10j: t-statistic vs z-statistic

mlwl8521 · February 10, 2014, 5:03pm

So I know how to use the Z statistic tables for a normal distribution where you know the standard deviation

The book says that for a nonnormal distribution where standard deviation is unknown, OR sample size is small(?)

http://3.bp.blogspot.com/_5u1UHojRiJk/TEdJJc6of2I/AAAAAAAAAIE/Ai0MW5VgIhg/s1600/t-table.jpg

I’m not sure I fully understand how to use these tables. I know that DF = degrees of freedom =

of observations minus 1, or n-1

So for example if we have 11 observations, so DF = 10. If we look at this chart and look at a 95% confidence range, then P = 0.025 on each tail. The score listed for DF = 10 is 2.228.

What is the importance of the 2.228 figure?

S2000magician · February 10, 2014, 7:12pm

It means that the area above μ + 2.228σ is 2.5%, and the area below μ – 2.228σ is 2.5%. It’s a critical value; the corresponding (5%, 2-tail) critical value for the standard normal distribution is 1.96.

Greenman72 · February 10, 2014, 10:14pm

So if the average height for an NBA player is 80 inches (6 foot 8 inches), with a standard deviation of three inches, a guy who’s 83 inches tall has a Z-score of 1, and he’s taller than 68.3% of all people in the NBA.

A guy who’s 86 inches tall will have a z-score of 2, and he’s taller than 95.44% of all people in the NBA.

A guy who’s 86.9 inches tall (2.3 * 3 inches, plus 80 inches) has a z-score of 2.3, and he’s taller than 97.5% of all people in the NBA. And there are 2.5% of the people who are still taller than him.

mlwl8521 · February 11, 2014, 9:04am

S2000magician:

mlwl8521:

So I know how to use the Z statistic tables for a normal distribution where you know the standard deviation

The book says that for a nonnormal distribution where standard deviation is unknown, OR sample size is small(?)

http://3.bp.blogspot.com/_5u1UHojRiJk/TEdJJc6of2I/AAAAAAAAAIE/Ai0MW5VgIhg/s1600/t-table.jpg

I’m not sure I fully understand how to use these tables. I know that DF = degrees of freedom =

of observations minus 1, or n-1

So for example if we have 11 observations, so DF = 10. If we look at this chart and look at a 95% confidence range, then P = 0.025 on each tail. The score listed for DF = 10 is 2.228.

What is the importance of the 2.228 figure?

It means that the area above μ + 2.228σ is 2.5%, and the area below μ – 2.228σ is 2.5%. It’s a critical value; the corresponding (5%, 2-tail) critical value for the standard normal distribution is 1.96.

This test is based on the assumption that σ is unknown though, right? So how would you be able to extrapolate meaningful data if you dont know σ?

S2000magician · February 11, 2014, 4:31pm

mlwl8521:

S2000magician:

mlwl8521:

So I know how to use the Z statistic tables for a normal distribution where you know the standard deviation

The book says that for a nonnormal distribution where standard deviation is unknown, OR sample size is small(?)

http://3.bp.blogspot.com/_5u1UHojRiJk/TEdJJc6of2I/AAAAAAAAAIE/Ai0MW5VgIhg/s1600/t-table.jpg

I’m not sure I fully understand how to use these tables. I know that DF = degrees of freedom =

of observations minus 1, or n-1

So for example if we have 11 observations, so DF = 10. If we look at this chart and look at a 95% confidence range, then P = 0.025 on each tail. The score listed for DF = 10 is 2.228.

What is the importance of the 2.228 figure?

It means that the area above μ + 2.228σ is 2.5%, and the area below μ – 2.228σ is 2.5%. It’s a critical value; the corresponding (5%, 2-tail) critical value for the standard normal distribution is 1.96.

This test is based on the assumption that σ is unknown though, right? So how would you be able to extrapolate meaningful data if you dont know σ?

If you don’t know σ, use s (sample standard deviation).