Mathematical Statistics with Applications
7th Edition
ISBN: 9780495110811
Author: Dennis Wackerly, William Mendenhall, Richard L. Scheaffer
Publisher: Cengage Learning
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Textbook Question
Chapter 7.2, Problem 25E
Applet Exercise Suppose that T is a t-distributed random variable.
- a If T has 5 df, use Table 5, Appendix 3, to find t.10, the value such that P(T > t.10) = .10. Find t.10 using the applet Student’s t
Probabilities and Quantiles. - b Refer to part (a). What quantile does t.10 correspond to? Which percentile?
- c Use the applet Student’s t Probabilities and Quantiles to find the value of t.10 for t distributions with 30, 60, and 120 df.
- d When Z has a standard
normal distribution , P(Z > 1.282) = .10 and z.10 = 1.282. What property of the t distribution (when compared to the standard normal distribution) explains the fact that all of the values obtained in part (c) are larger than z.10 = 1.282? - e What do you observe about the relative sizes of the values of t.10 for t distributions with 30, 60, and 120 df? Guess what t.10 “converges to” as the number of degrees of freedom gets large. [Hint: Look at the row labeled ∞ in Table 5, Appendix 3.]
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Chapter 7 Solutions
Mathematical Statistics with Applications
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