Question

Given a variable that has a t distribution with the specified degrees of freedom, what percentage of the time will its value fall in the indicated region? round your answer to one decimal place) (a) 10 df, between -2.23 and 2.23 ................ % (b) 10df, between -2.76 and 2.76 ................% (c) 24df, between -3.75 and 3.75 *.................. % (d) 24 df, between -3.47 and 3.47 *.................. % (e) 23df, outside the interval from -2.81 to 2.81 .............. % (f) 24df, to the left of -2.80 ..............% (g) 10df, to the right of 1.81 .................%

Answer 1

The percentage of the time that a variable with a t distribution falls in a specific region can be calculated using a t-table or a calculator. The percentages for the given regions with different degrees of freedom are: (a) 10 df, between -2.23 and 2.23 - 0.947%, (b) 10 df, between -2.76 and 2.76 - 0.955%, (c) 24 df, between -3.75 and 3.75 - 0.951%, (d) 24 df, between -3.47 and 3.47 - 0.947%, (e) 23 df, outside the interval from -2.81 to 2.81 - 0.044%, (f) 24 df, to the left of -2.80 - 0.048%, (g) 10 df, to the right of 1.81 - 0.035%.

Step-by-step explanation:

The percentage of the time that a variable with a t distribution falls in a specific region can be determined by calculating the area under the t distribution curve for that region. To calculate this percentage, we need to find the cumulative probability from the specific t value to the respective endpoints. We can use a t-table or a calculator to find the cumulative probabilities.

1. (a) For 10 degrees of freedom and between -2.23 and 2.23, the percentage is approximately 0.947.
2. (b) For 10 degrees of freedom and between -2.76 and 2.76, the percentage is approximately 0.955.
3. (c) For 24 degrees of freedom and between -3.75 and 3.75, the percentage is approximately 0.951.
4. (d) For 24 degrees of freedom and between -3.47 and 3.47, the percentage is approximately 0.947.
5. (e) For 23 degrees of freedom and outside the interval from -2.81 to 2.81, the percentage can be calculated by subtracting the cumulative probability from -2.81 to the respective endpoints from 1. The percentage is approximately 0.044.
6. (f) For 24 degrees of freedom and to the left of -2.80, the percentage can be calculated by finding the cumulative probability from the left tail to -2.80. The percentage is approximately 0.048.
7. (g) For 10 degrees of freedom and to the right of 1.81, the percentage can be calculated by finding the cumulative probability from 1.81 to the right tail. The percentage is approximately 0.035.