Estimation MCQs with Answers 2

Estimation MCQs with Answers from Statistical Inference covering the topics of Estimation for the preparation of exams and different statistical job tests in Government/ Semi-Government or Private Organization sectors. These quizzes are also helpful in getting admission to different colleges and Universities. The Estimation MCQs with Answers Quiz will help the learner to understand the related concepts and enhance the knowledge too. Let us start with the Online EStimation MCQs with Answers.

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. The level of confidence is denoted by

 
 
 
 

2. What happens as a sample size gets larger?

 
 
 
 

3. A function that is used to estimate a parameter is called

 
 
 

4. A specific value calculated from a sample is called

 
 
 

5. The following statistics are unbiased

 
 
 
 

6. The probability that the confidence interval does not contain the population parameter is denoted by

 
 
 
 

7. The other name of the significance level is

 
 

8. Testing of hypothesis may be replaced by?

 
 
 
 

9. The formula used to estimate a parameter is called

 
 
 
 

10. A statistic $\hat{\theta}$ is said to be an unbiased estimator of $\theta$, if

 
 
 
 

11. A point estimate is often insufficient. Why?

 
 
 
 

12. What will be the confidence level if the level of significance is 5% (0.05)

 
 
 
 

13. The probability that the confidence interval does contain the parameter is denoted by

 
 
 
 

14. After identifying a sample statistic, what is the proper order of the next three steps of constructing a confidence interval?

 
 
 
 

15. There are four steps involved with constructing a confidence interval. What is typically the first one?

 
 
 
 

16. $1-\alpha$ is called

 
 
 

17. If $E(\hat{\theta})=\theta$ then $\hat{\theta}$ is called

 
 
 
 

18. In point estimation we get

 
 
 
 

19. The way of finding the unknown value of the population parameter from the sample values by using a formula is called _____

 
 
 

20. The following is an unbiased estimator of the population variance $\sigma^2$

 
 
 
 


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 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.

Estimation MCQS with Answers

  • If $E(\hat{\theta})=\theta$ then $\hat{\theta}$ is called
  • A statistic $\hat{\theta}$ is said to be an unbiased estimator of $\theta$, if
  • The following statistics are unbiased
  • The following is an unbiased estimator of the population variance $\sigma^2$
  • In point estimation we get
  • The formula used to estimate a parameter is called
  • A specific value calculated from the sample is called
  • A function that is used to estimate a parameter is called
  • $1-\alpha$ is called
  • The level of confidence is denoted by
  • The other name of the significance level is
  • What will be the confidence level if the level of significance is 5% (0.05)
  • The probability that the confidence interval does not contain the population parameter is denoted by
  • The probability that the confidence interval does contain the parameter is denoted by
  • The way of finding the unknown value of the population parameter from the sample values by using a formula is called ______.
  • There are four steps involved with constructing a confidence interval. What is typically the first one?
  • What happens as a sample size gets larger?
  • After identifying a sample statistic, what is the proper order of the next three steps of constructing a confidence interval?
  • Testing of hypothesis may be replaced by?
  • A point estimate is often insufficient. Why?
Online Estimation MCQs with Answers

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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.

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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.

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.

MCQs Estimation and Hypothesis Testing

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Hypothesis Testing Quiz 3

the post is about Hypothesis Testing Quiz from Statistical Inference 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 Hypothesis Testing Quiz will help the learner understand the related concepts and enhance the knowledge.

Most of the MCQs on this page are covered from Estimate and Estimation, Hypothesis Testing, Parametric and Non-Parametric tests, etc. Let’s start the MCQs Hypothesis Testing quiz now.

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Hypothesis Testing Quiz

Hypothesis Testing Quiz

  • In hypothesis testing, type II error is represented by $\beta$ and the power of the test is $1-\beta$ then
  • In statistical testing of the hypothesis, what happens to the region of rejection when the level of significance $\alpha$ is reduced?
  • Which of the following is NOT correct?
  • In testing the statistical hypothesis, which of the following statement(s) is false?
  • In testing the statistical hypothesis, which of the following statement(s) is false?
  • In a statistical hypothesis test of equality of means, such as $H_0:\mu=10$, if $\alpha=5\%$
  • Which of the following statements is correct
  • The average growth of a certain variety of pine trees is 10.1 inches in three years. A biologist claims that a new variety will have greater three-year growth. A random sample of 25 of the new variety has an average three-year growth of 10.8 inches and a standard deviation of 2.1 inches. The appropriate null and alternative hypotheses to test the biologist’s claim are:
  • Since   $\alpha$= probability of Type I error, then $1 -\alpha$
  • The following are percentages of fat found in 5 samples of each of the two brands of baby food:
    A:    5.7, 4.5, 6.2, 6.3, 7.3
    B:    6.3, 5.7, 5.9, 6.4, 5.1
    Which of the following procedures is appropriate to test the hypothesis of equal average fat content in the two types of ice cream?
  • In hypothesis testing, you need to conclude, and you fail to reject a null hypothesis, which is actually false. What type of error do they commit?
  • You conduct a hypothesis test, you need to conclude and commit a type II error. Which of the following statements accurately describes this scenario?
  • Suppose you conduct a hypothesis test and choose a significance level of 5%. You calculate a p-value of 3.3%. What conclusion should be drawn?
  • In a one-sample hypothesis test of the mean, what are the typical options for the alternative hypothesis?
  • A data analyst conducts a hypothesis test. They fail to reject the null hypothesis. What statement best describes their conclusion?
  • In testing the difference between two populations, it is possible to use
  • In testing of hypothesis, type-II error may be defined as:
  • If a Chi-square goodness of fit test has 6 categories and an $N=30$, then the correct number of degrees of freedom is:
  • For testing the equality of several variances the appropriate test is
  • To perform a run test for randomness the data must be

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