The critical value for a 99% confidence interval is 2.779.
How to determine critical value of a random sample.
For a 99% confidence interval
Degrees of freedom = n - 1 = 27 - 1 = 26
For 26 df and 99% confidence interval,
Critical value = 2.779
Since it's a two-tailed test (upper and lower confidence bounds), allocate 0.5% to each tail. The remaining 99% is in the middle.
The critical value for a 99% confidence interval is often denoted as Zα/2, where α is the significance level, and α/2 is the tail probability.
Z α = Z(0.005)
using a standard normal distribution table.
The critical value Z for a cumulative probability of 0.005 is approximately 2.779.
Therefore, the critical value for a 99% confidence interval is 2.779.