Question

Use the Aleks calculator to solve the following problems.

Answer 1

(a) For a t-distribution with 12 degrees of freedom,
`\(P(t \leq -1.14) \approx 0.145\)`. (b) In a t-distribution with 28 degrees of freedom,
`\(c \approx 2.048\)` for
`\(P(-c < t < c) = 0.99\)`.

(a) Using a t-table or calculator, find
`\( P(t \leq -1.14) \)` for a t-distribution with 12 degrees of freedom. The value is approximately 0.145.

`\[ P(t \leq -1.14) \approx 0.145 \]`

(b) To find c such that
`\( P(-c < t < c) = 0.99 \)` for a t-distribution with 28 degrees of freedom, we need to find the critical value. Since the t-distribution is symmetric, we can find the c value by finding
`\( P(t < c) = 0.995 \)` (half of 0.99). Using a t-table or calculator, the critical value is approximately 2.048.

`\[ C \approx 2.048 \]`