Mathematical Statistics with Applications
7th Edition
ISBN: 9781133384380
Author: Dennis Wackerly; William Mendenhall; Richard L. Scheaffer
Publisher: Cengage Learning US
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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
Ch. 7.2 - Refer to Example 7.2. The amount of fill dispensed...Ch. 7.2 - Refer to Exercise 7.9. Assume now that the amount...Ch. 7.2 - A forester studying the effects of fertilization...Ch. 7.2 - Suppose the forester in Exercise 7.11 would like...Ch. 7.2 - The Environmental Protection Agency is concerned...Ch. 7.2 - If in Exercise 7.13 we want the sample mean to...Ch. 7.2 - Suppose that X1, X2,Xm and Y1, Y2,Yn are...Ch. 7.2 - Referring to Exercise 7.13, suppose that the...Ch. 7.2 - Applet Exercise Refer to Example 7.4. Use the...Ch. 7.2 - Applet Exercise Refer to Example 7.5. If 2 = 1 and...
Ch. 7.2 - Ammeters produced by a manufacturer are marketed...Ch. 7.2 - a If U has a 2 distribution with v df, find E(U)...Ch. 7.2 - Refer to Exercise 7.13. Suppose that n = 20...Ch. 7.2 - Prob. 22ECh. 7.2 - Applet Exercise a Use the applet Chi-Square...Ch. 7.2 - Applet Exercise Refer to Example 7.6. Suppose that...Ch. 7.2 - Applet Exercise Suppose that T is a t-distributed...Ch. 7.2 - Refer to Exercise 7.11. Suppose that in the forest...Ch. 7.2 - Applet Exercise Refer to Example 7.7. If we take...Ch. 7.2 - Applet Exercise Suppose that Y has an F...Ch. 7.2 - If Y is a random variable that has an F...Ch. 7.2 - Suppose that Z has a standard normal distribution...Ch. 7.2 - a Use Table 7, Appendix 3, to find F.01 for...Ch. 7.2 - Applet Exercise a Find t.05 for a t-distributed...Ch. 7.2 - Prob. 33ECh. 7.2 - Suppose that W1 and W2 are independent...Ch. 7.2 - Prob. 35ECh. 7.2 - Let S12 denote the sample variance for a random...Ch. 7.2 - Let Y1, Y2,,Y5 be a random sample of size 5 from a...Ch. 7.2 - Suppose that Y1, Y2,,Y5, Y6, Y,W, and U are as...Ch. 7.2 - Prob. 39ECh. 7.3 - The fracture strength of tempered glass averages...Ch. 7.3 - An anthropologist wishes to estimate the average...Ch. 7.3 - Suppose that the anthropologist of Exercise 7.43...Ch. 7.3 - Workers employed in a large service industry have...Ch. 7.3 - The acidity of soils is measured by a quantity...Ch. 7.3 - Prob. 47ECh. 7.3 - Prob. 48ECh. 7.3 - The length of time required for the periodic...Ch. 7.3 - Shear strength measurements for spot welds have...Ch. 7.3 - Refer to Exercise 7.50. If the standard deviation...Ch. 7.3 - Resistors to be used in a circuit have average...Ch. 7.3 - One-hour carbon monoxide concentrations in air...Ch. 7.3 - Unaltered bitumens, as commonly found in leadzinc...Ch. 7.3 - The downtime per day for a computing facility has...Ch. 7.3 - Prob. 56ECh. 7.3 - Twenty-five heat lamps are connected in a...Ch. 7.3 - Prob. 58ECh. 7.3 - Prob. 59ECh. 7.3 - Prob. 60ECh. 7.3 - Refer to Exercise 7.60. Suppose that n1 = n2 = n,...Ch. 7.3 - Prob. 62ECh. 7.3 - Refer to Exercise 7.62. Find the number of...Ch. 7.5 - Applet Exercise Suppose that Y has a binomial...Ch. 7.5 - Prob. 66ECh. 7.5 - Prob. 67ECh. 7.5 - Prob. 70ECh. 7.5 - Prob. 71ECh. 7.5 - A machine is shut down for repairs if a random...Ch. 7.5 - An airline finds that 5% of the persons who make...Ch. 7.5 - According to a survey conducted by the American...Ch. 7.5 - A pollster believes that 20% of the voters in a...Ch. 7.5 - a Show that the variance of Y/n, where Y has a...Ch. 7.5 - The manager of a supermarket wants to obtain...Ch. 7.5 - If the supermarket manager (Exercise 7.77) samples...Ch. 7.5 - Suppose that a random sample of 25 items is...Ch. 7.5 - Prob. 80ECh. 7.5 - Prob. 81ECh. 7.5 - Prob. 82ECh. 7.5 - Prob. 84ECh. 7.5 - Prob. 85ECh. 7.5 - Prob. 86ECh. 7.5 - Prob. 87ECh. 7 - The efficiency (in lumens per watt) of light bulbs...Ch. 7 - Refer to Exercise 7.88. What should be the mean...Ch. 7 - Prob. 90SECh. 7 - A retail dealer sells three brands of automobiles....Ch. 7 - From each of two normal populations with identical...Ch. 7 - Prob. 93SECh. 7 - Prob. 94SECh. 7 - The coefficient of variation (CV) for a sample of...Ch. 7 - Prob. 96SECh. 7 - Prob. 97SECh. 7 - Prob. 100SECh. 7 - Prob. 101SECh. 7 - Prob. 102SECh. 7 - Prob. 103SECh. 7 - Prob. 104SECh. 7 - If the probability that a person will suffer an...
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