Question

The value of t-score in a hypothesis testing is influenced by a variety of factors. Assuming that all other variables are held constant, explain how the value of t is influenced by each of the following: (1.5)

2. Increasing the difference between sample mean and the original population mean.

3. Increasing the variability of scores.

c.   Increasing the number of people in the sample.

Answer 1

(a)

Increasing the difference between sample mean and the original population mean ;

The value of t will increase

because

$t=\frac{\bar{x}-\mu _{0}}{s/\sqrt{n}}$

So, increasing $\bar{x}-\mu _{0}$ will increase the value of t, since $\bar{x}-\mu _{0}$ occurs in the numrator.

(b)

Increasing the variability of scores

The value of t will decrease

because

$t=\frac{\bar{x}-\mu _{0}}{s/\sqrt{n}}$

So, increasing s will decrease the value of t, since s occurs in the numrator.

(c)

Increasing the number of people in the sample.

The value of t will increase

because

$t=\frac{\bar{x}-\mu _{0}}{s/\sqrt{n}}$

So, increasing n will increase the value of t, since n occurs in the numrator.