find P( t > 5) for DF =2.
To find P(t > 5) for a given degrees of freedom (DF), we need to consult a t-distribution table or use statistical software. The probability is calculated by finding the area under the t-distribution curve for the region to the right of 5.
Since you mentioned DF = 2 (degrees of freedom), it means that you are referring to a t-distribution with 2 degrees of freedom. In this case, the distribution has thicker tails compared to the normal distribution.
Without a t-distribution table or software, it would be challenging to calculate this probability directly. However, assuming you have access to a t-distribution table or software, here are the general steps to find P(t > 5):
1. Look up the critical value for a t-distribution with 2 degrees of freedom at the desired significance level, usually denoted by alpha (α). The desired significance level could be 0.05, 0.01, or any other value.
2. Find the corresponding value in the t-distribution table or use software to determine the critical value.
3. The critical value, denoted by t*, will represent the point on the t-distribution where the area to the right is equal to the desired significance level (α).
4. The probability P(t > 5) is then equal to 1 minus the cumulative probability up to t*. This can be calculated using the t-distribution table or software.
Keep in mind that the t-distribution is symmetric around 0, so if you're dealing with the probability of t being greater than a positive value, you can also find the probability of t being less than the negative of that value (e.g., P(t < -5)) and subtract it from 1.
Note: The specific values for P(t > 5) for DF = 2 are not provided in this response, as they would need to be obtained from a t-distribution table or software.