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fundamentals of statistics

Questions and Answers of Fundamentals Of Statistics

90 Do video game players have superior visual attention skills? The Journal of conductal articles in Support of the Null Hypothesis (Vol. 6, 2009) conducted a study of video game players. In a second
84 The following two-way table gives data for a 2 * 3 factorial experiment with two observations for each factor–level combination. The data are saved in the LM10_84 filea. Identify the treatments
Suppose the USGA tests four different brands (A, B, C, D) of golf balls and two different clubs (driver, five-iron) in a 4 * 2 factorial design. Each of the eight Brand–Club combinations
76 Listening ability of infants. Science (Jan. 1, 1999) reported on the ability of seven-month-old infants to learn an unfamiliar language. In one experiment, 16 infants were trained in an artificial
68 Treatment for tendon pain. Refer to the British Journal of Sports Medicine (Feb. 1, 2004) study of chronic Achilles tendon pain, presented in Exercise 10 . Recall that each in a sample of 25
67 “Topsy-turvy” seasons in college football. Each week during the college football season the Associated Press (AP)ranks the top 25 Division I college football teams based on voting by
49 Chemical properties of whole wheat breads. Whole wheat breads contain a high amount of phytic acid, which tends to lower the absorption of nutrient minerals. The Journal of Agricultural and Food
47 Guilt in decision making. The effect of guilt emotion on how a decision maker focuses on the problem was investigated in the Jan. 2007 issue of the Journal of Behavioral Decision Making . A sample
36 The “name game.” Psychologists at Lancaster University(United Kingdom) evaluated three methods of name retrieval in a controlled setting ( Journal of Experimental Psychology—Applied , June
23 Refer to Exercises 21 and 22. Complete the following ANOVA table for each of the two dot plots: Source Treatments Error Total df SS MS F
Suppose the USGA wants to compare the mean distances reached of four different brands of golf balls struck with a driver. A completely randomized design is employed, with Iron Byron, the USGA’s
79 Consider the Poisson probability distribution shown here:What is the value of l ? 3x-3 P(x) x! (x = 0, 1, 2,...).
78 Consider a Poisson random variable with probability distributionWhat is the value of l ? 10%-10 P(x) = x! == (x = 0, 1, 2,...)
53 Compute the following: a. 6! 2!(6-2)! b. 5 c. (6)
52 Consider the following binomial probability distributiona. How many trials ( n ) are in the experiment?b. What is the value of p , the probability of success? p(x) = ()(7) (3) (x = 0,1,2,5)
45 Beach erosional hot spots. The U.S. Army Corps of Engineers did a study of beach erosional hot spots. The data on the nearshore bar condition for six beach hot spots are reproduced in the
44 Controlling the water hyacinth. Refer to the Annals of the Entomological Society of America (Jan. 2005) study of the number of insect eggs, x , on a blade of water hyacinth, presented in Exercise
43 Dust mite allergies. Exercise 23 gives the probability distribution for the number x of homes with high dust mite levels. The probability distribution is reproduced here:a. Find E1x2 . Give a
41 Gender in two-child families. Refer to the Human Biology(Feb. 2009) study on the gender of children in two-child families, Exercise 25. Recall that the National Health Interview Survey (NHIS) of
40 Consider the probability distribution shown here: x -4 -3 -2-101 1 2 3 P(x) .02 .07 .02 .07 .10 .15 a. Calculate , , and . 4 .30 .18 .10 .06 .02 b. Graph p(x). Locate , -2, and + 2 on the graph.
39 Consider the probability distributions shown here:a. Use your intuition to find the mean for each distribution.How did you arrive at your choice?b. Which distribution appears to be more variable?
