Mathematical Statistics with Applications

7th Edition

ISBN: 9780495110811

Author: Dennis Wackerly, William Mendenhall, Richard L. Scheaffer

Publisher: Cengage Learning

See similar textbooks

Concept explainers

Continuous Probability Distributions

Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could co…

Normal Distribution

Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a…

Videos

Textbook Question

Chapter 11.5, Problem 29E

Let Y₁, Y₂, . . . , Y_n be as given in Exercise 11.28. Suppose that we have an additional set of independent random variables W₁, W₂, . . . , W_m, where W_i is normally distributed with E(W_i) = γ₀ + γ₁c_i and V(W_i) = σ², for i = 1, 2, . . . , m. Construct a test of H₀ : β₁ = γ₁ against the Ha : β₁ ≠ γ₁.⁶

11.28 Suppose that Y₁, Y₂, . . . , Y_n are independent, normally distributed random variables with E(Y_i) = β₀ + β₁ x_i and V(Y_i) = σ², for i = 1, 2, . . . , n. Show that the likelihood ratio test of H₀ : β₁ = 0 versus H_a : β₁ ≠ 0 is equivalent to the t test given in this section.

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.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 11.5, Problem 27E

Chapter 11.5, Problem 30E

Students have asked these similar questions

A certain automobile manufacturer equips a particular model with either a turbo or a standard engine. Let X1 and X2 be fuel efficiencies for independently and randomly selected turbo and standard cars, respectively. Assume the two random variables are normally distributed with the following parameters: H = 22 and o,2 =1.44 (mean and variance of X1] Hi = 26 and = 2.25 [mean and variance of X2] Define a random variable Y as the difference between the first engine minus three times the second engine, X, - 3X, Find V(Y), the variance of the linear combination Y

Consider the one-way analysis of variance model Xij = µ + a; + Eij, i= 1,.., m, j= 1,..., ni, where ɛij ~ N(0,0²) are independent. Let n= n1 + · ·+ nm, ... ni 1 ni 1 X;. >Xii for i = 1,..., m, and X. = - ΣΣΧ. ni j=1 i=1 j=1 (a) Show that SS(TO) = SS(T) + SS(E), where SS(TO) = E E i=12j=1 (Xij – X..)², m m ni SS(T) Σι (X.-Χ.) and SS(E) -ΣΣ (Χ- X.) . i=1 i=1 j=1

Let Y1, Y2, Y3, Y4, and Y, be i.i.d. random variables from a population with mean µ and variance o². Further, let Y = (Y, +Y½ +Y3 +Y4+Y;) denote the average of these five random variables. Now consider a different estimator of µ called W w = }Y + }Y½ + }Y, + }Y, + Y, What is the variance of W? That is, calculate Var|W] Hint: Use the properties of expectations, variances, etc. 187 800 800 187

Chapter 11 Solutions

Mathematical Statistics with Applications

Ch. 11.3 - If 0 and 1 are the least-squares estimates for the...Ch. 11.3 - Prob. 2E Ch. 11.3 - Fit a straight line to the five data points in the...Ch. 11.3 - Auditors are often required to compare the audited...Ch. 11.3 - Prob. 5E Ch. 11.3 - Applet Exercise Refer to Exercises 11.2 and 11.5....Ch. 11.3 - Prob. 7E Ch. 11.3 - Laboratory experiments designed to measure LC50...Ch. 11.3 - Prob. 9E Ch. 11.3 - Suppose that we have postulated the model...

