Question

A) How does the t-score change as the deviation (M-μ) increases/decreases?

B) How does the t-score change as the sample variance increases/decreases?

C) How does the t-score change as the sample size increases/decreases?

Answer 1

The t score is calculated as:

Where M is the sample mean,

is the population mean

's' is the Sample standard deviation

and 'n' is the sample size

A) As we can see the t-score is directly proportional to (M-μ), hence t-score increases as (M-μ) increases and t-score decreases as (M-μ) decreases.

B) Sample variance is s² and as we can see that sample variance or the sample standard deviation is inversely proportional to the t-score so, as sample variance increases the t-score decreases and as the sample variance decreases the t-score also decreases.

C) From the formula, we can see that as the sample size increases the t-score also increases and as the sample size decreases the t-score also decreases.