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fundamentals of statistics

Questions and Answers of Fundamentals Of Statistics

144 Reverse-engineering gene identification. In Molecular Systems Biology (Vol. 3, 2007), geneticists at the University of Naples (Italy) used reverse engineering to identify genes.They calculated
143 Suppose the events B1, B2, and B3 are mutually exclusive and complementary events such that P1B12 = .2, P1B22 = .15, and P1B32 = .65. Consider another event A such that P1A2 = .4. If A is
142 Suppose the events B1, B2, and B3 are mutually exclusive and complementary events such that P1B12 = .2, P1B22 = .15, and P1B32 = .65. Consider another event A such that P1AB12 = .4, P1AB22 =
141 Suppose the events B1 and B2 are mutually exclusive and complementary events such that P1B12 = .75 and P1B22 = .25. Consider another event A such that P1AB12 = .3 and P1AB22 = .5.a. Find P1B1
36 T he data for a random sample of 10 paired observations are shown in the following table and saved in the LM9_36 file.a. If you wish to test whether these data are sufficient to indicate that the
140 Why is Bayes’s rule unnecessary for finding P1BA2 if events A and B are mutually exclusive?
139 Why is Bayes’s rule unnecessary for finding P1BA2 if events A and B are independent?
138 Explain the difference between the two probabilities P1AB2 and P1BA2
Electric wheelchairs are difficult to maneuver for many disabled people. In a paper presented at the 1st International Workshop on Advances in Service Robotics (March 2003), researchers applied
137 A straight flush in poker. Consider 5-card poker hands dealt from a standard 52-card bridge deck.Two important events are A: 5You draw a flush.6 B: 5You draw a straight.6[ Note: A flush consists
136 Volleyball positions. Intercollegiate volleyball rules require that after the opposing team has lost its serve, each of the six members of the serving team must rotate into new positions on the
135 Studying exam questions. A college professor hands out a list of 10 questions, 5 of which will appear on the final examination for the course. One of the students taking the course is pressed for
134 Selecting new-car options. A company sells midlevel models of automobiles in five different styles. A buyer can get an automobile in one of eight colors and with either standard or automatic
133 Selecting a maintenance support system. ARTHUR is the Norwegian Army’s high-tech radar system designed to identify and track “unfriendly” artillery grenades, calculate where enemy positions
132 Florida license plates. In the mid-1980s, the state of Florida ran out of combinations of letters and numbers for its license plates. Then, each license plate contained three letters of the
a. Calculate the difference between each pair of observations by subtracting observation 2 from observation 1.Use the differences to calculate xd and sd 2 .b. If m1 and m2 are the means of
131 Matching medical students with residencies. The National Resident Matching Program (NRMP) is a service provided by the Association of American Medical Colleges to match graduating medical
130 Mathematical theory of partitions. Mathematicians at the University of Florida solved a 30-year-old mathematics problem with the use of the theory of partitions ( Explore , Fall 2000). In
129 Multilevel marketing schemes. Successful companies such as Amway, Herbalife, and NuSkin employ multilevel marketing (MLM) schemes to distribute their products.In MLM, each distributor recruits
127 Kiwifruit as an iron supplement. Refer to the BMC Public Health (Vol. 10, 2010) study of the effectiveness of gold kiwifruit as an iron supplement in women with an iron deficiency, Exercise 107 .
126 U.S. Zip codes. The nine-digit Zip code has become an integral part of the U.S. postal system.a. How many different Zip codes are available for use by the postal service? (Assume that any
125 Traveling between cities. A salesperson living in city A wishes to visit four cities B , C , D , and E .a. If the cities are all connected by airlines, how many different travel plans could be
124 Selecting project teams. Suppose you are managing 10 employees and you need to form three teams to work on different projects. Assume that each employee may serve on any team. In how many
35 T he data for a random sample of six paired observations are shown in the following table and saved in the LM9_35 file. Sample from Population 2 4 17247 739648 Sample from Population 1 7 3 Pair
123 Picking a basketball team. Suppose you are to choose a basketball team (five players) from eight available athletes.a. How many ways can you choose a team (ignoring positions)?b. How many ways
122 Monitoring impedance to leg movements. In an experiment designed to monitor impedance to leg movement, Korean engineers attached electrodes to the ankles and knees of volunteers. Of interest were
121 Choosing portable grill displays. Refer to the Journal of Consumer Research (March 2003) study of how people attempt to influence the choices of others, Exercise 27 .Recall that students selected
119 An experiment consists of choosing objects without regard to order. How many sample points are there if you choose the following?a. 3 objects from 7b. 2 objects from 6c. 2 objects from 30d. 8
118 Determine the number of sample points contained in the sample space when you toss the following:a. 1 dieb. 2 dicec. 4 diced. n dice
34 A paired difference experiment produced the following data:nd = 16 x1 = 143 x2 = 150 xd = -7 sd 2 = 64a. Determine the values of t for which the null hypothesis m1 - m2 = 0 would be rejected in
117 Use the multiplicative rule to determine the number of sample points in the sample space corresponding to the experiment of tossing a coin the following number of times:a. 2 timesb. 3 timesc. 5
115 What is the difference between the permutations rule and the combinations rule?
114 Give a scenario where the partitions rule applies.
113 Give a scenario where the permutations rule applies.
112 Give a scenario where the multiplicative rule applies.
Refer to Example 31 . Suppose the consumer testing service is to choose the top 3 laundry detergents from the group of 10, but is not to rank them .a. In how many different ways can the testing
Five soldiers from a squadron of 100 are to be chosen for a dangerous mission.In how many ways can groups of 5 be formed?
