Chapter 7.2, Problem 32E

Applet Exercise

1. a Find t_.05 for a t-distributed random variable with 5 df.
2. b Refer to part (a). What is $P(T^2>t_{.05}^2)$?
3. c Find F_.10 for an F-distributed random variable with 1 numerator degree of freedom and 5 denominator degrees of freedom.
4. d Compare the value of F_.10 found in part (c) with the value of $t_{.05}^2$ from parts (a) and (b).
5. e In Exercise 7.33, you will show that if T has a t distribution with ν df, then U = T² has an F distribution with 1 numerator degree of freedom and ν denominator degrees of freedom. How does this explain the relationship between the values of F_.10 (1 num. df, 5 denom df) and $t_{.05}^2$ (5 df) that you observed in part (d)?

7.33    Use the structures of T and F given in Definitions 7.2 and 7.3, respectively, to argue that if T has a t distribution with ν df, then U = T² has an F distribution with 1 numerator degree of freedom and ν denominator degrees of freedom.