Question

Find the appropriate percentile from a​ t-distribution for constructing the following confidence interval.

Answer 1

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 ($\alpha/2$) .

The given confidence interval = 99%

⇒ Significance level = $\alpha=100\%-99\%=1\%=0.01$

Sample size : n=3

DEgree of freedom : df = n-1 = 2

Then, the  critical t- value for 99% confidence interval will be;

$t_{\alpha/2, df}=t_{0.01/2,\ 2}$

$t_{0.005 , 2}=\pm9.9248$   [From t-distribution table]

Hence, the appropriate percentile from a​ t-distribution for constructing the 99​% confidence interval with n = 3 is 9.9248.