Asked by Somtochi Ibezim on Jul 08, 2024

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Which of the following statements is true with respect to the t distribution?

A) The t distribution is more spread out than the standard normal distribution.
B) The t distribution is symmetrical.
C) The shape of the t distribution depends on the number of degrees of freedom.
D) All of these.
E) None of these.

T Distribution

This type of probability distribution comes into play when attempting to estimate the mean of a normally distributed population, specifically when dealing with a small sample size and lacking knowledge of the population's standard deviation.

Degrees Of Freedom

The number of values in a calculation that are free to vary, often related to the sample size, affecting the shape of various statistical distributions.

Standard Normal Distribution

A normal distribution with a mean of zero and a standard deviation of one, used as a basis for comparison in many statistical methodologies.

  • Comprehend the manner in which the t-distribution converges towards the normal distribution as degrees of freedom increase.
  • Understand that alterations in the sample mean do not affect the shape of the t-distribution.
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LP
Lindsey PerryJul 11, 2024
Final Answer :
D
Explanation :
The t distribution is indeed more spread out than the standard normal distribution, especially with smaller sample sizes, reflecting greater uncertainty. It is symmetrical around the mean, similar to the standard normal distribution. Additionally, the shape of the t distribution varies with the degrees of freedom, becoming more similar to the standard normal distribution as the degrees of freedom increase.