38 Consider the probability distribution for the random variable x shown here: x 10 p(x) .05 2220 30 .20 .30 .25 49 40 50 60 .10 .10 a. Find , 2, and . b. Graph p(x). c. Locate and the interval 20
37 Consider the probability distribution shown for the random variable x here:a. Find m = E1x2 .b. Find s2 = E3(x - m)24 .c. Find s.d. Interpret the value you obtained for m.e. In this case, can the
30 Federal civil trial appeals. The Journal of the American Law and Economics Association (Vol. 3, 2001) conducted a study of appeals of federal civil trials. A breakdown of the 678 civil cases that
29 Choosing portable grill displays. In a Journal of Consumer Research (Mar. 2003) marketing study of influencing consumer choices by offering undesirable alternatives, each of 124 college students
28 Ryder Cup miracle in golf. The Ryder Cup is a three-day golf tournament played between a team of golf professionals from the United States and a team from Europe. A total of 28 matches are played
26 Solar energy cells. According to Wired (June 2008), 35% of the world’s solar energy cells are manufactured in China.Consider a random sample of 5 solar energy cells, and let x represent the
24 Controlling the water hyacinth. Entomologists are continually searching for new biological agents to control the water hyacinth, one of the world’s worst aquatic weeds.An insect that naturally
16 Consider the following probability distribution:a. List the values that x may assume.b. What value of x is most probable?c. What is the probability that x is greater than 0?d. What is the
Craps is a popular casino game in which a player throws two dice and bets on the outcome (the sum total of the dots showing on the upper faces of the two dice). Consider a $5 wager. On the first toss
Recall the experiment of tossing two coins, and let x be the number of heads observed. Find the probability associated with each value of the random variable x , assuming that the two coins are fair.
Exit polls are conducted in selected locations as voters leave their polling places after voting. In addition to being used to predict the outcome of elections before the votes are counted, these
188 Sex composition patterns of children in families. In having children, is there a genetic factor that causes some families to favor one sex over the other? That is, does having boys or girls
187 Cigar smoking and cancer. The Journal of the National Cancer Institute (Feb. 16, 2000) published the results of a study that investigated the association between cigar smoking and death from
185 Purchasing microchips. An important component of your desktop or laptop personal computer (PC) is a microchip.The next table gives the proportions of microchips that a certain PC manufacturer
183 Series and parallel systems. Consider the two systems shown in the schematic on the next page . System A operates properly only if all three components operate properly.(The three components are
178 Elderly wheelchair user study. The American Journal of Public Health (Jan. 2002) reported on a study of elderly wheelchair users who live at home. A sample of 306 wheelchair users, age 65 or
176 Stacking in the NBA. In professional sports, stacking is a term used to describe the practice of African-American players being excluded from certain positions because of race. To illustrate the
175 Winning at roulette. Roulette is a very popular game in many American casinos. In Roulette, a ball spins on a circular wheel that is divided into 38 arcs of equal length, bearing the numbers 00,
173 Beach erosional hot spots. Beaches that exhibit high erosion rates relative to the surrounding beach are defined as erosional hot spots . The U.S. Army Corps of Engineers is conducting a study of
167 NHTSA new car crash testing. The National Highway Traffic Safety Administration (NHTSA) performs crash tests of new car models. The NHTSA has developed a“star” scoring system, with results
164 Find the numerical value of a. 6! b. c. (19) = g d. P e. f. (9) 0! g. P10 h. P 50
160 The accompanying Venn diagram illustrates a sample space containing six sample points and three events, A, B , and C . The probabilities of the sample points are P(1) = .3, P(2) = .2, P(3) = .1,
128 Randomization in a study of TV commercials. Gonzaga University professors conducted a study of over 1,500 television commercials and published their results in the Journal of Sociology, Social
120 Cheek teeth of extinct primates. Refer to the American Journal of Physical Anthropology (Vol. 142, 2010) study of the dietary habits of extinct mammals, Exercise 25 .Recall that 18 cheek teeth
116 Find the numerical values of a. e. 50 50 50 b. P f. 50 c. P g. P 100 d. (199) h. P 10
110 Auditing an accounting system. In auditing a firm’s financial statements, an auditor is required to assess the operational effectiveness of the accounting system. In performing the assessment,
97 NBA draft lottery. The National Basketball Association(NBA) utilizes a lottery to determine the order in which teams draft amateur (high school and college) players.Teams with the poorest
94 Random mutation of cells. Chance (Spring 2010) presented an article on the random mutation hypothesis developed by microbiologists. Under this hypothesis, when a wildtype organic cell (e.g., a
93 Seeded players at a shuffleboard tournament. Shuffleboard is an outdoor game popular with senior citizens. In single elimination shuffleboard tournaments, players are paired and play a match