Ch. 11.3 - Some data obtained by C.E. Marcellari on the...Ch. 11.3 - Processors usually preserve cucumbers by...Ch. 11.3 - J. H. Matis and T. E. Wehrly report the following...Ch. 11.4 - a Derive the following identity:...Ch. 11.4 - An experiment was conducted to observe the effect...Ch. 11.4 - Prob. 17E Ch. 11.4 - Prob. 18E Ch. 11.4 - A study was conducted to determine the effects of...Ch. 11.4 - Suppose that Y1, Y2,,Yn are independent normal...Ch. 11.4 - Under the assumptions of Exercise 11.20, find...Ch. 11.4 - Prob. 22E Ch. 11.5 - Use the properties of the least-squares estimators...Ch. 11.5 - Do the data in Exercise 11.19 present sufficient...Ch. 11.5 - Use the properties of the least-squares estimators...Ch. 11.5 - Let Y1, Y2, . . . , Yn be as given in Exercise...Ch. 11.5 - Prob. 30E Ch. 11.5 - Using a chemical procedure called differential...Ch. 11.5 - Prob. 32E Ch. 11.5 - Prob. 33E Ch. 11.5 - Prob. 34E Ch. 11.6 - For the simple linear regression model Y = 0 + 1x...Ch. 11.6 - Prob. 36E Ch. 11.6 - Using the model fit to the data of Exercise 11.8,...Ch. 11.6 - Refer to Exercise 11.3. Find a 90% confidence...Ch. 11.6 - Refer to Exercise 11.16. Find a 95% confidence...Ch. 11.6 - Refer to Exercise 11.14. Find a 90% confidence...Ch. 11.6 - Prob. 41E Ch. 11.7 - Suppose that the model Y=0+1+ is fit to the n data...Ch. 11.7 - Prob. 43E Ch. 11.7 - Prob. 44E Ch. 11.7 - Prob. 45E Ch. 11.7 - Refer to Exercise 11.16. Find a 95% prediction...Ch. 11.7 - Refer to Exercise 11.14. Find a 95% prediction...Ch. 11.8 - The accompanying table gives the peak power load...Ch. 11.8 - Prob. 49E Ch. 11.8 - Prob. 50E Ch. 11.8 - Prob. 51E Ch. 11.8 - Prob. 52E Ch. 11.8 - Prob. 54E Ch. 11.8 - Prob. 55E Ch. 11.8 - Prob. 57E Ch. 11.8 - Prob. 58E Ch. 11.8 - Prob. 59E Ch. 11.8 - Prob. 60E Ch. 11.9 - Refer to Example 11.10. Find a 90% prediction...Ch. 11.9 - Prob. 62E Ch. 11.9 - Prob. 63E Ch. 11.9 - Prob. 64E Ch. 11.9 - Prob. 65E Ch. 11.10 - Refer to Exercise 11.3. Fit the model suggested...Ch. 11.10 - Prob. 67E Ch. 11.10 - Fit the quadratic model Y=0+1x+2x2+ to the data...Ch. 11.10 - The manufacturer of Lexus automobiles has steadily...Ch. 11.10 - a Calculate SSE and S2 for Exercise 11.4. Use the...Ch. 11.12 - Consider the general linear model...Ch. 11.12 - Prob. 72E Ch. 11.12 - Prob. 73E Ch. 11.12 - An experiment was conducted to investigate the...Ch. 11.12 - Prob. 75E Ch. 11.12 - The results that follow were obtained from an...Ch. 11.13 - Prob. 77E Ch. 11.13 - Prob. 78E Ch. 11.13 - Prob. 79E Ch. 11.14 - Prob. 80E Ch. 11.14 - Prob. 81E Ch. 11.14 - Prob. 82E Ch. 11.14 - Prob. 83E Ch. 11.14 - Prob. 84E Ch. 11.14 - Prob. 85E Ch. 11.14 - Prob. 86E Ch. 11.14 - Prob. 87E Ch. 11.14 - Prob. 88E Ch. 11.14 - Refer to the three models given in Exercise 11.88....Ch. 11.14 - Prob. 90E Ch. 11.14 - Prob. 91E Ch. 11.14 - Prob. 92E Ch. 11.14 - Prob. 93E Ch. 11.14 - Prob. 94E Ch. 11 - At temperatures approaching absolute zero (273C),...Ch. 11 - A study was conducted to determine whether a...Ch. 11 - Prob. 97SE Ch. 11 - Prob. 98SE Ch. 11 - Prob. 99SE Ch. 11 - Prob. 100SE Ch. 11 - Prob. 102SE Ch. 11 - Prob. 103SE Ch. 11 - An experiment was conducted to determine the...Ch. 11 - Prob. 105SE Ch. 11 - Prob. 106SE Ch. 11 - Prob. 107SE

Knowledge Booster

$Statistics$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, statistics and related others by exploring similar questions and additional content below.

Solution Summary: The author enumerates the null and alternative hypotheses for testing H_0:beta

Concept explainers

Videos

Want to see the full answer?

Chapter 11 Solutions