- Group Project: It is of interest to determine which type of sports ball can be thrown the longest distance. The competition involves a tennis ball, a baseball, and a softball. Divide the class
- 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 field of study. The data need to fit the regression
- 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 pages 353 and 354 supply a considerable amount of
- 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. У х
- 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 exercise for more than two hours a week. Collect data
- 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 students should ask each person who comes through
- 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 at the same time every day, for two weeks. The hour
- 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 heads obtained. The students in group 2 will each
- 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 <3, 3 ≤X <6, 6 ≤X <9, and X ≥ 9.(a)
- 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. Complete a frequency table for each color
- 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 M&Ms for each group. (a) What is your
- 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 point of the article and graph.b. What are the
- 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 actually conducted at Yale University, 46 participants
- The following scores represent the final examination grades for an elementary statistics course:Test the goodness of fit between the observed class frequencies and the corresponding expected
- In Relief from Arthritis published by Thorsons Publishers, Ltd., John E. Croft claims that over 40% of those who suffer from osteoarthritis receive measurable relief from an ingredient produced by a
- In a study conducted at Virginia Tech on the development of ectomycorrhizal, a symbiotic relationship between the roots of trees and a fungus, in which minerals are transferred from the fungus to the
- 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) = 1/k for all of x1, x2, . . . , xk and 0
- (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 the 15 trucks? What does that mean?Exercise 3.7In
- 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, 22.5% were cocaine users and 54.4% marijuana
- 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 students, 4 of whom are minors?
- 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 page she will make(a) 4 or more errors?(b) No
- 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 eastern United States.Exercise 3.40A certain area of
- 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 a random sample of 100 units.(a) What is the mean
- 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 z = −2.16 and z = −0.65;(d) To the left of z =
- National security requires that defense technology be able to detect incoming projectiles or missiles. To make the defense system successful, multiple radar screens are required. Suppose that three
- 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 Jacqueline Killeen, phosphates contained in
- 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 time, turned out to be 1.0.(a) Does this seem to be
- 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 a box-and-whisker plot and comment on the nature
- 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. Comment on the outliers in the data. 2.0 3.0 0.3
- Consider Example 4.12 on page 189. Comment on any outliers.Example 4.12 Table 4.6: Nicotine Data for Example 4.12 1.74 1.97 2.31 1.92 1.47 2.55 1.69 1.09 1.79 2.28 1.70 1.64 1.24 2.03 0.85 1.86 1.58
- 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, 61,000, 59,000, 56,000, 63,000, 49,000, 53,000,
- 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. It is believed that when catalyst A is used, the
- 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 resulted in 28 of them being from McDonald’s. Use
- For a random sample X1, . . . , Xn, show that E(X: - 4)? = (X: – X)² + n(X – µ)². i=1 i=1
- 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 members were absent less than 10 hours. The union
- The following measurements were recorded for the drying time, in hours, of a certain brand of latex paint:Assuming that the measurements represent a random sample from a normal population, find a 95%
- Referring to Exercise 5.5, construct a 99% prediction interval for the kilometers traveled annually by an automobile owner in Virginia.Exercise 5.5A random sample of 100 automobile owners in the
- 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 100 items is taken from
- 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 the 95% tolerance limits that will contain 90% of
- 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 hardness characteristics. Defective mats are
- 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, 1.01, 1.03, 0.99, 1.00, 1.00, 0.99, 0.98, 1.01, 1.02,
- 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, an experiment is conducted using 12 of each
- The federal government awarded grants to the agricultural departments of 9 universities to test the yield capabilities of two new varieties of wheat. Each variety was planted on a plot of equal area
- 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 returns for 9 of the companies and the S&P 500
- 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 proportion of the voting population favoring 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 prior to being sold. Of a random sample of 500 MP3
- Construct a 95% confidence interval for σ2 in Exercise 5.9 on page 213.Exercise 5.9Regular consumption of presweetened cereals contributes to tooth decay, heart disease, and other degenerative
- State the null and alternative hypotheses to be used in testing the following claims and determine generally where the critical region is located:(a) The mean snowfall at Lake George during the month