92 Forest fragmentation study. In a Conservation Ecology(Dec. 2003) study of the causes of forest fragmentation, the researchers used advanced high-resolution satellite imagery to develop
87 Extinct New Zealand birds. Evolutionary Ecology Research(July 2003) did a study of the patterns of extinction in the New Zealand bird population . Consider the data on extinction status(extinct,
86 Fighting probability of fallow deer bucks. Refer to the Aggressive Behavior (Jan./Feb. 2007) study of fallow deer bucks fighting during the mating season, presented in Exercise 57 . Recall that
84 Sleep apnea and sleep stage transitioning. Refer to the sleep apnea study published in Chance (Winter 2009), Exercise 54 . Recall that the various stages of sleep for a large group of sleep apnea
78 Guilt in decision making. Refer to the Journal of Behavioral Decision Making (Jan. 2007) study of the effect of guilt emotion on how a decision maker focuses on the problem, Exercise 55 . The
74 A sample space contains six sample points and events A , B , and C , as shown in the Venn diagram on page 146 . The probabilities of the sample points are P(1) = .20, P(2) = .05, P(3) = .30, P(4)
72 An experiment results in one of five sample points with the following probabilities: P(E12 = .22, P(E22 = .31, P(E32 = .15, P(E42 = .22, and P(E52 = .1. The following events have been defined:Find
71 Consider the experiment defined by the accompanying Venn diagram, with the sample space S containing five sample points. The sample points are assigned the following probabilities: P(E12 = .1,
The Federal Trade Commission’s investigation of consumer product complaints has generated much interest on the part of manufacturers in the quality of their products. A manufacturer of an
Many medical researchers have conducted experiments to examine the relationship between cigarette smoking and cancer. Consider an individual randomly selected from the adult male population. Let A
61 Chemical signals of mice . The ability of a mouse to recognize the odor of a potential predator (e.g., a cat) is essential to the mouse’s survival. The chemical makeup of these odors—called
59 Federal civil trial appeals. The Journal of the American Law and Economics Association (Vol. 3, 2001) published the results of a study of appeals of federal civil trials. The accompanying table,
58 Cell phone handoff behavior. A “handoff” is a term used in wireless communications to describe the process of a cell phone moving from a coverage area of one base station to another. Each base
57 Fighting probability of fallow deer bucks. In Aggressive Behavior (Jan./Feb. 2007), zoologists investigated the likelihood of fallow deer bucks fighting during the mating season. During a 270-hour
56 Abortion provider survey. The Alan Guttmacher Institute Abortion Provider Survey is a survey of all 238 known nonhospital abortion providers in the United States( Perspectives on Sexual and
55 Guilt in decision making. The effect of guilt emotion on how a decision maker focuses on the problem was investigated in the Jan. 2007 issue of the Journal of Behavioral Decision Making . A total
54 Sleep apnea and sleep stage transitioning. Sleep apnea is a common sleep disorder characterized by collapses of the upper airway during sleep. Chance (Winter 2009)investigated the role of sleep
51 Toxic chemical incidents. Process Safety Progress (Sept.2004) reported on an emergency response system for incidents involving toxic chemicals in Taiwan. The system has logged over 250 incidents
47 T he outcomes of two variables are (Low, Medium, High)and (On, Off), respectively. An experiment is conducted in which the outcomes of each of the two variables are observed. The probabilities
46 Consider the following Venn diagram, whereFind the following probabilities:a. P1Ac2b. P1Bc2c. P1Ac B2d. P1A B2e. P1A B2f. P1Ac Bc2 g. Are events A and B mutually exclusive? Why? P(E1).10,
45 Consider the following Venn diagram, where P(E22 = P(E32 = 15, P(E42 = P(E52 = 120, P(E62 = 110, P(E72 = 15 :Find each of the following probabilities: A E E5 E2 B EA E3 E E6 S
Family Planning Perspectives reported on a study of over 200,000 births in New Jersey over a recent two-year period. The study investigated the link between the mother’s race and the age at which
Consider a die-toss experiment in which the following events are defined:A: {Toss an even number.}B: {Toss a number less than or equal to 3.} a. Describe AU B for this experiment. b. Describe A B for
27 Choosing portable grill displays. University of Maryland marketing professor R. W. Hamilton studied how people attempt to influence the choices of others by offering undesirable alternatives (
26 Museum management . In the Museum Management and Curatorship (June 2010) study of the criteria used to evaluate museum performance, the managers of 30 leading museums of contemporary art were
25 Cheek teeth of extinct primates . In the American Journal of Physical Anthropology (Vol. 142, 2010) study of the dietary habits of extinct mammals, 18 cheek teeth extracted from skulls of an
23 Sociology fieldwork methods . University New Mexico professor Jane Hood conducted a study of the fieldwork methods used by qualitative sociologists. She discovered that fieldwork methods could be
21 Going online for health information . A cyberchondriac is defined as a person who regularly searches the Web for health care information. A recent Harris Poll surveyed 1,010 U.S. adults by
