Group Project: It is of interest to determine which type of sports ball can be thrown the longest distance. The competition involves a tennis
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
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
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.
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
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
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
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
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
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.
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
By comparing appropriate regions of Venn diagrams, verify that (a) (A∩B)∪(A∩B')=A; (b) A'∩(B'∪C)=(A'∩B')∪(A'∩C).
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
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
The following scores represent the final examination grades for an elementary statistics course:Test the goodness of fit between the observed class
In Relief from Arthritis published by Thorsons Publishers, Ltd., John E. Croft claims that over 40% of those who suffer from osteoarthritis receive
In a study conducted at Virginia Tech on the development of ectomycorrhizal, a symbiotic relationship between the roots of trees and a fungus, in
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)
(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
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,
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
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
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
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
Given a continuous uniform distribution, show that(a) μ = A + B/2 and(b) σ2 = (B − A)2/12 .
Suppose X follows a continuous uniform distribution from 1 to 5. Determine the conditional probability P(X > 2.5 | X ≤ 4).
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
National security requires that defense technology be able to detect incoming projectiles or missiles. To make the defense system successful,
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
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
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
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.
Consider Example 4.12 on page 189. Comment on any outliers.Example 4.12
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,
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.
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
For a random sample X1, . . . , Xn, show that
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
The following measurements were recorded for the drying time, in hours, of a certain brand of latex paint:Assuming that the measurements represent a
Referring to Exercise 5.5, construct a 99% prediction interval for the kilometers traveled annually by an automobile owner in Virginia.Exercise 5.5A
A manufacturer turns out a product item that is labeled either “defective” or “not defective.” In order to estimate the proportion defective,
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
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
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,
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,
The federal government awarded grants to the agricultural departments of 9 universities to test the yield capabilities of two new varieties of wheat.
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
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.
(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
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
Construct a 95% confidence interval for σ2 in Exercise 5.9 on page 213.Exercise 5.9Regular consumption of presweetened cereals contributes to tooth
State the null and alternative hypotheses to be used in testing the following claims and determine generally where the critical region is located:(a)
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 ,
A study was conducted at Virginia Tech to determine if certain static arm-strength measures have an influence on the dynamic
Consider a 2nd-order response surface model that contains the linear, pure quadratic and cross product terms as follows:yi = Î²0 +
The Statistics Consulting Center at Virginia Tech analyzed data on normal woodchucks for the Department of Veterinary Medicine. The variables of
Physical fitness testing is an important aspect of athletic training. A common measure of the magnitude of cardiovascular fitness is the maximum
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
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
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
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
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
Suppose we have a linear equation through the origin (Exercise 7.28) Î¼Y|x= Î²x.(a) Estimate the regression line passing
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
Organophosphate (OP) compounds are used as pesticides. However, it is important to study their effect on species that are exposed to them. In the
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
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
The following data are given:(a) Fit the cubic model Î¼Y|x = Î²0 + Î²1x + Î²2x2 +
The following data reflect information from 17 U.S. Navy hospitals at various sites around the world. The regressors are workload variables, that is,
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
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
For the model of Exercise 7.49 on page 340, test the hypothesis that Î²1= 2 against the alternative that Î²1 2. Use
The study Loss of Nitrogen Through Sweat by Preadolescent Boys Consuming Three Levels of Dietary Protein was conducted by the Department of Human
The printout in Figure 8.4 on page 373 gives information on Tukeys test, using PROC GLM in SAS, for the aggregate data in Example 8.1.
Personnel in the Materials Engineering Department at Virginia Tech conducted an experiment to study the effects of environmental factors on the
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
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
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
Another type of system that is employed in engineering work is a group of parallel components or a parallel system. In this more conservative
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
If a random variable X is defined such that E[(X − 1)2] = 10 and E[(X − 2)2] = 6, find μ and σ2.
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
Random variables X and Y follow a joint distributionDetermine the correlation coefficient between X and Y .
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
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
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
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
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
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
Given the joint density functionfind P(1 < Y < 3 | X = 1).
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
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
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
Let X denote the reaction time, in seconds, to a certain stimulus and Y denote the temperature (¦F) at which a certain reaction starts
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
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
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
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
Consider the density function(a) Evaluate k.(b) Find F(x) and use it to evaluate P(0.3 < X < 0.6).
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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