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

In summary, the sample size is small (less than 40) and the data may not be normally distributed, making it appropriate to use the Student's t-distribution to construct a confidence interval for the mean of the population. However, other considerations such as the symmetry and properties of the t-distribution and whether the data resemble samples from this distribution should also be taken into account.
  • #1
joe98
27
0
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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  • #2
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.
 
  • #3
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?
 
  • #4
so Stephen, your suggesting its not suitable to use tdistribution because its not normally disstributed but could there be any other reasons?
 
  • #5
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.
 

1. What is a Student's t-distribution?

A Student's t-distribution is a probability distribution that is used to construct confidence intervals and perform hypothesis testing when the sample size is small and the population standard deviation is unknown.

2. How is a Student's t-distribution different from a normal distribution?

A Student's t-distribution has a flatter peak and thicker tails compared to a normal distribution. This is because it takes into account the added uncertainty when estimating the population standard deviation from a small sample size.

3. When should I use a Student's t-distribution to construct a confidence interval?

A Student's t-distribution should be used when the sample size is small (typically less than 30), the population standard deviation is unknown, and the population follows a normal distribution.

4. How do I calculate a confidence interval using a Student's t-distribution?

To calculate a confidence interval using a Student's t-distribution, you will need to know the sample mean, sample standard deviation, and sample size. You will also need to choose a confidence level, such as 95% or 99%. Using a t-table or a statistical software, you can then find the t-value for your chosen confidence level and degrees of freedom (sample size - 1). The confidence interval can then be calculated by adding and subtracting the t-value multiplied by the standard error of the mean from the sample mean.

5. What is the purpose of using a Student's t-distribution to construct a confidence interval?

The purpose of using a Student's t-distribution to construct a confidence interval is to more accurately estimate the true population mean when the sample size is small and the population standard deviation is unknown. This allows for a more robust inference about the population mean based on a limited sample size.

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