Match the terms mentioned List I with the definitions mentioned in List II.
| List-I | List-II | ||
| (A) | Confidence interval | (I) | In a hypothesis test, the probability of making wrong decision when the null hypothesis is true. |
| (B) | Margin of error | (II) | The number of independent pieces of information on which an approximation is based. |
| (C) | Significance level | (III) | A range of values, derived from sample statistic which is likely to contain the value of an unknown population parameter. |
| (D) | Degree of freedom | (IV) | In a confidence interval, the range of values, above and below the sample statistic. |
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → (A) - (III), (B) - (IV), (C) - (I), (D) - (II)
(A) Confidence interval
This matches (III) A range of values, derived from sample statistic which is likely to contain the value of an unknown population parameter, for example \( \bar{x}\pm 1.96\,\frac{\sigma}{\sqrt{n}} \) for 95% confidence.
(B) Margin of error
This matches (IV) In a confidence interval, the range of values, above and below the sample statistic, that is, the amount added to and subtracted from the sample statistic (\( 1.96\,\frac{\sigma}{\sqrt{n}} \) in the example of (A)).
(C) Significance level
This matches (I) In a hypothesis test, the probability of making wrong decision when the null hypothesis is true. This is α, the probability of rejecting a true null hypothesis (Type I error).
(D) Degree of freedom
This matches (II) The number of independent pieces of information on which an approximation is based; for a sample of size n used to estimate a mean, it is n − 1.
So the matching is (A)-(III), (B)-(IV), (C)-(I), (D)-(II).