Which of the following statements are true?

I. The sampling distribution of
¯
x
has standard deviation
σ
√
n
even if the population is not normally distributed.
II. The sampling distribution of
¯
x
is normal if the population has a normal distribution.
III. When
n
is large, the sampling distribution of
¯
x
is approximately normal even if the the population is not normally distributed.
I and II
I and III
II and III
I, II, and III
None of the above gives the complete set of true responses.

Question

12-08-2022
Mathematics

contestada

Which of the following statements are true?

I. The sampling distribution of
¯
x
has standard deviation
σ
√
n
even if the population is not normally distributed.
II. The sampling distribution of
¯
x
is normal if the population has a normal distribution.
III. When
n
is large, the sampling distribution of
¯
x
is approximately normal even if the the population is not normally distributed.
I and II
I and III
II and III
I, II, and III
None of the above gives the complete set of true responses.

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ayfat23 ayfat23 · Answer 1 · 2022-08-16T21:56:29+02:00

The statements that are true as regards sampling distribution is option D which are are:

The sampling distribution of ¯x¯ has standard deviation σ /√n even if the population is not normally distributed.
The sampling distribution of ¯x¯ is normal if the population has a normal distribution.
When n is large, the sampling distribution of ¯x¯ is approximately normal even if the the population is not normally distributed.

What is sampling distribution?

A sampling distribution can be described as a the probability distribution of a statistic which can be gotten from the larger number of samples with respect to a specific population.

It should be noted that sampling distribution of a given population represent the distribution of frequencies with respect to the range of different outcomes.

Therefore option D is correct.

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