Category: Estimate and Estimation

MCQs from Statistical Inference cover the topics of Estimation and Hypothesis Testing 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 quiz MCQs will help the learner to understand the related concepts and enhance the knowledge too.

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

Online MCQs Estimation Test

1. By decreasing $\overline{X}$ the length of the confidence interval for $\mu$

 No effect

 Increases

 None of these

 Decreases

2. If $\mu=130, \overline{X}=150, \sigma=5$, and $n=10$. What Statistic is appropriate.

 $F$

 $Z$

 $\chi^2$

 $t$

3. If the population Standard Deviation is unknown and the sample size is less than 30, then Confidence Interval for the population mean ($\mu$) is

 $\overline{X} \pm t_{\frac{\alpha}{2}} \frac{S}{\sqrt{n}}$

 $\overline{X} \pm t_{\frac{\alpha}{2}} \frac{\sigma^2}{\sqrt{n}}$

 $\overline{X} \pm Z_{\frac{\alpha}{2}} \frac{S}{\sqrt{n}}$

 $\overline{X} \pm t_{\frac{\alpha}{2}(n-1)} \frac{S}{\sqrt{n}}$

4. The width of confidence interval decreases if the confidence coefficient is

 Decreased

 Fixed

 One

 Increased

5. A statistician calculates a 95% confidence interval for $\mu$ when $\sigma$ is known. The confidence interval is Rs 18000 to 22000, and then amount of sample means $\overline{X}$ is:

 RS 18000

 RS 20000

 RS 40000

 RS 22000

6. In a $Z$-test the number of degrees of freedom is

 None of these

 $1$

 $n-2$

 $n-1$

7. t-distribution is used when

 $ \sigma^2 $ is unknown

 Population is normal

 Sample is small

 All of these options

8. A large sample contains more than

 20 values

 30 values

 5 values

 10 values

9. If $1-\alpha=0.90$ then value of $Z_{\frac{\alpha}{2}}$ is

 2.328

 1.645

 1.96

 2.575

10. In applying t-test

 $ n $ is small

 $ n $ is large

 $ \sigma $ is known

 $ \sigma $ is unknown

11. A sample is considered a small sample if the size is

 Less than 30

 100

 30 or less

 60

12. For $\alpha=0.05$, the critical value of $Z_{0.05}$ is equal to

 2.33

 1.96

 1.645

 2.58

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Statistical inference is a branch of statistics in which we draw conclusions (make some wise decisions) about the population parameter by using sample information. Statistical inference can be further divided into Estimation of the Population 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 an 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.