The tutor shows an example of z vs t.

From yesterday’s post, we have the following parameters:

• x: 14.4
• sample standard deviation: 3.3
• sample size: 25

We estimated the percent of the population between 10.2 and 12.9. Using the t-statistic with df=24, we arrived at 21.9%.

What if we just use a normal approximation, with the same sample mean and standard deviation, to once again estimate the percentage of the population between 10.2 and 12.9? Using the TI-83 Plus, we can key in

1. 2nd VARS
2. 2 (for normal cdf)
3. 10.2, 12.9, 14.4, 3.3)

Doing so, we arrive at 22.3%. So the comparison is 21.9% (t-statistic) vs 22.3% (normal). Proportionally, the difference is about 2%. Perhaps, for sample size 25 (df=24), the normal approximation can be very close to the t-statistic.

HTH:)

Source:

TI-83 Plus manual. Texas Instruments, 1999.

Jack of Oracle Tutoring by Jack and Diane, Campbell River, BC.