Question

a) Consider a t distribution with 10 degrees of freedom. Compute P(t≤−1.48). Round your answer to at least three decimal places. P(t≤−1.48)= (b) Consider a t distribution with 15 degrees of freedom. Find the value of c such that P(−c<:

Answer 1

(a)
`\(P(t \leq -1.48) = 0.083\)`

(b) For a t distribution with 15 degrees of freedom, (c) is approximately 1.753.

Step-by-step explanation:

(a) To compute
`\(P(t \leq -1.48)\)` for a t distribution with 10 degrees of freedom, we refer to a t-table or a statistical calculator. From the t-table, we find the cumulative probability associated with the t-value -1.48 and 10 degrees of freedom. The result is approximately 0.083, rounded to three decimal places.

(b) For the second part, we're looking for the value of (c) such that
`\(P(-c < t < c)\)` for a t distribution with 15 degrees of freedom. We need to find the t-value associated with the cumulative probability of 0.025 (half of the 5% significance level, as we're looking for the two-tailed critical value). Consulting the t-table or using a statistical calculator, we find (c) to be approximately 1.753.

In summary, the final answers are (a)
`\(P(t \leq -1.48) = 0.083\)` and (b) for a t distribution with 15 degrees of freedom, (c) is approximately 1.753. These values are obtained by referencing the t-table or using statistical software to find the cumulative probabilities associated with the given t-values and degrees of freedom.