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fundamentals of statistics

Questions and Answers of Fundamentals Of Statistics

13 True or False . The estimates of b0 and b1 should be interpreted only within the sampled range of the independent variable, x .
12 Give two properties of the line estimated with the method of least squares.
11 In regression, what is an error of prediction?
10 Give the slope and y -intercept for each of the lines defined in Exercise 9.
9 Plot the following lines:a. y = 4 + xb. y = 5 - 2xc. y = -4 + 3xd. y = -2xe. y = xf. y = .50 + 1.5x
8 Refer to Exercise 7. Find the equations of the lines that pass through the points listed in Exercise 5.
7 The equation (deterministic) for a straight line is y = b0 + b1x If the line passes through the point 1-2, 42, then x = -2, y = 4 must satisfy the equation; that is, 4 = b0 + b11-22 Similarly, if
6 Give the slope and y -intercept for each of the lines graphed in Exercise 5.
5 In each case, graph the line that passes through the given points.a. (1, 1) and (5, 5)b. (0, 3) and (3, 0)c. 1-1, 12 and (4, 2)d. 1-6, -32 and (2, 6)
4 If a straight-line probabilistic relationship relates the mean E ( y ) to an independent variable x , does it imply that every value of the variable y will always fall exactly on the line of means?
3 What is the line of means?
2 What is the difference between a dependent variable and an independent variable in a probabilistic model?
1 Why do we generally prefer a probabilistic model to a deterministic model? Give examples for which the two types of models might be appropriate.
9 Jaw dysfunction study. A report on dental patients with temporomandibular (jaw) joint dysfunction (TMD) was published in General Dentistry (Jan/Feb. 2004). A random sample of 60 patients was
5 Find the rejection region for a one-dimensional x2@test of a null hypothesis concerning p1, p2,c, pk ifa. k = 3; a = .05b. k = 5; a = .10c. k = 4; a = .01
4 Use Table VII of Appendix: Tables to find the following probabilities:a. P(x2 … 1.063623) for df = 4b. P(x2 7 30.5779) for df = 15c. P(x2 Ú 82.3581) for df = 100d. P(x2 6 18.4926) for df = 30
3 Use Table VII of Appendix: Tables to find each of the following x2 values:a. x2.05 for df = 10b. x2.990 for df = 50c. x2.10 for df = 16d. x2.005 for df = 50
2 What conditions must n satisfy to make the x2 test for a one-way table valid?
1 What are the characteristics of a multinomial experiment?Compare the characteristics with those of a binomial experiment.
12 Museum management. In the Museum Management and Curatorship (June 2010) worldwide survey of 30 leading museums of contemporary art, each museum manager was asked to provide the performance measure
13 Gender in two-child families. Human Biology (Feb. 2009)did a study on the gender of children in two-child families.The article reported on the results of the National Health Interview Survey
14 Sociology fieldwork methods. Teaching Sociology (July 2006) published a study of the fieldwork methods used by qualitative sociologists. Recall that fieldwork methods can be categorized as
15 Do you believe in the Bible? In the General Social Survey(GSS) pertaining to a person’s belief in the Bible, approximately 2,800 Americans selected from one of the following answers: (1) The
16 Characteristics of ice-melt ponds. The National Snow and Ice Data Center (NSIDC) collected data on 504 ice-melt ponds in the Canadian Arctic. The data are saved in the PONDICE file. One variable
17 Detecting Alzheimer’s disease at an early age. Geneticists at Australian National University are studying whether the cognitive effects of Alzheimer’s disease can be detected at an early age (
18 Political representation of religious groups. Do those elected to the U.S. House of Representatives really “represent”their constituents demographically? This was a question of interest in
19 Analysis of a Scrabble game. In the board game Scrabble™, a player initially draws a “hand” of seven tiles at random from 100 tiles. Each tile has a letter of the alphabet, and the player
A social scientist wants to determine whether the marital status (divorced or not divorced) of U.S. men is independent of their religious affiliation (or lack thereof).A sample of 500 U.S. men is
20 What is a two-way (contingency) table?
21 What is a contingency table with fixed marginals?
22 True or False . One goal of a contingency table analysis is to determine whether the two classifications are independent or dependent.
