Asked by Jamie Stallings on Jun 30, 2024

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As the number of degrees of freedom for a t distribution increases, the difference between the t distribution and the standard normal distribution

A) becomes larger.
B) becomes smaller.
C) stays the same.
D) fluctuates.

Degrees of Freedom

Refers to the number of independent values or quantities which can be assigned to a statistical distribution or to the number of independent choices left after fixing the parameters of a system.

T Distribution

A type of probability distribution that is symmetrical and bell-shaped, used in hypothesis testing for small sample sizes.

Normal Distribution

A bell-shaped distribution that is symmetric about the mean, where data near the mean are more frequent in occurrence.

  • Understand the relationship between the t distribution and the standard normal distribution as degrees of freedom increase.
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AN
Aline NyanomeJul 05, 2024
Final Answer :
B
Explanation :
As the number of degrees of freedom for a t distribution increases, the t distribution becomes closer and closer to a standard normal distribution. This is because the t distribution approaches normality as the sample size increases, so the difference between them becomes smaller.