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What does when the sample size and degrees of freedom is sufficiently large the difference between a t distribution and the normal distribution becomes negligible mean?
The t-distribution and the normal distribution are not exactly the same. The t-distribution is approximately normal, but since the sample size is so small, it is not exact. But n increases (sample size), degrees of freedom also increase (remember, df = n - 1) and the distribution of t becomes closer and closer to a normal distribution. Check out this picture for a visual explanation: http://www.uwsp.edu/PSYCH/stat/10/Image87.gif
What are characteristics of the X2?
It is not negative. it is positively skewed, and it approaches a normal distribution as the degrees of freedom increase. Its shape is NEVER based on the sample size.
When do you use a z - table compared with when you use a t - table?
For statistical tests based on (Student's) t-distribution you use the t-table. This is appropriate for small sample sizes - up to around 30. For larger samples (or degrees of freedom), the t-distribution becomes very close to the Standard Normal distribution so you use the z-tables.
Does the t distribution always has n degrees of freedom?
Yes it does.
How to calculate the degrees of freedom for t-distribution?
n-1
