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 the probability P(t greater than or equal to -1.50) for a t-distribution with 30 degrees of freedom, you can follow these steps:
Step 1: Start by writing down the given information. In this case, we have the degrees of freedom (df) = 30 and the value of t (t = -1.50).
Step 2: Use a t-table or a statistical software to find the cumulative probability associated with the given t-value. Look for the row corresponding to 30 degrees of freedom and the column closest to -1.50. The cumulative probability in that cell represents P(t less than -1.50).
Step 3: Subtract the probability found in step 2 from 1 to find P(t greater than or equal to -1.50). This is because the t-distribution is symmetric, and P(t greater than or equal to -1.50) is equal to 1 - P(t less than -1.50).
Step 4: Round the resulting probability to at least three decimal places to obtain the final answer.
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 follow these steps:
Step 1: Start by writing down the given information. In this case, we have the degrees of freedom (df) = 6 and the desired probability (P(-c < t < c) = 0.95).
Step 2: Understand that P(-c < t < c) represents the area under the t-distribution curve between -c and c. Since the t-distribution is symmetric, finding this value is equivalent to finding the value of c that corresponds to (1 - 0.95)/2 = 0.025 in each tail of the distribution.
Step 3: Use a t-table or a statistical software to find the critical value for the desired tail probability. Look for the row corresponding to 6 degrees of freedom and the value closest to 0.025. The positive critical value represents c.
Step 4: Round the resulting critical value to at least three decimal places to obtain the final answer.
Remember that the t-distribution table is widely available, and statistical software can also be used to find these values more accurately.