List - I List - II A. Type I error I. Accept $H_0$ when it is false B. Type II error II. $H_0 : \mu = \mu_0 \text{ and } \sigma^2 = \sigma_0^2$ C. Simple Hypothesis III. Reject $H_0$ when it is true D. Composite Hypothesis IV. $H_0 : \mu = \mu_0 \text{ and } \sigma^2 \text{ is unknown}$
This question requires matching statistical terms related to hypothesis testing with their definitions or examples.
Matching Statistical Concepts
Type I Error
A Type I error occurs when the null hypothesis ($H_0$) is rejected, but it is actually true. This corresponds to option III.
Type II Error
A Type II error occurs when the null hypothesis ($H_0$) is not rejected (accepted), but it is actually false. This corresponds to option I.
Simple Hypothesis
A simple hypothesis completely specifies the population distribution, meaning it states exact values for all parameters. An example is $H_0 : \mu = \mu_0 \text{ and } \sigma^2 = \sigma_0^2$, where $\mu_0$ and $\sigma_0^2$ are specific constants. This corresponds to option II.
Composite Hypothesis
A composite hypothesis does not specify exact values for all parameters, allowing for a range of possibilities. For example, $H_0 : \mu = \mu_0 \text{ and } \sigma^2 \text{ is unknown}$ or $H_0 : \mu \le \mu_0$. This corresponds to option IV.
Summary of Matches
- A. Type I error matches III. Reject $H_0$ when it is true
- B. Type II error matches I. Accept $H_0$ when it is false
- C. Simple Hypothesis matches II. $H_0 : \mu = \mu_0 \text{ and } \sigma^2 = \sigma_0^2$
- D. Composite Hypothesis matches IV. $H_0 : \mu = \mu_0 \text{ and } \sigma^2 \text{ is unknown}$
The correct combination is A-III, B-I, C-II, D-IV.
Important Questions from Hypothesis testing
If α is the level of significance and if (1 − α) is increased, then the width of the confidence interval of mean:
The analysis of variance technique was introduced by:
The power of a test is:
The term ‘Analysis of variance’ was introduced by:
Which of the following can be applied as a goodness-of-fit test?
