The t-Test is used to measure the similarities and differences between two populations.
Concept #1: In order to measure the similarities and differences between populations we utilize a t score.
Example #1: A student wishing to calculate the amount of arsenic in cigarettes decides to run two separate methods in her analysis. The results (shown in ppm) are shown below
Sample Method 1 Method 2
1 110.5 104.7
2 93.1 95.8
3 63.0 71.2
4 72.3 69.9
5 121.6 118.7
Is there a significant difference between the two analytical methods under a 95% confidence interval?
Example #2: You want to determine if concentrations of hydrocarbons in seawater measured by fluorescence are significantly different than concentrations measured by a second method, specifically based on the use of gas chromatography/flame ionization detection (GC-FID). You measure the concentration of a certified standard reference material (100.0 µM) with both methods seven (n=7) times. Specifically, you first measure each sample by fluorescence, and then measure the same sample by GC-FID. The concentrations determined by the two methods are shown below.
Sample Fluorescence GC-FID
1 100.2 101.1
2 100.9 100.5
3 99.9 100.2
4 100.1 100.2
5 100.1 99.8
6 101.1 100.7
7 100.0 99.9
Calculate the appropriate t-statistic to compare the two sets of measurements.
Example #3: A sample of size n = 100 produced the sample mean of 16. Assuming the population deviation is 3, compute a 95% confidence interval for the population mean.
Practice: The average height of the US male is approximately 68 inches. What is the probability of selecting a group of males with average height of 72 inches or greater with a standard deviation of 5 inches?