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statistics principles and methods

Questions and Answers of Statistics Principles And Methods

Construct a transformation curve that transforms uniform variates on a scale from 0 to 1 to Poisson values for λ = 2 per year and t = 1 year. Generate 30 variates using the transformation curve to
Construct a transformation curve that transforms uniform variates on a scale from 0 to 1 to geometric values for p = 0.1. Generate 30 variates using the transformation curve to obtain 30 geometric
Construct a transformation curve that transforms uniform variates on a scale from 0 to 1 to binomial values for N = 10 and p = 0.1. Generate 30 variates using the transformation curve to obtain 30
Construct a transformation curve that transforms uniform variates on a scale from 0 to 1 to uniform variates on a scale from 10 to 20 of integer values. Generate 30 variates using the transformation
The arrival of school buses at a maintenance station can be modeled as a Poisson process with a rate of 5 arrivals per day.(a) What is the probability that exactly 3 buses arrive in a 1-day
The arrival of aircraft to an airport can be modeled as a Poisson process with a rate of 10 arrivals per hour.(a) What is the probability that exactly 5 aircrafts arrive in a 1-h period?(b) What is
It was determined from historical records of inspecting inflatable liferafts onboard vessels that 5 in 100 are defective and will not properly inflate. (a) For a randomly selected vessel that has
It was reported in 1993 that 1 in 200 carry the defective gene that causes inherited colon cancer. For a random sample of 1000 individuals, what is the distribution of the number of individuals who
During World War II, an economical procedure for testing syphilitic (i.e., diseased) men among military inductees was initiated to test the blood of groups of n men by combining the blood samples of
A k-out-of-n system is defined as a system that functions if and only if at least k out of the n individual components in the system function. If individual components function independently of one
A k-out-of-n system is defined as a system that functions if and only if at least k out of the n individual components in the system function. If individual components function independently of one
A defense contractor developed a new welding process of high-strength metal for use in constructing submarines. The new process was used and the resulting welds were tested using a specialized
An automobile manufacturer is considering the recall of 100,000 cars to correct a safety device in them. The number of automobiles with defective safety devices is estimated to be about 10% of the
A shipment contains 60 individually sealed boxes that contain electronic devices. It was determined from historical records that shipping damages were on the average 10% of the devices in a
A box contains 100 fasteners with five defective fasteners among them. A connection requires the use of six fasteners. Having two or more fasteners will have an adverse impact on the safe use of the
A lot of products contains 100 units with 10 defective units among these 100 units. Compute the probability of sampling at least 1 defective unit in a sample of size 10 units. Is a sample size of 10
A bidding strategy assumes that five successes are necessary in ten bids. Use the negative binomial distribution to compute the probability of having a 5th success on the 10th trial for a success
Use the negative binomial distribution to compute the probability of having a 10th success on the 10th trial for a success probability in a trial (p) of 0.1.
Use the negative binomial distribution to compute the probability of having a 3rd success on the 10th trial for a success probability in a trial (p) of 0.1.
A seam weld is inspected using a nondestructive evaluation method and was determined to have defects following a Poisson process with a rate λ = 0.05 per ft. A pressure vessel contains 20 ft of this
Extreme wave loads follow a Poisson distribution with an occurrence rate λ = 0.01 per year. What is the probability of occurrence of two extreme loads in a year? What is the probability of no
The failure rate of an electronic device is λ = 0.001 per year of continuous operation. What is the probability of occurrence of two failures in a year? What is the probability of no failures in 5
Derive Equations 4.15 and 4.16 using Equations 3.70 and 3.74.
An insurance company reviews insurance claims received for payment, and rejects 40% of the claims. The insurance claims follow a Poisson process with a rate λ = 200 claims per year. What is the
Insurance claims follow a Poisson process with a rate λ = 100 claims per year. (a) What is the mean and standard deviation of the number of claims per year? (b) What is the probability of receiving
The overload occurrence of an offshore facility due to extreme waves can be modeled by a Poisson process with a rate λ = 0.5. What is the probability of occurrence of two overloads in a year? What
Over the past 15 years, the numbers of hurricanes per year to cause damage in a particular city were 4, 2, 1, 3, 0, 2, 1, 3, 5, 2, 3, 1, 1, 2, and 0. What is the probability of not having hurricane
A home construction company has determined at a home subdivision that the probability of finding unusual soil conditions is 0.15 per house site requiring blasting to excavate for a house’s
A 10-year record of tornadoes per year to land in a particular region is 2, 2, 1, 3, 2, 1, 0, 2, 3, and 1.What is the probability of not having tornados in any 1 year? What are the average and
An oil exploration company has determined at a site that the oil discovery probability is 0.65 per well. Assume that the oil exploration attempts, that is, the wells, are independent,(a) What is the
A missile defense system is intended to kill any incoming missiles directed at a country. The missile defense system has a successful-kill probability of 0.85 per attempt by the system. Assume that
A furniture manufacturer performs final inspections on furniture pieces produced. The pieces are classified as follows with associated probabilities: flawless (0.90 probability), with cosmetic
A manufacturer of processors for communication devices has established that the defect probability of its manufacturing process is 0.05.(a) What is the probability of having at the most two defective
The probability that a flood of a specified magnitude occurs in any 1 year is 0.1. What is the probability that in the next 10 years (a) exactly two such floods will occur, (b) no more than one such
A medication could lead to side effects requiring the use of a secondary drug to counter the effects.The probability of a user experiencing side effects is 0.01. What is the probability of (a) no
A fair coin is tossed ten times. What is the probability of getting (a) exactly six heads, (b) exactly three tails, (c) no heads, (d) three or fewer heads, (e) six or more tails, and (f) at least
An assembly plant of electronic devices uses a chip type that has a defect probability of 0.02. The chip’s defect can be identified only at the quality testing stage of the completed device. What
Piles are used to support the foundation of a structure. The failure probability of a pile during proof testing is 0.1. Determine the following:(a) The probability of three failed piles out of ten
The probability of a flood in any 1 year is 0.05. In a 10-year period, what is the probability of (a) no floods, (b) two or fewer floods, (c) from one to three floods?
