what is the critical value t that satisfies the condition that the t distribution with 8 degrees of freedom has probability .10 to the right of t?
To find the critical value t that satisfies the condition that the t-distribution with 8 degrees of freedom has probability 0.10 to the right of t, we can follow these steps:
1. Identify the degrees of freedom: In this case, the degrees of freedom are given as 8.
2. Determine the desired probability: The condition states that the probability to the right of t is 0.10.
3. Find the critical value: To find the critical value, we need to look up the value from the t-distribution table or use a statistical calculator.
Using a statistical calculator or t-distribution table, we can calculate the critical value t. The critical value t for a t-distribution with 8 degrees of freedom and a probability of 0.10 to the right can be found to be approximately 1.3973.
So, the critical value t that satisfies the condition is approximately 1.3973.
To find the critical value t for a given probability, you can use a t-distribution table or statistical software.
Since you are looking for the t-value that corresponds to a probability of 0.10 to the right (or in the upper tail) of t, we need to find the t-value associated with the cumulative probability of 0.90 (1 - 0.10).
Using a t-distribution table, you can find the critical value by locating the row corresponding to the degrees of freedom (in this case, 8) and the column corresponding to the desired cumulative probability (0.90). The value at the intersection of this row and column will be the critical value.
If you have access to statistical software, it can calculate the critical value directly. For example, in R programming language, you can use the qt() function to find the critical value. In this case, you would use the command:
```
qt(0.90, df = 8, lower.tail = FALSE)
```
The output would give you the critical value t that satisfies the condition.
Keep in mind that the critical value can differ depending on the significance level or one-tailed vs. two-tailed testing. So, make sure you are using the appropriate method and probability for your specific context.