To solve these problems, we need to use the Student's t-distribution table or software to find the probabilities based on the given degrees of freedom.

Problem 1

1. We have a t-score of 1.844 with 20 degrees of freedom.
   • We are looking for $P(T > 1.844)$.
   • This is the probability of obtaining a t-score greater than 1.844 for a t-distribution with 20 degrees of freedom.

Solution for Problem 1

Using a t-distribution calculator or table:

• For $t = 1.844$ with 20 degrees of freedom, the right-tail probability $P(T > 1.844) \approx 0.04$ (rounded to two decimal places).

Problem 2

2. We have a t-score of -2.205 with 19 degrees of freedom.
   • We are looking for $P(T < -2.205)$.
   • This is the probability of obtaining a t-score less than -2.205 for a t-distribution with 19 degrees of freedom.

Solution for Problem 2

Using a t-distribution calculator or table:

• For $t = -2.205$ with 19 degrees of freedom, the left-tail probability $P(T < -2.205) \approx 0.02$ (rounded to two decimal places).

Final Answers

1. $P(T > 1.844) = 0.04$
2. $P(T < -2.205) = 0.02$

Would you like further details on these calculations?

Related Questions

1. What is the t-distribution, and how does it differ from the normal distribution?
2. How does the probability change if we increase or decrease the degrees of freedom?
3. What is the significance of the right-tail and left-tail probabilities in the t-distribution?
4. How can you calculate these probabilities using statistical software like Excel or R?
5. How would the answers change if we were looking for two-tailed probabilities?

Tip

When working with t-scores, degrees of freedom have a strong impact on the shape of the distribution, with higher degrees of freedom making it closer to the normal distribution.