# Confidence Interval MCQs 4

MCQs from Statistical Inference covering the topics of Estimation Confidence Interval MCQs 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 Estimation and Confidence interval MCQs will help the learner to understand the related concepts and enhance the knowledge too. Let us start with Confidence Interval MCQs

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. If the population standard deviation $\sigma$ is known, the confidence interval for the population mean $\mu$ is based on

2. If $(1-\alpha)$ is increased, the width of a confidence interval is

3. By increasing the sample size, the precision of the confidence interval is ______.

4. By decreasing the sample size, the confidence interval becomes

5. A statistician calculates a 95% confidence interval for $\mu$ and $\sigma$ is known. The confidence interval is RS 18000 to RS 22000, the amount of the sample mean $\overline{X}$ is

6. A single value used to estimate the value of the population parameter is called

7. A range of values calculated from the sample data and it is likely to contain the true value of the parameter with some probability is called

8. The shape of the t-distribution depends upon the

9. A confidence interval will be widened if

10. The distance between an estimate and the estimated parameter is called

11. A 95% confidence interval for the mean of a population is such that

12. The estimator is said to be _________ if the mean of the estimator is not equal to the mean of the population parameter.

13. The probability associated with the confidence interval is called

14. Estimation can be classified into

15. The number of values that are free to vary after a certain restriction is applied to the data is called

16. The confidence interval becomes narrow by increasing the

17. If the population standard deviation $\sigma$ is doubled, the width of the confidence interval for the population mean $\mu$ (the upper limit of the confidence interval — the lower limit of the confidence interval) will be

18. $(1-\alpha)$ is called

19. If the population standard deviation $\sigma$ is unknown, and the sample size is small ($n\le 30$), the confidence interval for the population mean $\mu$ is based on

20. Estimates given in the form of confidence intervals are called

Most of the MCQs on this page are covered from Estimate and Estimation, Testing of Hypothesis, Parametric and Non-Parametric tests, etc.

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.

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.

### Online Confidence Interval MCQs

• Estimates given in the form of confidence intervals are called
• $(1-\alpha)$ is called
• If $(1-\alpha)$ is increased, the width of a confidence interval is
• By decreasing the sample size, the confidence interval becomes
• The confidence interval becomes narrow by increasing the
• The distance between an estimate and the estimated parameter is called
• By increasing the sample size, the precision of the confidence interval is _______
• The number of values that are free to vary after a certain restriction is applied to the data is called
• A 95% confidence interval for the mean of a population is such that A confidence interval will be widened if
• A statistician calculates a 95% confidence interval for $\mu$ and $\sigma$ is known.
• The confidence interval is RS 18000 to RS 22000, and the amount of the sample mean $\overline{X}$ is
• If the population standard deviation $\sigma$ is known, the confidence interval for the population mean $\mu$ is based on
• If the population standard deviation $\sigma$ is unknown, and the sample size is small ($n\le 30$), the confidence interval for the population mean $\mu$ is based on
• The shape of the t-distribution depends upon the
• If the population standard deviation $\sigma$ is doubled, the width of the confidence interval for the population mean $\mu$ (the upper limit of the confidence interval — the lower limit of the confidence interval) will be
• A range of values calculated from the sample data and it is likely to contain the true value of the parameter with some probability is called
• The estimator is said to be ________ if the mean of the estimator is not equal to the mean of the population parameter.
• Estimation can be classified into
• A single value used to estimate the value of the population parameter is called
• The probability associated with the confidence interval is called

It is important to note that the point estimates are simpler to calculate but lack information about precision. On the other hand, interval estimates provide more information but require more calculations too, and often rely on assumptions about the data. Therefore, the choice between point estimation and interval estimation depends on the specific research question and how much detail a researcher needs about the population parameter being estimated.

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