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 90% confidence interval?

Answer 1

Answer: 2.1318

Step-by-step explanation:

The critical value of t for ($1-\alpha$)% confidence interval is the  vt-value in students' t- distribution table corresponding to significance level $\alpha/2$ and degree of freedom n-1 (n= sample size) .

A per given , we have

sample size : n= 5

Degree of freedom : df = n-1 = 4

Confidence level : $1-\alpha=0.90$

Significance level : $\alpha: 1-0.90=0.10$

Then , By students' t- distribution table:

Critical t- value for 90% confidence interval will be :

$t_{\alpha/2, df}=t_{0.05, 4} =2.1318$

Hence, the t-value we use for the 90% confidence interval = 2.1318