Important Statistical Inference Quiz 5

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. The following statistics are unbiased estimators

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

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

 The sample proportion

 The sample mean

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

 All of the statements are true.

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

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

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

3. 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

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

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

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

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

4. Confidence lists for mean when population SD is known

 Mean $\pm t_{\alpha/2}$ SE

 Mean $\pm$ SD

 Mean $\pm Z_{\alpha/2}$ SE

 Mean $\pm$ SE

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

 $n_1+n_2-2$

 $n$

 $n_1+n_2-1$

 $n-1$

6. 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:

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

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

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

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

7. 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

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

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

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

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

8. 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

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

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

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

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

9. 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

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

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

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

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

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

 $\overline{X}=\frac{\sum X}{n}$

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

 $\hat{p}=\frac{X}{n}$

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

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

 Biased

 Consistent

 Sufficient

 Unbiased

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

 E(Variance) = Mean

 E(statistic) = Parameter

 E(Mean) = Variance

 E(Sample mean) = Proportion

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

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

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

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

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

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

 $2n-1$

 $n-1$

 $2n-2$

 $2n+1$

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

 2.326

 2.575

 1.645

 1.96

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

 32.4%

 40%

 80%

 47.6%

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

 Decreased sample size

 Increased sample size

 Increased confidence level

 Increased variability

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

 64.3

 40

 -24.3

 20

19. 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

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

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

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

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

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

 Interval estimate

 Estimation

 Estimator

 Estimate

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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?

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