Statistics for Data Analyst

MCQs from the Statistical Inference Quiz cover the topics of estimation and hypothesis testing for the preparation of exams and different statistical job tests in the government/semi-government or private organization sectors. These Quizzes are also helpful in getting admission to other colleges and Universities. The Estimation Statistical Inference Quiz will help the learner understand the related concepts and enhance their knowledge.

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 unknown and the sample size ($n$) is greater than 30, the confidence interval for the population mean $\mu$ is

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

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

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

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

2. If $n_1, n_2\le 30$ the confidence interval estimate for the difference of two population means ($\mu_1-\mu_2$) when population standard deviations $\sigma_1, \sigma_2$ are unknown but equal in case of pooled variates is:

 $(\overline{X}_1 -\overline{X}_2) \pm Z_{\frac{\alpha}{2}} \sqrt{
\frac{\sigma_1^2}{n_1}+\frac{\sigma_2^2}{n_2}}$

 $(\overline{X}_1 -\overline{X}_2) \pm t_{\frac{\alpha}{2}(v)} S_p\sqrt{
\frac{1}{n_1}+\frac{1}{n_2}}$

 $(\overline{X}_1 -\overline{X}_2) \pm Z_{\frac{\alpha}{2}} \sqrt{
\frac{S_1^2}{n_1}+\frac{S_2^2}{n_2}}$

 $(\overline{X}_1 -\overline{X}_2) \pm t_{\frac{\alpha}{2}(v)} \sqrt{
\frac{s_1^2}{n_1}+\frac{s_2^2}{n_2}}$

3. Each of the following increases the width of a confidence interval except

 Increased sample size

 Decreased sample size

 Increased confidence level

 Increased variability

4. If t-distribution for two independent samples $n_1=n_2=n$, then the degrees of freedom will be

 $n-1$

 $2n-1$

 $2n+1$

 $2n-2$

5. If the population standard deviation ($\sigma$) is known and the sample size ($n$) is less than or equal to or more than 30, the confidence interval for the population mean ($\mu$) will be

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

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

 $\hat{p} \pm Z_{\frac{\alpha}{2}} \sqrt{\frac{\hat{p}\hat{q}}{n}}$

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

6. What does it mean when someone calculates a 95% confidence interval?

 One can be 95% confident that the interval will include the population parameter.

 All of the statements are true.

 The process used will capture the true population parameter 95% of the time in the long run.

 One can be 5% confidence that the interval will not include the population parameter.

7. If the population standard deviation $\sigma$ is unknown and the sample size $n$ is less than or equal to 30, the confidence interval for the population mean $\mu$ is

 $\overline{X} \pm Z_{\frac{\alpha}{2}} \frac{\sigma}{\sqrt{n-1}}$

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

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

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

8. For $n$ paired number of observations, the degrees of freedom for the Paired Sample t-test will be

 $n_1+n_2-1$

 $n_1+n_2-2$

 $n-1$

 $n$

9. A statistic is an unbiased estimator of a parameter if:

 E(Variance) = Mean

 E(Sample mean) = Proportion

 E(statistic) = Parameter

 E(Mean) = Variance

10. Confidence lists for mean when population SD is known

 Mean $\pm$ SD

 Mean $\pm$ SE

 Mean $\pm Z_{\alpha/2}$ SE

 Mean $\pm t_{\alpha/2}$ SE

11. The following statistics are unbiased estimators

 All these (Sample mean, Sample proportion, and Sample variance)

 The sample proportion

 The sample variance $s^2=\frac{\sum (X-\overline{X})^2}{n-1}$

 The sample mean

12. Which one of the following is a biased estimator?

 $\hat{p}=\frac{X}{n}$

 $\overline{X}=\frac{\sum X}{n}$

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

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

13. Suppose the 90% confidence Interval for population mean $\mu$ is -24.3 cents to 64.3 cents, the sample mean $\overline{X}$ is

 -24.3

 20

 64.3

 40

14. A 95% confidence interval for a population proportion is 32.4% to 47.6%, and the value of the sample proportion $\hat{p}$ is

 80%

 32.4%

 47.6%

 40%

15. Mean and median are both estimators of population mean ______.

 Biased

 Unbiased

 Sufficient

 Consistent

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

 2.326

 1.96

 1.645

 2.575

17. ‘Statistic’ is an estimator, and its computed value(s) is called

 Estimate

 Estimator

 Interval estimate

 Estimation

18. In the case of paired observations (for a small sample $n\le 30$), the confidence interval estimate for the difference of two populations means $\mu_1-\mu_2=\mu_d$ is

