Which of the following are correct?
(A) A statistical hypothesis is a statement about the population parameter which may be true or false.
(B) In a statistical hypothesis testing procedure, a Type I error is made when the null hypothesis is accepted when it is false.
(C) In a statistical hypothesis testing procedure, a Type II error is made when the null hypothesis is rejected when it is true.
(D) The number of degrees of freedom of a statistic is the number of independent variates used to compute that statistic.
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → (A) and (D) only
In hypothesis testing, a Type I error is rejecting \(H_0\) when it is true, and a Type II error is accepting \(H_0\) when it is false.
Checking the statements
(A) A statistical hypothesis is a statement about the population parameter which may be true or false. — Correct. This is the definition of a statistical hypothesis; the sample is used to decide whether to accept it.
(B) In a statistical hypothesis testing procedure, a Type I error is made when the null hypothesis is accepted when it is false. — Incorrect. Accepting a false \(H_0\) is a Type II error.
(C) In a statistical hypothesis testing procedure, a Type II error is made when the null hypothesis is rejected when it is true. — Incorrect. Rejecting a true \(H_0\) is a Type I error.
(D) The number of degrees of freedom of a statistic is the number of independent variates used to compute that statistic. — Correct. This is the definition of degrees of freedom: the number of values that can vary freely. For example, \(\sum (x - \bar{x}) = 0\) fixes one of the n deviations, so the sample variance has \(n - 1\) degrees of freedom.