Which of the following are true? Select one or more:

(a) The t-distribution is dependent on the sample size.

(b) The t-distribution does not depend on the sample size.

(c) The t-distribution has more values at the extremes than a standard normal distribution.

(d) The t-distribution has fewer values at the extremes than a standard normal distribution.

(e) The t-distribution is bell-shaped and centered at its degrees of freedom.

(f) The t-distribution is bell-shaped and centered at 0.

(g) With larger samples, the t-distribution is closer to a normal distribution.

(h) With smaller samples, the t-distribution is closer to a normal distribution.

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Zachariah

5 July, 02:36

Which of the following are true? Select one or more:

(a) The t-distribution is dependent on the sample size.

(b) The t-distribution does not depend on the sample size.

(c) The t-distribution has more values at the extremes than a standard normal distribution.

(d) The t-distribution has fewer values at the extremes than a standard normal distribution.

(e) The t-distribution is bell-shaped and centered at its degrees of freedom.

(f) The t-distribution is bell-shaped and centered at 0.

(g) With larger samples, the t-distribution is closer to a normal distribution.

(h) With smaller samples, the t-distribution is closer to a normal distribution.

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Answers (1)

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Dolce · Answer 1

As given below.

Explanation:

1. The t-distribution is based and dependent on the sample size.

2. The t-distribution is more valued at the extremes thus has a standard normal distribution.

3. The t-distribution is bell-shaped and is centered at 0.

4. The t-distribution is a kind of bell-shaped and is centered at its degrees of freedom.

5. With larger samples, the t-distribution is close to the normal distribution.

Being symmetric in shape and a bell-shaped distribution of the normal distribution this is more prone to produce the values that are found its mean. Its an estimation of the unknown parameters and uncertainty of data. In case the deviation of the errors was known, the normal distribution would be used instead of the t-distribution or student's distribution.