Statistics HW Help: How to Calculate T-Distribution for Small Sample Sizes?

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SUMMARY

The discussion focuses on calculating the t-distribution for small sample sizes in a statistics homework problem involving a population of five units with measurements 76, 77, 78, 81, and 82. The population mean is established as 78.8, with a standard deviation of 2.58844. Participants are tasked with listing all possible samples of size three, computing their means, standard deviations, and 95% confidence intervals using the t-distribution. The goal is to determine how many confidence intervals contain the population mean and to verify this using the empirical rule.

PREREQUISITES
  • Understanding of basic statistics concepts such as mean and standard deviation.
  • Familiarity with t-distribution and its application for small sample sizes.
  • Knowledge of confidence intervals and how to calculate them.
  • Ability to list combinations of samples from a given population.
NEXT STEPS
  • Learn how to calculate t-distribution values using statistical software like R or Python's SciPy library.
  • Research methods for constructing confidence intervals for small sample sizes.
  • Explore the empirical rule and its application in verifying statistical results.
  • Study the concept of sampling distributions and their significance in inferential statistics.
USEFUL FOR

Students studying statistics, educators teaching statistical methods, and anyone needing assistance with t-distribution calculations for small sample sizes.

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Homework Statement



I need help solving this problem:

Let A, B, C, D, and E are 6 units of a population. The measurements associated with A, B, C. D, E units are 76, 77, 78, 81, and 82, respectively.

-Find the population mean and its standard deviation

-List all possible samples of size 3 from those 5 units

-From each sample, compute the mean, standard deviation, and 95% confidence interval. Use t-distribution to estimate the tα/2 because we have a small size.

-How many intervals contain population mean? Can you verify your result with empirical rule? Do they agree?

Homework Equations


The Attempt at a Solution



I know the mean is 78.8 and standard deviation is 2.58844
 
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I have solved out everything, I just need help to know how I get the t-distribution?
 

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