he week that the advertisement appears in the paper, the section of the paper in which the advertisement appears, or daily fluctuations in the interest rate. What role does randomization play in your
=+the week that the advertisement appears in the paper, the section of the paper in which the advertisement appears, or daily fluctuations in the interest rate. What role does randomization play in
=+lender would like to determine which advertisement format is most successful in attracting customers to call for more information. Describe an experiment that would provide the information needed
=+2.70 A mortgage lender routinely places advertisements in a local newspaper. The advertisements are of three different types: one focusing on low interest rates, one featuring low fees for
=+slightly at different locations in the kiln, and firing temperature may also affect cracking. Discuss the design of an experiment to collect information that could be used to decide between the
=+2.69 A manufacturer of clay roofing tiles would like to investigate the effect of clay type on the proportion of tiles that crack in the kiln during firing. Two different types of clay are to be
=+to plant the four types of grasses. What role would randomization play in this determination? Identify any confounding variables. Would this study be considered an observational study or an
=+be used include undisturbed native grasses, managed native grasses, undisturbed nonnative grasses, and managed nonnative grasses. You are allowed a plot of land 500 m square to study. Explain how
=+2.68 You have been asked to determine on what types of grasslands two species of birds, northern harriers and short-eared owls, build nests. The types of grasslands to
=+record the amount of the bill and of the tip and whether he stood or squatted.a. Describe the treatments and the response variable.b. Discuss possible extraneous factors and how they could be
=+of Server Posture on Restaurant Tipping,” Journal of Applied Social Psychology [1993]: 678–685). In the experiment, the waiter would flip a coin to determine whether he would stand or squat
=+2.67 Researchers at the University of Houston decided to test the hypothesis that restaurant servers who squat to the level of their customers would receive a larger tip (“Effect
=+b. List two socioeconomic factors that would be appropriate to use for stratification. Explain how each factor would relate to the consumption of alcohol in general and of wine in particular.
=+a. Why might stratification by province be a good thing?
=+2.66 The article “Heavy Drinking and Problems among Wine Drinkers” (Journal of Studies on Alcohol [1999]:467–471) investigates whether wine drinkers tend to drink less excessively than those
=+c. This experiment was not conducted in a double-blind manner. Do you think it would have been a good idea to make this a double-blind experiment? Explain.
=+b. Do you think it was important that the men participating in the experiment were not told whether they were receiving creatine or the placebo? Explain.
=+a. What extraneous variables are identified in the given statement, and what strategy did the researchers use to deal with them?
=+“looked at 19 men, all about 25 years of age and similar in weight, lean body mass, and capacity to lift weights. Ten were given creatine—25 grams a day for the first week, followed by 5 grams
=+2.65 An article in the San Luis Obispo Tribune (September 7, 1999) described an experiment designed to investigate the effect of creatine supplements on the development of muscle fibers. The
=+not. Assuming that the assignment of subjects to the treatment (vodka) and control groups was made at random, do you think there are any confounding factors that would make conclusions based on
=+tonics (tonic water alone), but all subjects were told they were drinking vodka tonics. The researchers then measured the level of nicotine cravings (by monitoring heart rate, skin conductance,
=+2.64 Does alcohol consumption cause increased cravings for cigarettes? Research at Purdue University suggests this is so (see CNN.com web site article “Researchers Find Link Between Cigarette
=+study focused on clinical decision-making.Evaluate this experimental design. Do you think this is a good design or a poor design, and why? If you were designing such a study, what, if anything,
=+identical gestures, and were taped from the same position. Researchers asked 720 primary care doctors at meetings of the American College of Physicians or the American Academy of Family Physicians
=+eliminated those differences by videotaping actors—two black men, two black women, two white men, and two white women—describing chest pain from identical scripts. They wore identical gowns,
=+pain or a heart attack. Scientists blamed differences in illness severity, insurance coverage, patient preference, and health care access. The researchers
=+2.63 Do ethnic group and gender influence the type of care that a heart patient receives? The following passage is from the article “Heart Care Reflects Race and Sex, Not Symptoms” (USA Today,
=+2.62 According to the article “Effect of Preparation Methods on Total Fat Content, Moisture Content, and Sensory Characteristics of Breaded Chicken Nuggets and Beef Steak Fingers” (Family and
=+This statement was based on the fact that only 51 percent of those responding to a mail survey indicated that they were satisfied with their jobs. Describe any potential sources of bias that might
=+2.61 The article “Workers Grow More Dissatisfied” in the San Luis Obispo Tribune (August 22, 2002) states that “a survey of 5000 people found that while most Americans continue to find their
=+b. Is it reasonable to generalize the results of this experiment to all children? Explain.
