Question

Which of the following statement is true?

I. A statistic describes the characteristic of a population.

II. If we triple the sample size, then the standard deviation of the sampling distribution of the sample mean will decrease by a factor of 1/sqrt(3)

III. The standard deviation of a t-distribution becomes larger as we decrease the degrees of freedom.

1. II only

2. III only

3. I only

4. II and III

5.!, II, and III

Answer 1

The following statement is true;

II. If we triple the sample size, then the standard deviation of the sampling distribution of the sample mean will decrease by a factor of 1/sqrt(3)

Explaintaion: As standard deviation of the sampling distribution of the sample mean is = S (say,).

If n is tripled than the standard deviation will be,

III. The standard deviation of a t-distribution becomes larger as we decrease the degrees of freedom.

Explaination: standard deviation become smaller if we increse sample size, and also become larger if we decrease sample size. For t distribution, degrees of freedom = sample size - 1.

4) II and III (ans)

[ Statement I is false because,A parameter is a characteristic of a population. A statistic is a characteristic of a sample.]

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