Questions and Answers of Essentials of Statistics

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Group Project: It is of interest to determine which type of sports ball can be thrown the longest distance. The competition involves a tennis

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This project can be done in groups or by individuals. Each person or group must find a set of data, preferably from (but not restricted to) their

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Consider the data set for Exercise 7.58, page 341 (hospital data), repeated here.(a) The SAS PROC REG outputs provided in Figures 7.26 and 7.27 on

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Consider the fictitious set of data shown below, where the line through the data is the fitted simple linear regression line. Sketch a residual plot.

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The class should be divided into pairs of students for this project. Suppose it is conjectured that at least 25% of students at your university

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The class should be divided into groups of four people. The four students in each group should go to the college gym or a local fitness center. The

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Have groups of students observe the number of people who enter a specific coffee shop or fast-food restaurant over the course of an hour, beginning

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Divide the class into two groups of approximately equal size. The students in group 1 will each toss a coin 10 times (n1) and count the number of

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Let X = number of hours each student in the class slept the night before. Create a discrete variable by using the following arbitrary intervals: X

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Take 5 class periods to observe the shoe color of individuals in class. Assume the shoe color categories are red, white, black, brown, and other.

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Give each student a bag of chocolate M&Ms. Divide the students into groups of 5 or 6. Calculate the relative frequency distribution for color of

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By comparing appropriate regions of Venn diagrams, verify that (a) (A∩B)∪(A∩B')=A; (b) A'∩(B'∪C)=(A'∩B')∪(A'∩C).

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Find an article in the popular media (newspaper, magazine, Web site) that includes a graph in addition to the text.a. Briefly summarize the main

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Does the black grease beneath football players’ eyes really reduce glare or does it just make them look intimidating? In a variation of a study

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The following scores represent the final examination grades for an elementary statistics course:Test the goodness of fit between the observed class

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In Relief from Arthritis published by Thorsons Publishers, Ltd., John E. Croft claims that over 40% of those who suffer from osteoarthritis receive

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In a study conducted at Virginia Tech on the development of ectomycorrhizal, a symbiotic relationship between the roots of trees and a fungus, in

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A random variable X that assumes the values x1, x2, . . . , xk is called a discrete uniform random variable if its probability mass function is f(x)

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(a) In Exercise 3.7, how many of the 15 trucks would you expect to have blowouts?(b) What is the variance of the number of blowouts experienced by

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According to USA Today (March 18, 1997), of 4 million workers in the general workforce, 5.8% tested positive for drugs. Of those testing positive,

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What is the probability that a waitress will refuse to serve alcoholic beverages to only 2 minors if she randomly checks the IDs of 5 among 9

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On average, a textbook author makes two wordprocessing errors per page on the first draft of her textbook. What is the probability that on the next

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Find the mean and variance of the random variable X in Exercise 3.40, representing the number of hurricanes per year to hit a certain area of the

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A company purchases large lots of a certain kind of electronic device. A method is used that rejects a lot if 2 or more defective units are found in

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Given a continuous uniform distribution, show that(a) μ = A + B/2 and(b) σ2 = (B − A)2/12 .

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Suppose X follows a continuous uniform distribution from 1 to 5. Determine the conditional probability P(X > 2.5 | X ≤ 4).

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Given a standard normal distribution, find the area under the curve that lies(a) To the left of z = −1.39;(b) To the right of z = 1.96;(c) Between

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National security requires that defense technology be able to detect incoming projectiles or missiles. To make the defense system successful,

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For the data of Exercise 4.4, calculate the variance using the formula(a) Of form (4.2.1);(b) In Theorem 4.1.Exercise 4.4According to ecology writer

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Consider Case Study 4.2 on page 170. Suppose 18 specimens were used for each type of paint in an experiment andthe actual difference in mean drying

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The following data represent the length of life,in seconds, of 50 fruit flies subject to a new spray in a controlled laboratory experiment:Construct

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The following data represent the length of life in years, measured to the nearest tenth, of 30 similar fuel pumps:Construct a box-and-whisker plot.

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Consider Example 4.12 on page 189. Comment on any outliers.Example 4.12

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A taxi company tests a random sample of 10 steel-belted radial tires of a certain brand and records the following tread wear: 48,000, 53,000, 45,000,

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The concentration of an active ingredient in the output of a chemical reaction is strongly influenced by the catalyst that is used in the reaction.