- 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 , or Z. The second factor is the type of detergent,
- A study was conducted at Virginia Tech to determine if certain static arm-strength measures have an influence on the €œdynamic lift€ characteristics of an individual. Twenty-five
- Consider a 2nd-order response surface model that contains the linear, pure quadratic and cross product terms as follows:yi = Î²0 + Î²1x1i + Î²2x2i + Î²11x2
- The Statistics Consulting Center at Virginia Tech analyzed data on normal woodchucks for the Department of Veterinary Medicine. The variables of interest were body weight in grams and heart weight in
- Physical fitness testing is an important aspect of athletic training. A common measure of the magnitude of cardiovascular fitness is the maximum volume of oxygen uptake during strenuous exercise. A
- 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 for β1.Data From Exercise 7.5Temperature, x
- 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 for β1.Data From Exercise 7.6Normal Stress, x
- 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 interval for Î²1.Data From Exercise 7.3
- 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 Exercise 7.8 Placement Test
- 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 Exercise 7.9 Advertising Costs ($)
- Suppose we have a linear equation through the origin (Exercise 7.28) Î¼Y|x= Î²x.(a) Estimate the regression line passing through the origin for the following data:(b) Suppose
- 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 the 0.05 level of significance.Data From Exercise
- Organophosphate (OP) compounds are used as pesticides. However, it is important to study their effect on species that are exposed to them. In the laboratory study Some Effects of Organophosphate
- 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 of the animal and the amount of feed that was
- 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 test administered while they were still seniors in
- The following data are given:(a) Fit the cubic model Î¼Y|x = Î²0 + Î²1x + Î²2x2 + Î²3x3.(b) Predict Y when x = 2. 3 4 5 6 5 3 2 3 2.
- The following data reflect information from 17 U.S. Navy hospitals at various sites around the world. The regressors are workload variables, that is, items that result in the need for personnel in a
- 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 squid. The data are given as follows:In the study, 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 obtained.(Data from Myers, Montgomery, and
- For the model of Exercise 7.49 on page 340, test the hypothesis that Î²1= 2 against the alternative that Î²1‰ 2. Use a P-value in your conclusion. x2 1.32 6.40 15.05
- The study Loss of Nitrogen Through Sweat by Preadolescent Boys Consuming Three Levels of Dietary Protein was conducted by the Department of Human Nutrition and Foods at Virginia Tech to determine
- 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. Give conclusions regarding paired comparisons using
- Personnel in the Materials Engineering Department at Virginia Tech conducted an experiment to study the effects of environmental factors on the stability of a certain type of copper-nickel alloy. 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 Fabric Properties, conducted at Virginia Tech, was
- 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 system, it is decided that 3 components will be
- 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 tire-quality experts examine stacks of tires and
- Another type of system that is employed in engineering work is a group of parallel components or a parallel system. In this more conservative approach, the probability that the system operates is
- 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 has the density functionUse Theorem 2.6 to
- 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 clearance for takeoff at a certain airport is a random
- Random variables X and Y follow a joint distributionDetermine the correlation coefficient between X and Y. S2, 0
- 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 containing 3 oranges, 2 apples, and 3 bananas, a
- 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 restaurant operates both a drive through facility and a
- 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 previous year. Suppose that the number of word
- 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 replacement.LetFind the probability that at least
- 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 a period of one year, is given in Exercise
- 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 density of Y;(c) (d) 4ryz? 4ryz, 0< x, y <
- Given the joint density functionfind P(1 < Y < 3 | X = 1). 6-1-y f(x, y) = (0, 0
- 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 times a technician is called on an emergency call.
- 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 that they range between 0 and 1. Suppose that X
- 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 pressure for the right tire and Y denote the actual
- Let X denote the reaction time, in seconds, to a certain stimulus and Y denote the temperature (—¦F) at which a certain reaction starts to take place. Suppose that two random variables X
- 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 proportions of the time that the drive-through and
- 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 and Y is the number of apples in the sample,
- 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 ‰¤ 1);(c) P(X >Y);(d) P(X + Y = 4).(e)
- 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 period, is characterized by the following discrete
- Consider the density function(a) Evaluate k.(b) Find F(x) and use it to evaluate P(0.3 < X < 0.6). (kVT, 0
- An investment firm offers its customers municipal bonds that mature after varying numbers of years. Given that the cumulative distribution function of T, the number of years to maturity for a