 $\overline{d} \pm t_{\frac{\alpha}{2}(n-1)}\frac{s_!^2+s_2^2}{\sqrt{n}}$

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

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

 $\overline{d} \pm t_{\frac{\alpha}{2}(n_1+n_2-1)}\frac{s_d}{\sqrt{n}}$

19. For a normal population with a known population standard deviations $\sigma_1$ and $\sigma_2$, the confidence interval estimate for the difference between two population means $(\mu_1-\mu_2)$ is

 $(\overline{X}_1 -\overline{X}_2) \pm Z_{\frac{\alpha}{2}} \sqrt{
\frac{\sigma_1^2\sigma_2}{n_1n_2}}$

 $(\overline{X}_1 -\overline{X}_2) \pm Z_{\frac{\alpha}{2}} \sqrt{
\frac{\sigma_1^2+\sigma_2}{n_1+n_2}}$

 $(\overline{X}_1 -\overline{X}_2) \pm Z_{\frac{\alpha}{2}} \sqrt{
\frac{\sigma_1^2}{n_1}+\frac{\sigma_2^2}{n_2}}$

 $(\overline{X}_1 -\overline{X}_2) \pm Z_{\frac{\alpha}{2}} \sqrt{
\frac{S_1^2}{n_1}+\frac{S_2^2}{n_2}}$

20. For a large sample, the confidence interval estimate for the difference between two population proportions $p_1-p_2$ is

 $(\hat{p}_1 – \hat{o}_2) \pm Z_{\frac{\alpha}{2}} \sqrt{\frac{\hat{p}_1\hat{q}_1+\hat{p}_2\hat{q}_2}+{n_1n_2}}$

 $(\hat{p}_1 – \hat{o}_2) \pm Z_{\frac{\alpha}{2}} \sqrt{\frac{\hat{p}_1\hat{q}_1+\hat{p}_2\hat{q}_2}+{n_1+n_2}}$

 $(\hat{p}_1 – \hat{o}_2) \pm Z_{\frac{\alpha}{2}} \sqrt{\hat{p}_1\hat{q}_1+\hat{p}_2\hat{q}_2}$

 $(\hat{p}_1 – \hat{o}_2) \pm Z_{\frac{\alpha}{2}} \sqrt{\frac{\hat{p}_1\hat{q}_1}{n_1} + \frac{\hat{p}_2\hat{q}_2}{n_2}}$

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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 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.

Statistical Inference Quiz

• The following statistics are unbiased estimators
• A statistic is an unbiased estimator of a parameter if:
• Which one of the following is a biased estimator?
• For $n$ paired number of observations, the degrees of freedom for the Paired Sample t-test will be
• If t-distribution for two independent samples $n_1=n_2=n$, then the degrees of freedom will be
• If $1-\alpha=0.90$ then value of $Z_{\frac{\alpha}{2}}$ is
• If the population standard deviation ($\sigma$) is known and the sample size ($n$) is less than or equal to or more than 30, the confidence interval for the population mean ($\mu$) will be
• If the population standard deviation ($\sigma$) is unknown and the sample size ($n$) is greater than 30, the confidence interval for the population mean $\mu$ is
• If the population standard deviation $\sigma$ is unknown and the sample size $n$ is less than or equal to 30, the confidence interval for the population mean $\mu$ is
• Suppose the 90% confidence Interval for population mean $\mu$ is -24.3 cents to 64.3 cents, the sample mean $\overline{X}$ is
• A 95% confidence interval for a population proportion is 32.4% to 47.6%, and the value of the sample proportion $\hat{p}$ is
• For a normal population with a known population standard deviations $\sigma_1$ and $\sigma_2$, the confidence interval estimate for the difference between two population means $(\mu_1-\mu_2)$ is
• If $n_1, n_2\le 30$ the confidence interval estimate for the difference of two population means ($\mu_1-\mu_2$) when population standard deviations $\sigma_1, \sigma_2$ are unknown but equal in case of pooled variates is:
• In the case of paired observations (for a small sample $n\le 30$), the confidence interval estimate for the difference of two populations means $\mu_1-\mu_2=\mu_d$ is
• For a large sample, the confidence interval estimate for the difference between two population proportions $p_1-p_2$ is
• Each of the following increases the width of a confidence interval except
• ‘Statistic’ is an estimator, and its computed value(s) is called
• Confidence lists for mean when population SD is known
• Mean and median are both estimators of population mean _________.
• What does it mean when someone calculates a 95% confidence interval?

MCQs General Knowledge

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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

Please go to Confidence Interval MCQs 4 to view the test

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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