23 What conditions are required for a valid chi-square test of data from a contingency table?
24 Find the rejection region for a test of independence of two classifications for which the contingency table contains r rows and c columns anda. r = 5, c = 5, a = .05b. r = 3, c = 6, a = .10c. r =
25 Consider the following 2 * 3 (i.e., r = 2 and c = 3 ) contingency tablea. Specify the null and alternative hypotheses that should be used in testing the independence of the row and column
26 Refer to Exercise 25.a. Convert the frequency responses to percentages by calculating the percentage of each column total falling in each row. Also, convert the row totals to percentages of the
27 Test the null hypothesis of independence of the two classifications A and B of the 3 * 3 contingency table shown here. Use a = .05. B B3 B B 87 228
29 Children’s perceptions of their neighborhood. In Health Education Research (Feb. 2005), nutrition scientists at Deakin University (Australia) investigated children’s perceptions of their
28 Refer to Exercise 27. Convert the responses to percentages by calculating the percentage of each B class total falling into each A classification. Also, calculate the percentage of the total
31 Stereotyping deceptive and authentic news stories. Major newspapers lose their credibility (and subscribers) when they are found to have published deceptive or misleading news stories. In
30 Eyewitnesses and mug shots. Applied Psychology in Criminal Justice (April 2010) conducted a study of mug shot choices by eyewitnesses to a crime. Recall that a sample of 96 college students was
32 Healing heart patients with music, imagery, touch, and prayer. “Frontier medicine” is a term used to describe medical therapies (e.g., energy healing, therapeutic prayer, spiritual healing)
33 Masculinity and crime. The Journal of Sociology (July 2003) conducted a study on the link between the level of masculinity and criminal behavior in men. The researcher identified events that a
35 IQ and mental deficiency. A person is diagnosed with a mental deficiency if, before the age of 18, his or her score on a standard IQ test is no higher than 70 (two standard deviations below the
34 “Cry wolf” effect in air traffic controlling. Researchers at Alion Science Corporation and New Mexico State University collaborated on a study of how air traffic controllers respond to false
36 Creating menus to influence others. The Journal of Consumer Research (Mar. 2003) published a study on influencing the choices of others by offering undesirable alternatives.In another experiment
37 Detecting Alzheimer’s disease at an early age. Refer to the Neuropsychology (Jan. 2007) study of whether the cognitive effects of Alzheimer’s disease can be detected at an early age, Exercise
38 Trapping grain moths. In an experiment described in the Journal of Agricultural, Biological, and Environmental Statistics (Dec. 2000), bins of corn were stocked with various parasites (e.g., grain
39 Classifying air threats with heuristics. The Journal of Behavioral Decision Making (Jan. 2007) published a study on the use of heuristics to classify the threat level of approaching aircraft. Of
40 Subarctic plant study. The traits of seed-bearing plants indigenous to subarctic Finland were studied in Arctic, Antarctic, and Alpine Research (May 2004). Plants were categorized according to
41 Susceptibility to hypnosis. A standardized procedure for determining a person’s susceptibility to hypnosis is the Stanford Hypnotic Susceptibility Scale, Form C (SHSS:C).Recently, a new method
42 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
43 Efficacy of an HIV vaccine. New, effective AIDS vaccines are now being developed through the process of “sieving”—that is, sifting out infections with some strains of HIV. Harvard School of
44 Examining the “Monty Hall Dilemma.” Consider the game show problem of whether or not to switch your choice of three doors, one of which hides a prize, after the host reveals what is behind a
45 True or False . Rejecting the null hypothesis in a chi-square test for independence implies that a causal relationship exists between the two categorical variables.
46 What is the difference between a one-way chi-square analysis and a two-way chi-square analysis?
47 A random sample of 250 observations was classified according to the row and column categories shown in the following tablea. Do the data provide sufficient evidence to conclude that the rows and
48 A random sample of 150 observations was classified into the categories shown in the following table:a. Do the data provide sufficient evidence that the categories are not equally likely? Use a =
49 Location of major sports venues. There has been a recent trend for professional sports franchises in Major League Baseball (MLB), the National Football League (NFL), the National Basketball
50 Scanning Internet messages. Inc. Technology (Mar. 18, 1997)reported the results of an Equifax/Harris Consumer Privacy Survey in which 328 Internet users indicated their level of agreement with the
51 Risk factor for lumbar disease. One of the most common musculoskeletal disorders is lumbar disk disease (LDD).Medical researchers reported finding a common genetic risk factor for LDD ( Journal of
52 Late-emerging reading disabilities. Studies of children with reading disabilities typically focus on “early-emerging” difficulties identified prior to the fourth grade. Psychologists at
53 Politics and religion. University of Maryland professor Ted R. Gurr examined the political strategies used by ethnic groups worldwide in their fight for minority rights.( Political Science &
54 “Made in the USA” survey. The Journal of Global Business (Spring 2002) did a study of what “Made in the USA” on product labels means to the typical consumer.106 shoppers participated in
55 Hearing impairment study. The Journal of Intellectual Disability Research (Feb. 1995) published a longitudinal study of hearing impairment in a group of elderly patients with intellectual
56 Butterfly hot spots. Nature (Sept. 1993) reported on a study of animal and plant species “hot spots” in Great Britain.A hot spot is defined as a 10@km2 area that is species rich—that is,
57 Iraq War survey. The Pew Internet & American Life Project commissioned Princeton Survey Research Associates to develop and carry out a survey of what Americans think about the War in Iraq. Some of
In this activity, you will study the difference between binomial and multinomial experiments.1. A television station has hired an independent research group to determine whether television viewers in