Suppose you have 12 construction workers and you wish to assign 3 to jobsite 1, 4 to jobsite 2, and 5 to jobsite 3. In how many different ways can you make this assignment?
Suppose you are supervising four construction workers.You must assign three to job 1 and one to job 2. In how many different ways can you make this assignment?
Suppose you wish to drive, in sequence, from a starting point to each of five cities, and you wish to compare the distances—and, ultimately, the costs—of the different routes. How many different
Suppose there are five dangerous military missions, each requiring one soldier. In how many different ways can 5 soldiers from a squadron of 100 be assigned to these five missions?
Consider the experiment discussed in Example 106 of tossing a coin 10 times.Show how we found that there were 210 = 1,024 sample points for this experiment
There are 20 candidates for three different executive positions: E1, E2, and E3.How many different ways could you fill the positions?
A product can be shipped by four airlines, and each airline can ship via three different routes. How many distinct ways exist to ship the product?
111 Selecting archaeological dig sites. Archaeologists plan to perform test digs at a location they believe was inhabited several thousand years ago. The site is approximately 10,000 meters long and
32 What conditions are required for valid large-sample inferences about md ? small-sample inferences?
31 In a paired difference experiment, when should the observations be paired, before or after the data are collected?
109 Study of the effect of songs with violent lyrics. A series of designed experiments was conducted to examine the effects of songs with violent lyrics on aggressive thoughts and hostile feelings (
108 Stress and diet study. Researchers at the University of South Florida investigated the effects of diet on the physiology and behavior of rats ( USF News , Oct. 17, 2009).One group of rats was fed
107 Kiwifruit as an iron supplement. Massey University (New Zealand) researchers have designed a 16-week study to determine the effectiveness of gold kiwifruit as an iron supplement in women with an
106 Census sampling. In addition to its decennial enumeration of the population, the U.S. Census Bureau regularly samples the population for demographic information such as income, family size,
30 What are the advantages of using a paired difference experiment over an independent samples design?
105 Random-digit dialing. To ascertain the effectiveness of their advertising campaigns, firms frequently conduct telephone interviews with consumers by using random-digit dialing .With this method,
104 Suppose that a population contains N = 200,000 elements.Use a computer or Table I of Appendix: Tables, to select a random sample of n = 10 elements from the population.Explain how you selected
103 Suppose you wish to sample n = 3 elements from a total of N = 600 elements.a. Count the number of different samples by using combinatorial mathematics.b. If random sampling is to be employed,
102 Suppose you wish to sample n = 2 elements from a total of N = 10 elements.a. Count the number of different samples that can be drawn, first by listing them and then by using combinatorial
101 Define a blind study
100 What is a random-number generator?
99 How are random samples related to representative samples?
98 Define a random sample.
A designed experiment in the medical field involving human subjects is referred to as a clinical trial . One recent clinical trial was designed to determine the potential of using aspirin in
Suppose you wish to randomly sample five households from a population of 100,000 households.a. How many different samples can be selected?b. Use a random-number generator to select a random sample.
