Questions: Find (t0.99) for (T) distribution with 27 degrees of freedom. (t0.99=1.314) (Round the answer to 3 decimal places)

Transcript text: Find $t_{0.99}$ for $T$ distribution with 27 degrees of freedom. \[ t_{0.99}=1.314 \quad \text { (Round the answer to } 3 \text { decimal places) } \] Question Help: Message instructor

Solution

Solution Steps

To find the critical value $ t_{0.99} $ for a $ T $ distribution with 27 degrees of freedom, we need to use the inverse cumulative distribution function (CDF) for the $ T $ distribution. This value corresponds to the 99th percentile of the distribution.

Step 1: Determine the Degrees of Freedom

We are given that the degrees of freedom $ df = 27 $.

Step 2: Calculate the Critical Value

To find $ t_{0.99} $, we need to determine the value of $ t $ such that the area to the left of $ t $ under the $ T $ distribution with 27 degrees of freedom is 0.99. This is calculated as follows: \[ t_{0.99} \approx 2.4727 \]

Step 3: Round the Result

Rounding $ t_{0.99} $ to three decimal places gives: \[ t_{0.99} \approx 2.473 \]