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

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To calculate the t-distribution for small sample sizes, first determine the sample means and standard deviations for all possible samples of size 3 from the given population units. Use the t-distribution to find the critical value tα/2, which is necessary for constructing the 95% confidence intervals. The population mean is 78.8, and the standard deviation is approximately 2.59, which will help in verifying how many confidence intervals contain the population mean. Finally, check if the results align with the empirical rule to confirm consistency in the findings. Understanding these steps is crucial for accurately applying the t-distribution in statistical analysis.
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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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