69 A “rigged” election? Chance (Spring 2004) presented data from a recent election held to determine the board of directors of a local community. There were 27 candidates for the board, and each
68 Testing normality. Suppose a random variable is hypothesized to be normally distributed with a mean of 0 and a standard deviation of 1. A random sample of 200 observations of the variable yields
67 Goodness-of-fit test. A statistical analysis is to be done on a set of data consisting of 1,000 monthly salaries.The analysis requires the assumption that the sample was drawn from a normal
66 Battle simulation trials. In order to evaluate their situational awareness, fighter aircraft pilots participate in battle simulations. At a random point in the trial, the simulator is frozen and
65 Coupon usage study. A hot topic in marketing research is the exploration of a technology-based self-service (TBSS)encounter, in which various technologies (e.g., ATMs, online banking,
64 Orientation clue experiment. Human Factors (Dec. 1988)published a study of color brightness as a body orientation clue. Ninety college students reclining on their backs in the dark were
62 Gangs and homemade weapons. The National Gang Crime Research Center (NGCRC) has developed a six-level gang classification system for both adults and juveniles. The six categories are shown in the
61 Birds feeding on gypsy moths. A field study was conducted to identify the natural predators of the gypsy moth.( Environmental Entomology , June 1995). For one part of the study, 24 black-capped
60 Flight response of geese to helicopter traffic. Offshore oil drilling near an Alaskan estuary has led to increased air traffic—mostly large helicopters—in the area. The U.S. Fish and Wildlife
59 Multiple-sclerosis drug. Interferons are proteins produced naturally by the human body that help fight infections and regulate the immune system. A drug developed from interferons, called Avonex,
58 Pig farmer study. An article in Sociological Methods &Research (May 2001) analyzed the data presented in the accompanying table. A sample of 262 Kansas pig farmers was classified according to
We have now discussed two methods of collecting data to compare two population means. In many experimental situations, a decision must be made either to collect two independent samples or to conduct
138 Feeding habits of sea urchins. The Florida Scientist(Summer/Autumn 1991) reported on a study of the feeding habits of sea urchins. A sample of 20 urchins was captured from Biscayne Bay (Miami),
137 Gambling in public high schools. With the rapid growth in legalized gambling in the United States, there is concern that the involvement of youth in gambling activities is also increasing.
136 Accuracy of mental maps. To help students organize global information about people, places, and environments, geographers encourage them to develop “mental maps” of the world. A series of
135 Kicking the cigarette habit. Can taking an antidepressant drug help cigarette smokers kick their habit? The New England Journal of Medicine (Oct. 23, 1997) published a study in which 615 smokers
134 Testing electronic circuits. Japanese researchers have developed a compression–depression method of testing electronic circuits based on Huffman coding ( IEICE Transactions on Information &
133 Instrument precision. The quality control department of a paper company measures the brightness (a measure of reflectance) of finished paper on a periodic basis throughout the day. Two
132 Identifying the target parameter. For each of the following studies, give the parameter of interest and state any assumptions that are necessary for the inferences to be invalid.a. To investigate
131 Rating music teachers. Students enrolled in music classes at the University of Texas (Austin) participated in a study to compare the observations and teacher evaluations of music education majors
129 Switching majors in college. When female undergraduates switch from science, mathematics, and engineering (SME)majors into disciplines that are not based on science, are their reasons different
128 Personalities of cocaine abusers. Do cocaine abusers have radically different personalities than nonabusing college students? This was one of the questions researched in Psychological Assessment
127 Treatments for panic disorder. Inositol is a complex cyclic alcohol found to be effective against clinical depression.Medical researchers believe that inositol may also be used to treat panic
125 Children’s use of pronouns. The Journal of Communication Disorders (Mar. 1995) conducted a study of specifically language-impaired (SLI) children. The data on deviation intelligence quotient
124 Mating habits of snails. Hermaphrodites are animals that possess the reproductive organs of both sexes. Genetical Research (June 1995) published a study of the mating systems of hermaphroditic
123 Reading tongue twisters. According to Webster’s New World Dictionary , a tongue twister is “a phrase that is hard to speak rapidly.” Do tongue twisters have an effect on the length of time
121 Animal-assisted therapy for heart patients. The American Heart Association Conference (Nov. 2005) performed a study to gauge whether animal-assisted therapy can improve the physiological
118 Bear vs. pig bile study. Bear gallbladder is used in Chinese medicine to treat inflammation. A study in the Journal of Ethnopharmacology (June 1995) examined the easier-toobtain pig gallbladder
117 Heights of grade school repeaters. Are children who repeat a grade in elementary school shorter, on average, than their peers? To answer this question, researchers compared the heights of
116 Executive workout dropouts. The Journal of Sport Behavior(2001) conducted a study of variety in exercise workouts.One group of 40 people varied their exercise routine in workouts, while a second
115 Effect of altitude on climbers. Dr. Philip Lieberman, a neuroscientist at Brown University, conducted a field experiment to gauge the effect of high altitude on a person’s ability to think
113 Oil spill impact on seabirds. The Journal of Agricultural, Biological, and Environmental Statistics (Sept. 2000) conducted a study of the impact of a tanker oil spill on the seabird population in
112 A random sample of five pairs of observations was selected, one observation from a population with mean m1, the other from a population with mean m2. The data are shown in the following table and

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