Question

A teacher wants to see if a new unit on factoring is helping students learn. She has five randomly selected students take a pre-test and a post test on the material. The scores are out of 20. Has there been improvement? (pre-post) What value of t would you use for the 95% confidence interval?

Answer 1

Answer:

The t-value used for the 95% confidence interval of paired data is 2.776.

Step-by-step explanation:

The confidence interval formula for mean difference for a paired data is as follows:

$CI=\bar x_{d}\pm t_{\alpha/2, (n-1)}\times \frac{s_{d}}{\sqrt{n}}$

Here,

$\bar x_{d}$ = sample mean of the difference,

$s_{d}$ = sample standard deviation of the difference,

n = sample size (both samples are of same size).

$t_{\alpha/2, (n-1)}$ = critical value of t

(n - 1) = degrees of freedom

The information provided is:

n = 5

Confidence level = 95%

The critical value of t is:

$t_{\alpha/2, (n-1)}=t_{0.05/2, (5-1)}$

               $=t_{0.025, 4}$

               $=2.776$

*Use a t-table for the critical value of t.

Thus, the t-value used for the 95% confidence interval of paired data is 2.776.