Answer: 9.9248
Step-by-step explanation:
We know that the critical t- value for confidence interval is a two-tailed value from the t-distribution table corresponding to degree of freedom (df = n-1 , where n is the sample size) and the significance level ([tex]\alpha/2[/tex]) .
The given confidence interval = 99%
⇒ Significance level = [tex]\alpha=100\%-99\%=1\%=0.01[/tex]
Sample size : n=3
DEgree of freedom : df = n-1 = 2
Then, the critical t- value for 99% confidence interval will be;
[tex]t_{\alpha/2, df}=t_{0.01/2,\ 2}[/tex]
[tex]t_{0.005 , 2}=\pm9.9248[/tex] [From t-distribution table]
Hence, the appropriate percentile from a t-distribution for constructing the 99% confidence interval with n = 3 is 9.9248.