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According to the Roanoke Times, in a particular year McDonald’s sold 42.1% of the market share of hamburgers. A random sample of 75 burgers sold

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For a random sample X1, . . . , Xn, show that

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A labor union is becoming defensive about gross absenteeism by its members. The union leaders had always claimed that, in a typical month, 95% of its

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The following measurements were recorded for the drying time, in hours, of a certain brand of latex paint:Assuming that the measurements represent a

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Referring to Exercise 5.5, construct a 99% prediction interval for the kilometers traveled annually by an automobile owner in Virginia.Exercise 5.5A

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A manufacturer turns out a product item that is labeled either “defective” or “not defective.” In order to estimate the proportion defective,

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A random sample of 25 tablets of buffered aspirin contains, on average, 325.05 mg of aspirin per tablet, with a standard deviation of 0.5 mg. Find

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A certain supplier manufactures a type of rubber mat that is sold to automotive companies. The material used to produce the mats must have certain

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Consider the situation of Case Study 5.1 with a larger sample of metal pieces. The diameters are as follows: 1.01, 0.97, 1.03, 1.04, 0.99, 0.98,

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A taxi company is trying to decide whether to purchase brand A or brand B tires for its fleet of taxis. To estimate the difference in the two brands,

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The federal government awarded grants to the agricultural departments of 9 universities to test the yield capabilities of two new varieties of wheat.

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Fortune magazine (March 1997) reported the total returns to investors for the 10 years prior to 1996 and also for 1996 for 431 companies. The total

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Compute 95% confidence intervals for the proportion of defective items in a process when it is found that a sample of size 100 yields 8 defectives.

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(a) A random sample of 200 voters in a town is selected, and 114 are found to support an annexation suit. Find the 96% confidence interval for the

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A manufacturer of MP3 players conducts a set of comprehensive tests on the electrical functions of its product. All MP3 players must pass all tests

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Construct a 95% confidence interval for σ2 in Exercise 5.9 on page 213.Exercise 5.9Regular consumption of presweetened cereals contributes to tooth

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State the null and alternative hypotheses to be used in testing the following claims and determine generally where the critical region is located:(a)

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Consider combinations of three factors in the removal of dirt from standard loads of laundry. The first factor is the brand of the detergent, X, Y ,

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A study was conducted at Virginia Tech to determine if certain static arm-strength measures have an influence on the €œdynamic

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Consider a 2nd-order response surface model that contains the linear, pure quadratic and cross product terms as follows:yi = Î²0 +

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The Statistics Consulting Center at Virginia Tech analyzed data on normal woodchucks for the Department of Veterinary Medicine. The variables of

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Physical fitness testing is an important aspect of athletic training. A common measure of the magnitude of cardiovascular fitness is the maximum

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With reference to Exercise 7.5 on page 304,(a) Evaluate s2;(b) Construct a 95% confidence interval for β0;(c) Construct a 95% confidence interval

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With reference to Exercise 7.6 on page 304,(a) Evaluate s2;(b) Construct a 99% confidence interval for β0;(c) Construct a 99% confidence interval

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With reference to Exercise 7.3 on page 304,(a) Evaluate s2;(b) Construct a 99% confidence interval for Î²0;(c) Construct a 99% confidence

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Test the hypothesis that β0 = 10 in Exercise 7.8 on page 305 against the alternative that β0 < 10. Use a 0.05 level of significance.Data From

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Test the hypothesis that β1 = 6 in Exercise 7.9 on page 305 against the alternative that β1 < 6. Use a 0.025 level of significance.Data From

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Suppose we have a linear equation through the origin (Exercise 7.28) Î¼Y|x= Î²x.(a) Estimate the regression line passing

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Use an analysis-of-variance approach to test the hypothesis that β1 = 0 against the alternative hypothesis β1 ≠ 0 in Exercise 7.5 on page 304 at

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Organophosphate (OP) compounds are used as pesticides. However, it is important to study their effect on species that are exposed to them. In the

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An experiment was conducted to determine if the weight of an animal can be predicted after a given period of time on the basis of the initial weight

