In reference to the Inferential Statistics, which of the following is NOT correct?
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → If sufficiently large random samples with replacement are drawn from a population, then the sampling distribution of the sample means approaches a binomial distribution.
Each option is checked as a statement; the answer is the one statement that is not true.
Option (1) 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.
Option (2) The standard deviation of the sampling distribution of a statistics is known as its standard error. — Correct. This is the definition of the standard error.
Option (3) If sufficiently large random samples with replacement are drawn from a population, then the sampling distribution of the sample means approaches a binomial distribution. — Incorrect. By the central limit theorem, the sampling distribution of the sample mean approaches a normal distribution, not a binomial distribution.
Option (4) In a statistical hypothesis testing, a Type-I error is made when null hypothesis is rejected when it is true. — Correct. A Type-I error is rejecting a true null hypothesis; accepting a false one is a Type-II error.
CBSE Applied Mathematics (Class XII):
Central Limit Theorem
