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:
[tex]CI=\bar x_{d}\pm t_{\alpha/2, (n-1)}\times \frac{s_{d}}{\sqrt{n}}[/tex]
Here,
[tex]\bar x_{d}[/tex] = sample mean of the difference,
[tex]s_{d}[/tex] = sample standard deviation of the difference,
n = sample size (both samples are of same size).
[tex]t_{\alpha/2, (n-1)}[/tex] = critical value of t
(n - 1) = degrees of freedom
The information provided is:
n = 5
Confidence level = 95%
The critical value of t is:
[tex]t_{\alpha/2, (n-1)}=t_{0.05/2, (5-1)}[/tex]
[tex]=t_{0.025, 4}[/tex]
[tex]=2.776[/tex]
*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.
