Consider a t distribution with 30 degrees of freedom. Compute P(t "greater than or equal to" -1.50). Round your answer to at least three decimal places.
Consider a t distribution with 6 degrees of freedom. Find the value of c such that P(-c <t<c)=0.95. Round your answer to at least three decimal places.
To compute P(t "greater than or equal to" -1.50) for a t distribution with 30 degrees of freedom, you can use a t-distribution table or a statistical calculator.
1. Using a table:
- Locate the row corresponding to the degrees of freedom (30) in the t-table.
- Find the column corresponding to the critical value closest to -1.50.
- Determine the probability value associated with that critical value.
- Since you are interested in the probability of t "greater than or equal to" -1.50, subtract the probability value from 1.
- Round your answer to at least three decimal places.
2. Using a statistical calculator:
- Input the degrees of freedom (30) and the lower value (-1.50) into the calculator.
- Calculate the cumulative probability or the respective tail probability.
- Round your answer to at least three decimal places.
For the second question, to find the value of c such that P(-c < t < c) = 0.95 for a t distribution with 6 degrees of freedom, you can again use a t-distribution table or a statistical calculator.
1. Using a table:
- Look for the probability value closest to 0.95 in the t-table.
- Find the corresponding critical value.
- The critical value you find represents both -c and c in this case.
- Round your answer to at least three decimal places.
2. Using a statistical calculator:
- Input the degrees of freedom (6) and the cumulative probability (0.95) into the calculator.
- Determine the critical values associated with these probabilities.
- The positive critical value gives you c in this case.
- Round your answer to at least three decimal places.