In reference to the Inferential Statistics, which of the following statements are correct?
A. The number of degrees of freedom of a statistic is the number of independent variates used to compute the statistic.
B. A confidence interval is a range that could be expected to contain the population parameter of interest.
C. In a hypothesis test, the significance level is the probability of making wrong decision when the null hypothesis is true.
D. The confidence level of the sampling distribution of a statistic is known as its standard error.
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → A, B and C only
The standard error of a statistic is the standard deviation of its sampling distribution. The level of significance α is the probability of rejecting H0 when it is true (a Type I error).
So degrees of freedom count the independent values, a confidence interval estimates the parameter, α is the probability of a Type I error, and the standard error is a standard deviation, not a confidence level.
Checking the statements
(A) The number of degrees of freedom of a statistic is the number of independent variates used to compute the statistic. — Correct. For example, n values with a fixed mean have n − 1 independent values.
(B) A confidence interval is a range that could be expected to contain the population parameter of interest. — Correct. A confidence interval is an interval estimate of the parameter.
(C) In a hypothesis test, the significance level is the probability of making wrong decision when the null hypothesis is true. — Correct. When H0 is true, the wrong decision is to reject it, and its probability is α.
(D) The confidence level of the sampling distribution of a statistic is known as its standard error. — Incorrect. The standard error is the standard deviation of the sampling distribution.