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.]

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

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Chapter 7.2, Problem 24E

Chapter 7.2, Problem 26E

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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. 22E Ch. 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. 33E Ch. 7.2 - Suppose that W1 and W2 are independent...Ch. 7.2 - Prob. 35E Ch. 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. 39E Ch. 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. 47E Ch. 7.3 - Prob. 48E Ch. 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. 56E Ch. 7.3 - Twenty-five heat lamps are connected in a...Ch. 7.3 - Prob. 58E Ch. 7.3 - Prob. 59E Ch. 7.3 - Prob. 60E Ch. 7.3 - Refer to Exercise 7.60. Suppose that n1 = n2 = n,...Ch. 7.3 - Prob. 62E Ch. 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. 66E Ch. 7.5 - Prob. 67E Ch. 7.5 - Prob. 70E Ch. 7.5 - Prob. 71E Ch. 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. 80E Ch. 7.5 - Prob. 81E Ch. 7.5 - Prob. 82E Ch. 7.5 - Prob. 84E Ch. 7.5 - Prob. 85E Ch. 7.5 - Prob. 86E Ch. 7.5 - Prob. 87E Ch. 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. 90SE Ch. 7 - A retail dealer sells three brands of automobiles....Ch. 7 - From each of two normal populations with identical...Ch. 7 - Prob. 93SE Ch. 7 - Prob. 94SE Ch. 7 - The coefficient of variation (CV) for a sample of...Ch. 7 - Prob. 96SE Ch. 7 - Prob. 97SE Ch. 7 - Prob. 100SE Ch. 7 - Prob. 101SE Ch. 7 - Prob. 102SE Ch. 7 - Prob. 103SE Ch. 7 - Prob. 104SE Ch. 7 - If the probability that a person will suffer an...

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Solution Summary: The author explains how to compute the value of t_0.10 using the applet Student's t probabilities and quantiles.

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Chapter 7 Solutions