Question

Find the critical value \( t_{c} \) for the confidence level \( c=0.98 \) and sample size \( n=25 \). Click the icon to view the t-distribution table.

Answer 1

To find the critical value for a 98% confidence level with 24 degrees of freedom, check a t-distribution table or use a calculator with the invT function. This corresponds to a one-tailed critical value at a total area of 0.99 in the t-distribution.

Step-by-step explanation:

To find the critical value tc for the confidence level c=0.98 with a sample size of n=25, we first need to determine the degrees of freedom, which is n - 1. In this case, degrees of freedom would be 25 - 1 = 24. We then look at a t-distribution table or use a calculator function, such as invT, to find the critical t value that corresponds to the desired confidence level with degrees of freedom at 24.

For a 98% confidence level, our tc value will represent the critical value that has 1% of the distribution's tail beyond it on each side in a two-tailed test (since 0.98 + (0.01*2) = 1). This equates to looking for a total area of 0.99 when using one-tailed values in your t-distribution table or computational tool. The exact critical t value can vary slightly depending on the source of your t-distribution table.