Student's t- distribution to construct a confidence interval question

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Discussion Overview

The discussion revolves around the appropriateness of using the Student's t-distribution to construct a confidence interval based on provided summary statistics of a data set. The focus includes considerations of sample size, distribution characteristics, and the context of the problem, which appears to be homework-related.

Discussion Character

  • Homework-related
  • Debate/contested
  • Conceptual clarification

Main Points Raised

  • One participant suggests that it is appropriate to use the t-distribution because the sample size is less than 40, indicating a small sample size.
  • Another participant questions the clarity of the problem, specifically asking for what the confidence interval is being constructed (e.g., the mean of the population). They highlight the importance of a complete problem statement.
  • There is a discussion about the assumption of normality in the population from which the sample is drawn, with one participant noting that the suitability of the t-distribution may depend on this assumption.
  • Another participant raises the question of whether there are additional reasons beyond normality that might affect the suitability of the t-distribution.
  • One participant prompts a consideration of the properties of the t-distribution, such as symmetry, and whether the data resemble samples from this distribution.

Areas of Agreement / Disagreement

Participants express differing views on the appropriateness of using the t-distribution, particularly regarding the normality of the underlying population and the completeness of the problem statement. The discussion remains unresolved with multiple competing perspectives.

Contextual Notes

Participants note the potential dependence of the t-distribution's applicability on the normality of the population and the characteristics of the data, but these aspects are not fully explored or resolved.

joe98
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The following are summary statistics for a data set. Would it be appropriate to use the
Student's t- distribution to construct a confidence interval for these data?
Explain clearly!

Sample size = 10
Mean = 8.905
Median = 6.105
Standard deviation = 9.690
Minimum = 0.512
Maximum = 39.920
Q1 = 1.967
Q3 = 8.103

My answer would be it would be appropriate since n is less than 40(small sample size), we can use t distribution.

Any other explanations guys
 
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joe98 said:
Would it be appropriate to use the
Student's t- distribution to construct a confidence interval for these data?

A confidence interval for what? The mean of the population they were sampled from?

This is a homework type problem, right? We begin to see why homework section wants such problems posed in a orderly format that includes a complete statement of the problem.

I suppose the issue here might be how much your numerical tables for the t-statistic depend on the population being normally distributed and whether you think your sample is.from a normally distributed population.
 
Stephen Tashi said:
A confidence interval for what? The mean of the population they were sampled from?

thats right, and that's the data given in the question,

the question says if it is suitable to use t distribution to construct a confidence interval using the given data.

Somehow i have to explain how its possible?

Any ideas?
 
so Stephen, your suggesting its not suitable to use tdistribution because its not normally disstributed but could there be any other reasons?
 
joe98 said:
so Stephen, your suggesting its not suitable to use tdistribution because its not normally disstributed but could there be any other reasons?

Joe, just simply look how t distribution looks. Is it symmetric? What about other properties? Do your data look like samples from this distribution? Etc.
 

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