Category: Testing of Hypothesis

Multiple Choice Questions (MCQs about Hypothesis Testing) from Statistical Inference for the preparation of exam and different statistical job tests in Government/ Semi-Government or Private Organization sectors. These tests are also helpful to getting admission to different colleges and Universities.

MCQs Hypothesis Testing

1. The region of acceptance of $H_0$ is called

 Critical region

 Test statistics

 Type-I error

 Acceptance region

2. When critical region is located on both side of the curve, it is called

 One tail test

 Two-tailed test

 Left tailed test

 Right tailed teset

3. If $\alpha=0.05$%, the value of one-tailed $Z$ test will be

 1.96

 1.64

 2.33

 2.58

4. Which one is an example of two-tailed test

 $ H_1:\mu$

 $ H_1:\mu >0 $

 $ H_1:\mu \ge 0 $

 $ H_1:\mu \ne 0 $

5. The probability of rejecting a false $H_0$ is

 Level of significance

 Level of confidence

 Critical region

 Power of test

6. A ________ error is made if $H_1$ is true but $H_0$ is accepted

 Type-I

 Type-II

 Sampling error

 The standard error of the mean

7. A deserving player is not selected in national team, it is an example of

 Type-II error

 Type-I error

 Correct decision

 Sampling error

8. Type-I error will occur if an innocent person is

 Arrested by police

 Not arrested

 Police care for him

 None ot these

9. The level of significance is the risk of

 Rejecting $H_0$ when $H_0$ is true

 Rejecting $H_0$ when $H_1$ is correct

 Rejecting $H_1$ when $H_1$ is correct

 Accepting $H_0$ when $H_0$ is correct

10. A statistic on the basis of which a decision is made about the hypothesis of interest is called

 Test statistics

 Significance level

 Statement of hypothesis

 Critical region

11. In a Z-test, the number of degrees of freedom is

 $ n-2 $

 $ n-1 $

 1

 None of these

12. If population standard deviation is known and $n>30$ then appropriate test statistics mean comparison is

 t-test

 F-test

 Z-test

 $ \chi^2 $-test

13. The probability of rejecting a true hypothesis is called

 Critical region

 Level of significance

 Test statistics

 Statement of hypothesis

14. The choice of one-tailed test and two-tailed test depends upon

 Null hypothesis

 Alternative hypothesis

 Composite hypothesis

 None of these

15. The region of rejection of $H_0$ is called

 Critical region

 Test statistics

 Type-I error

 Acceptance region

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

Application of $\chi^2$ distribution is the test of goodness of fit. It is possible to test the hypothesis that a population has a specified theoretical distribution using the $\chi^2$ distribution. The theoretical distribution may be Normal, Binomial, Poisson, or any other distribution.

The Chi-Square Goodness of Fit Test enables to check whether there is a significant difference between an observed frequency distribution and a theoretical frequency distribution (expected frequency distribution) based on some theoretical models, that is (how well it fits the distribution of data we have actually observed).

A goodness of fit test between observed and expected frequencies is based upon

\[\chi^2 = \sum\limits_{i=1}^k \left[ \frac{(OF_i – EF_i)^2}{EF_i} \right] \]

where $OF_i$ represents the observed and $EF_i$ the expected frequencies. for the $i$th class and $k$ is the number of possible outcomes or the number of different classes.

Degrees of Freedom

• If expected frequencies can be computed without estimation of population parameters from sample statistics, then the number of degrees of freedom is $v=k-1$.
  As we have only constraint (that is, the sum of expected frequencies is equal to the sum of observed frequencies, so we subtracted 1 from $k$.
• If the expected frequencies can be computed only by estimating $m$ population parameters from sample statistics, then degrees of freedom is $v=k-1-m$.

It is important to note that

• The computed $\chi^2$ value will be small, if the observed frequencies are close to the corresponding expected frequencies indicating a good fit.
• The computed $\chi^2$ value will be large, if observed and expected frequencies have a great deal of difference, indicating a poor fit.
• A good fit leads to the acceptance of the null hypothesis that the sample distribution agrees with the hypothetical or theoretical distribution.
• A bad fit leads to the rejection of the null hypothesis.

Critical Region

The critical region under the $\chi^2$ curve will fall in the right tail of the distribution. We find the critical value of $\chi^2_{\alpha}$ from the table for a specified level of significance $\alpha$ and $v$ degrees of freedom.

Decision

If the computed $\chi^2$ value is greater than the critical $\chi^2_{\alpha}$ the null hypothesis will be rejected. Thus $\chi^2> \chi^2_{\alpha}$ constitutes the critical region.

Some Requirements

The Chi-Square Goodness of fit test should not be applied unless each of the expected frequencies is at least equal to 5. When there are smaller expected frequencies in several, these should be combined (merged). The total number of frequencies should not be less than fifty.

Note that we must look with suspicion upon circumstances where $\chi^2$ is too close to zero since it is rare that observed frequencies agree to well with expected frequencies. To examine such situations, we can determine whether the computed value of $\chi^2$ is less than $\chi^2_{0.95}$ to decide that the agreement is too good at the 0.05 level of significance.