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

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