12 Compute each of the following a. d. (2) (5) b. e. 6) 6 (9) 5 c.
10 The following Venn diagram describes the sample space of a particular experiment and events A and B :a. Suppose the sample points are equally likely. Find P ( A )and P ( B ).b. Suppose P(1) = P(2)
9 An experiment results in one of the following sample points: E1, E2, E3, E4, and E5. == a. Find P(E3) if P(E) = .1, P(E2) and P(Es) = .1 = .2, P(E4) = .1, b. Find P(E3) if P(E1) = P(E3), P(E2) =
The American Association for Marriage and Family Therapy (AAMFT) is a group of professional therapists and family practitioners that treats many of the nation’s couples and families. The AAMFT
Consider the experiment of tossing two unbalanced coins. Because the coins are not balanced, their outcomes ( H or T ) are not equiprobable. Suppose the correct probabilities associated with the
In 1974therewasasuspicionthatthenumberoflungcancercases
Consider theshiftedmultiplicativePoissonmodelinthecasewhere r = s = 2. Showthatthelikelihoodequationsareequivalenttothefollowingequa-tion in
The databelowareconcernedwith1545fraternaltwinsofoppositesex and theircriminalbehaviour.Eachtwinpairisclassifiedaftertheircriminalstatus, resulting inthefollowingtable.a)
A teachingassistantattheUniversityofCopenhagenconsumed384 hard-boiled eggsintheacademicyear1968/69andnotedeverydayhowmanyofthe eggsbrokeduringcookingsothattheegg-whiteflowedintotheboilingwater,and
Colour blindnessismorecommonamongmalesthanfemales.This could beduetocolourbeinginheritedviaageneontheX-chromosome, wheremales haveonlyone,whereasfemaleshavetwo.Waaler(1927)collectedthefollowingdata
The haptoglobintypeforhumansaredeterminedbyasinglediallelic gene withallelesHb1andHb2.ThegenotypesaredenotedHb1,Hb1Hb2,andHb2.Haptoglobin typesweredeterminedfor607menand1439women,selectedat random
The logarithmic distributionisadistributiononintegerswithdensityfor θ ∈ (0, 1). Williams(1943)investigatedthedistributionofthenumberofpub-lications perauthorina1913volumeof
150 Petridishespreparedwithstreptomycinwereeachsubjectedto one millionE-colibacteria.Ifabacteriummutatestobecomeresistant,itwillgrowa
Let X1, ...,Xn be asamplefromagammadistributionwithunknown shape andscale.a) DerivethelikelihoodratioandWaldteststatisticsforthehypothesis H0 : α = 1, i.e.
Let X and Y be independentandexponentiallydistributedrandom variableswith E(X) = λ1 and E(Y ) = λ2 where λ = (λ1, λ2) ∈ R2+. andlet(X1, Y1), ..., (Xn, Yn) be
Twomethodsforanalysingstarchcontentinpotatoesaretobeana-lysed andcompared.Sixteenpotatoeswithvaryingcontentofstarcharemeasuredby the twomethodswithresultsdisplayedin Table7.1.
Consider theParetodistributionwithfixedthreshold c (c = 1 in Exer-cise 3.3)andindexparameter θ > 0:Assuming thattheseareParetodistributedwiththreshold c = 50 and indexpara-meter θi > 0, i =
The databelowarebasedonFisher(1947)andrepresenttheweight of theheartin16catsasapercentageoftheweightofthebody.Doyouseeany differencebetweenmaleandfemalecats? Gender Percentage of heart weight Female
Let X ∼ binom(n, μ), μ ∈ (0, 1). Determinethefollowingapprox-imate confidenceintervalsfortheunknownprobabilityofsuccess μ:a) Aconfidenceintervalbasedonthequadraticscorestatistic Q(X,μ);b)
Let X followalog-normaldistributionasinExercise1.3withpara-meters (ξ,σ2) ∈ R × R+ which arebothconsideredunknown.Inotherwords, Y = logX with Y ∼ N(ξ,σ2). Consider asample X1, ...,Xn from
Consider againtheinversenormaldistributionasinExercise3.4with densitywith respecttostandardLebesguemeasureon R+ and considerthesubfamily P0 determined bytherestriction μ = 1, parametrizedwith λ.
Consider thesituationinExercise3.6,where (X,Y ) are random variablestakingvaluesin R+ × N0 with densitywith respectto ν × m, where ν is thestandardLebesguemeasureon R+ and m is countingmeasureon

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