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The following data represent the chemistry grades for a random sample of 12 freshmen at a certain college along with their scores on an intelligence

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The following data are given:(a) Fit the cubic model Î¼Y|x = Î²0 + Î²1x + Î²2x2 +

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The following data reflect information from 17 U.S. Navy hospitals at various sites around the world. The regressors are workload variables, that is,

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An experiment was conducted to study the size of squid eaten by sharks and tuna. The regressor variables are characteristics of the beaks of the

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A study was performed on a type of bearing to find the relationship of amount of wear y to x1= oil viscosity and x2= load. The following data were

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For the model of Exercise 7.49 on page 340, test the hypothesis that Î²1= 2 against the alternative that Î²1‰ 2. Use

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The study Loss of Nitrogen Through Sweat by Preadolescent Boys Consuming Three Levels of Dietary Protein was conducted by the Department of Human

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The printout in Figure 8.4 on page 373 gives information on Tukey€™s test, using PROC GLM in SAS, for the aggregate data in Example 8.1.

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Personnel in the Materials Engineering Department at Virginia Tech conducted an experiment to study the effects of environmental factors on the

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The purpose of the study The Incorporation of a Chelating Agent into a Flame Retardant Finish of a Cotton Flannelette and the Evaluation of Selected

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In a support system in the U.S. space program, a single crucial component works only 85% of the time. In order to enhance the reliability of the

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Consider Exercise 2.58 on page 79. Can it be said that the ratings given by the two experts are independent? Explain why or why not.Exercise 2.58Two

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Another type of system that is employed in engineering work is a group of parallel components or a parallel system. In this more conservative

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The total time, measured in units of 100 hours, that a teenager runs her hair dryer over a period of one year is a continuous random variable X that

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If a random variable X is defined such that E[(X − 1)2] = 10 and E[(X − 2)2] = 6, find μ and σ2.

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Repeat Exercise 2.83 on page 88 by applying Theorem 2.5 and Corollary 2.6.Exercise 2.83The length of time, in minutes, for an airplane to obtain

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Random variables X and Y follow a joint distributionDetermine the correlation coefficient between X and Y .

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For the random variables X and Y in Exercise 2.31 on page 72, determine the correlation coefficient between X and Y.Exercise 2.31From a sack of fruit

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For the random variables X and Y whose joint density function is given in Exercise 2.32 on page 72, find the covariancExercise 2.32A fast-food

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A large industrial firm purchases several new word processors at the end of each year, the exact number depending on the frequency of repairs in the

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Suppose that you are inspecting a lot of 1000 light bulbs, among which 20 are defectives. You choose two light bulbs randomly from the lot without

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The density function of the continuous random variable X, the total number of hours, in units of 100 hours, that a family runs a vacuum cleaner over

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The joint probability density function of the random variables X, Y , and Z isFind(a) the joint marginal density function of Y and Z;(b) the marginal

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Given the joint density functionfind P(1 < Y < 3 | X = 1).

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Let X denote the number of times a certain numerical control machine will malfunction: 1, 2, or 3 times on any given day. Let Y denote the number of

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Let X denote the diameter of an armored electric cable and Y denote the diameter of the ceramic mold that makes the cable. Both X and Y are scaled so

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Each rear tire on an experimental airplane is supposed to be filled to a pressure of 40 pounds per square inch (psi). Let X denote the actual air

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Let X denote the reaction time, in seconds, to a certain stimulus and Y denote the temperature (—¦F) at which a certain reaction starts

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A fast-food restaurant operates both a drive through facility and a walk-in facility. On a randomly selected day, let X and Y, respectively, be the

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From a sack of fruit containing 3 oranges, 2 apples, and 3 bananas, a random sample of 4 pieces of fruit is selected. If X is the number of oranges

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If the joint probability distribution of X and Y is given byfor x = 0, 1, 2, 3; y = 0, 1, 2,find(a) P(X ‰¤ 2, Y = 1);(b) P(X >2, Y

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Suppose it is known from large amounts of historical data that X, the number of cars that arrive at a specific intersection during a 20-second time

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Consider the density function(a) Evaluate k.(b) Find F(x) and use it to evaluate P(0.3 < X < 0.6).

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An investment firm offers its customers municipal bonds that mature after varying numbers of years. Given that the cumulative distribution function

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