=+a. The researchers concluded that the blood cholesterol level was lower for children in the intervention group. Is it reasonable to conclude that the parental counseling and subsequent reduction in
=+2.60 The paper “Prospective Randomized Trial of Low Saturated Fat, Low Cholesterol Diet During the First Three Years of Life” (Circulation [1996]: 1386–1393) describes an experiment in which
=+Describe a potential confounding variable that illustrates why it is unreasonable to conclude that a change in marital status causes a change in crime risk.
=+number of violent crimes per 1000 people, 12 years of age or older, to be 51 for the never married, 42 for the divorced or separated, 13 for married individuals, and 8 for the widowed. Does being
=+2.59 “Crime Finds the Never Married” is the conclusion drawn in an article from USA Today (June 29, 2001). This conclusion is based on data from the Justice Department’s National Crime
=+b. Is it reasonable to conclude that drinking soda or fruit punch causes the observed increased risk of diabetes?Why or why not?
=+a. Do you think that the study described was an observational study or an experiment?
=+fundamentally flawed. “These allegations are inflammatory. Women who drink a lot of soda may simply have generally unhealthy lifestyles” said Richard Adamson of the American Beverage
=+their health or the health of their family would not consume these beverages” said Walter Willett of the Harvard School of Public Health who helped conduct the study.The sugar and beverage
=+2.58 A study of more than 50,000 U.S. nurses found that those who drank just one soda or fruit punch a day tended to gain much more weight and had an 80% increased risk in developing diabetes
=+b. Give an example of a potentially confounding variable that would make it unwise to draw the conclusion that hours of television watched at a young age is the cause of the increased risk of
=+a. Is the study described an observational study or an experiment?
=+In this study, researchers looked at records of 2500 children who were participating in a long-term health study.They found that 10% of these children had attention disorders at age 7 and that
=+2.57 The article “Tots’ TV-Watching May Spur Attention Problems” (San Luis Obispo Tribune, April 5, 2004)describes a study that appeared in the journal Pediatrics.
=+4. After evaluating your proposed design, are there any changes you would like to make to your design?Explain.
=+3. At the end of Section 2.3 there are 10 questions that can be used to evaluate an experimental design. Answer these 10 questions for the design proposed in Step 2.
=+2. Propose an experiment that would provide data to address the question from Step 1. Be specific about how subjects might be selected, what the experimental conditions (treatments) would be, and
=+1. Working with a partner, select one of the areas of potential research suggested in the passage from the paper and formulate a specific question that could be addressed by performing an
=+2. Do you think it would be possible to collect data that could lead to a value for the average burger size that would be better than 2.4 oz.? If so, explain how you would recommend collecting such
=+1. The authors of the article believe that the use of 2.4 oz. as the average size of a burger sold at McDonald’s is “conservative,” which would result in the estimate of 992.25 million pounds
=+This activity can be completed as an individual or as a team. Your instructor will specify which approach (individual or team) you should use.
=+4. Based on the feedback you received in Step 3, would you modify your original sampling plan? If not, explain why this is not necessary. If so, describe how the plan would be modified.
=+Macs (introduced in 1968), 4.0 oz. Quarter Pounders(introduced in 1973), or other sandwiches.”comments you received. Now reverse roles, and provide a critique of the plan devised by the other
=+“McDonald’s does not publish sales and profits of individual items. Thus, it is not possible to estimate how many of McDonald’s first 100 billion beef burgers sold were 1.6 oz hamburgers, 3.2
=+hamburgers. This estimate was based on the assumption that the average weight of a burger sold would be 2.4 oz.This is the average of the weight of a regular hamburger(1.6 oz.) and a Big Mac (3.2
=+Journal of Preventative Medicine [2005]:379–381) estimated that 992.25 million pounds of saturated fat would be consumed as McDonald’s sells its next 100 billion
=+3. Summarize the resulting data in a brief report that explains whether your findings are consistent with the Stroop effect.A c t i v i t y 2.3 McDonald’s and the Next 100 Billion Burgers
=+2. When you are satisfied with your experimental design, carry out the experiment. You will need to construct your list of colored words and a corresponding list of colored bars to use in the
=+how randomization is incorporated into your design. What is your response variable? How will you measure it? How many subjects will you use in your experiment, and how will they be chosen?

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