$. Let N be an integer-valued random variable whose value n depends only on the values of the first n $Z_i$s. Suppose $E(N)<\infty$, then $E(Z_1+Z_2+\cdots+Z_n)=E( N)E(Z_i)$ is called
• Which of the following statements describes an interval estimate?
• What is the maximum expected difference between a population parameter and a sample estimate?
• What are the main components of a confidence interval?

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.

### 9 thoughts on “Online Estimation MCQs 1”

1. Thank you so much for your website, it is a great help for students like me. Very grateful to souls like you.

2. Excellent, its realy great work u done Sir Imdad . thanks

• Thanks, keep visiting and sharing the website.

• Each pdf file at the end of post also contains answers of all MCQS at last page.

4. sir please send mcqs if possible for nts Gat Subject stat. I am asst. prof at degree college Karachi. Thanks sir

• Thanks. Hope soon will update accordingly.