96 Risk of a natural-gas pipeline accident. Process Safety Progress (Dec. 2004) published a risk analysis for a natural-gas pipeline between Bolivia and Brazil. The most likely scenario for an
95 Testing a psychic’s ability. Consider an experiment in which 10 identical small boxes are placed side by side on a table. A crystal is placed at random inside one of the boxes.A self-professed
91 Detecting traces of TNT. University of Florida re -searchers in the Department of Materials Science and Engineering have invented a technique that rapidly detects traces of TNT ( Today , Spring
90 Intrusion detection systems. A computer intrusion detection system (IDS) is designed to provide an alarm whenever someone intrudes (e.g., through unauthorized access)into a computer system. A
89 Ambulance response time. Geographical Analysis (Jan.2010) presented a study of Emergency Medical Services(EMS) ability to meet the demand for an ambulance.In one example, the researchers presented
88 Probability of winning a war. Before a country enters into a war, a prudent government will assess the cost, utility, and probability of a victory. University of Georgia professor P. L. Sullivan
85 Are you really being served red snapper? Red snapper is a rare and expensive reef fish served at upscale restaurants.Federal law prohibits restaurants from serving a cheaper, look-alike variety of
83 Health risks to beachgoers. Refer to the University of Florida study of health risks to beachgoers, Exercise 22 .According to the study, 6 out of 1,000 people exposed to wet sand for a 10-minute
82 Study of ancient pottery. Chance (Fall 2000) conducted a study of ancient pottery found at the Greek settlement of Phylakopi. Of the 837 pottery pieces uncovered at the excavation site, 183 were
81 Appraisals and negative emotions. According to psychological theory, each negative emotion one has is linked to some thought (appraisal) about the environment. This theory was tested in the
80 Twitter and wireless Internet. According to the Pew Internet& American Life Project (Oct. 2009), 54% of Internet users have a wireless connection to the Internet via a laptop, cell phone, game
79 Speeding linked to fatal car crashes. According to the National Highway Traffic and Safety Administration’s National Center for Statistics and Analysis (NCSA),“Speeding is one of the most
77 National firearms survey. The Harvard School of Public Health conducted a study of privately held firearm stock in the United States. In a representative household telephone survey of 2,770
76 Do you have a library card? According to a September 2008 Harris poll, 68% of all American adults have a public library card. The percentages do differ by gender—62% of males have library cards
75 A box contains two white, two red, and two blue poker chips. Two chips are randomly chosen without replacement, and their colors are noted. Define the following events:A: 5Both chips are of the
73 Two fair dice are tossed, and the following events are defined:A: 5The sum of the numbers showing is odd.6 B: 5The sum of the numbers showing is 9, 11, or 12.6 Are events A and B independent? Why?
70 An experiment results in one of three mutually exclusive events A , B , and C . It is known that P1A2 = .30, P1B2 = .55, and P1C2 = .15, Find each of the following probabilities:a. P1A ∪ B2b.
69 For two independent events A and B , P1A2 = .4 and P1B2 = .2.a. Find P1A ∩ B2.b. Find P1AB2.c. Find P1A ∩ B2.
68 For two events A and B, P1A2 = .4, P1B2 = .2, and P1AB2 = .6.a. Find P1A ∩ B2.b. Find P1BA2.
67 For two events A and B, P1A2 = .4, P1B2 = .2, and P1A ∩ B2 = .1.a. Find P1AB2.b. Find P1BA2.c. Are A and B independent events?
66 Defend or refute each of the following statements:a. Dependent events are always mutually exclusive.b. Mutually exclusive events are always dependent.c. Independent events are always mutually
65 Give the formula for finding P1BA2.
64 Give the multiplicative rule of probability fora. two independent events.b. any two events.
63 Explain the difference between an unconditional probability and a conditional probability.
Recall from Example 5 that the American Association for Marriage and Family Therapy (AAMFT) found that 25% of divorced couples are classified as“fiery foes” (i.e., they communicate through their
Refer to the consumer product complaint study in Example 15 .The percentages of complaints of various types during and after the guarantee period are shown in Table 6 .Define the following events:A:
Consider the experiment of tossing a fair die, and let A = {Observe an even number.}B = {Observe a number less than or equal to 4.}Are A and B independent events?
A county welfare agency employs 10 welfare workers who interview prospective food stamp recipients. Periodically, the supervisor selects, at random, the forms completed by two workers and
In a classic psychology study conducted in the early 1960s, Stanley Milgram performed a series of experiments in which a teacher is asked to shock a learner who is attempting to memorize word pairs
To develop programs for business travelers staying at convention hotels, Hyatt Hotels Corp. commissioned a study of executives who play golf. The study revealed that 55% of the executives admitted
62 Galileo’s passe-dix game. Passe-dix is a game of chance played with three fair dice. Players bet whether the sum of the faces shown on the dice will be above or below 10.During the late 16th
60 Employee behavior problems . The Organizational Development Journal (Summer 2006) reported on the results of a survey of human resource officers (HROs) at major firms. The focus of the study was
53 Gene expression profiling. Gene expression profiling is a state-of-the-art method for determining the biology of cells. In Briefings in Functional Genomics and Proteomics(Dec. 2006), biologists at
52 Scanning errors at Wal-Mart. The National Institute of Standards and Technology (NIST) mandates that for every 100 items scanned through the electronic checkout scanner at a retail store, no more
50 Study of analysts’ forecasts. The Journal of Accounting Research (March 2008) published a study on relationship incentives and degree of optimism among analysts’forecasts. Participants were
49 Social networking Web sites in the United Kingdom. In the United States, MySpace and FaceBook are considered the two most popular social networking Web sites.In the United Kingdom (UK), the
48 Three fair coins are tossed. We wish to find the probability of the event A: 5Observe at least one head.6a. Express A as the union of three mutually exclusive events.Using the expression you
44 A pair of fair dice is tossed. Define the following events:A: 5You will roll a 7 1i.e., the sum of the numbers of dots on the upper faces of the two dice is equal to 7).6 B: 5At least one of the

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