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fundamentals of statistics

Questions and Answers of Fundamentals Of Statistics

111 Two independent random samples are taken from two populations. The results of these samples are summarized in the following table:a. Form a 90% confidence interval for (m1 - m2).b. Test H0: (m1 -
110 Independent random samples were selected from two binomial populations. The size and number of observed successes for each sample are shown in the following table:a. Test H0: 1p1 - p22 = 0
109 Independent random samples were selected from two normally distributed populations with means m1 and m2, respectively. The sample sizes, means, and variances are shown in the following table:a.
108 Two independent random samples were selected from normally distributed populations with means and variances(m1, s21) and (m2, s22), respectively. The sample sizes, means, and variances are shown
107 For each of the following, identify the target parameter as m1 - m2, p1 - p2, or s1 2 >s2 2 .a. Comparison of average SAT scores of males and females.b. Difference between mean waiting times at
106 List the assumptions necessary for each of the following inferential techniques:a. Large-sample inferences about the difference (m1 - m2)between population means, using a two-sample z
105 Pentagon speeds up order-to-delivery times. Following the initial Persian Gulf War, the Pentagon changed its logistics processes to be more corporate-like. The extravagant “justin-case”
104 Detection of rigged school milk prices (cont’d). Refer to the investigation into collusive bidding in the northern Kentucky school milk market, presented in Exercises 28 and 68. In competitive
103 Is honey a cough remedy? The Archives of Pediatrics and Adolescent Medicine (Dec. 2007) ran a study of honey as a children’s cough remedy. The data (cough improvement scores) for the 33
102 Patent infringement case. Refer to the Chance (Fall 2002)description of a patent infringement case against Intel Corp., presented in Exercise 22. The zinc measurements for three locations listed
100 Mongolian desert ants. Refer to the Journal of Biogeography(Dec. 2003) study of ants in Mongolia (central Asia), presented in Exercise 25, in which you compared the mean number of ants at two
99 How do you choose to argue? Refer to the Thinking and Reasoning (Oct. 2006) study of the cognitive skills required for successful arguments, presented in Exercise 23.Recall that 52 psychology
98 Bulimia study. Refer to Exercise 19. The “fear of negative evaluation” (FNE) scores for the 11 bulimic females and 14 females with normal eating habits are reproduced in the table below and
97 Children’s recall of TV ads. Refer to the Journal of Advertising (Spring 2006) study of children’s recall of television commercials, Exercise 15. You used a smallsample t test to test the null
96 Independent random samples were selected from each of two normally distributed populations, n1 = 6 from population 1 and n2 = 4 from population 2. The data are shown in the following table and
94 Specify the appropriate rejection region for testing against H0: s1 2 = s2 2 in each of the following situations:a. Ha: s1 2 7 s2 2 ; a = .05, n1 = 25, n2 = 20b. Ha: s1 2 6 s2 2 ; a = .05, n1 =
93 For each of the cases that follow, identify the rejection region that should be used to test H0: s1 2 = s2 2 against Ha: s1 2 s2 2 . Assume that n1 = 8 and n2 = 40.a. a = .20b. a = .10c. a =
92 For each of the cases that follow, identify the rejection region that should be used to test H0: s1 2 = s2 2 against Ha: s1 2 7 s2 2 . Assume that n1 = 20 and n2 = 30.a. a = .10b. a = .05c. a =
91 Given n1 and n2, find the following probabilities:a. n1 = 2, n2 = 30, P(F Ú 4.18)b. n1 = 24, n2 = 14, P(F 6 1.94)c. n1 = 9, n2 = 1, P(F … 6,022.0)d. n1 = 30, n2 = 30, P(F 7 1.84)
90 Use Tables VIII, IX, X, and XI of Appendix: Tables to find each of the following F -values:a. F.05, where n1 = 8 and n2 = 5b. F.01, where n1 = 20 and n2 = 14c. F.025, where n1 = 10 and n2 = 5d.
89 True or false . H0: s1 2 = s2 2 is equivalent to H0: s1 2 >s2 2 = 0.
88 True or false . The F -statistic used for testing H0: s1 2 = s2 2 against Ha: s1 2 6 s2 2 is F = (s1)2>(s2)2.
87 What conditions are required for valid inferences about(s1)2>(s2)2 ?
86 Describe the sampling distribution of (s1)2>(s2)2 for normal data.
In Example 4 ( Section 2 ), we used the two-sample t -statistic to compare the mean reading scores of two groups of “slow learners” who had been taught to read by two different methods. The data
Find the p -value for the test in Example 10 , using the F -tables in Appendix:Tables . Compare this with the exact p -value obtained from a computer printout.
An experimenter wants to compare the metabolic rates of white mice subjected to different drugs. The weights of the mice may affect their metabolic rates; thus, the experimenter wishes to obtain mice
85 Scouting an NFL free agent. In seeking a free-agent NFL running back, a general manager is looking for a player with high mean yards gained per carry and a small standard deviation. Suppose the GM
84 Rat damage in sugarcane. Poisons are used to prevent rat damage in sugarcane fields. The U.S. Department of Agriculture is investigating whether the rat poison should be located in the middle of
79 Bulimia study. Refer to the American Statistician (May 2001) study comparing the “fear of negative evaluation”(FNE) scores for bulimic and normal female students, presented in Exercise 19.
76 Find the appropriate values of n1 and n2 (assume that n1 = n2 ) needed to estimate (m1 - m2) witha. A sampling error equal to 3.2 with 95% confidence.From prior experience, it is known that s1
75 Suppose you want to estimate the difference between two population means correct to within 2.2 with probability.95. If prior information suggests that the population variances are approximately
74 If the sample-size calculation yields a value of n that is too large to be practical, how should you proceed?
72 In determining the sample sizes for estimating m1 - m2, how do you obtain estimates of the population variances(s1)2 and (s2)2 used in the calculations?
68 Detection of rigged school milk prices (cont’d). Market allocation is a common form of collusive behavior in bidrigging conspiracies. Under collusion, the same dairy usually controls the same
65 Killing insects with low oxygen. In a Journal of Agricultural, Biological, and Environmental Statistics (Sept. 2000) study of the mortality of rice weevils exposed to low oxygen, 31,386 of 31,421
63 Racial profiling by the LAPD. Racial profiling is a term used to describe any police action that relies on ethnicity rather than behavior to target suspects engaged in criminal activities. Does
60 Is steak your favorite barbeque food? July is National Grilling Month in the United States. On July 1, 2008, The Harris Poll #70 reported on a survey of Americans’ grilling preferences. When
58 Sketch the sampling distribution of 1pn 1 - pn 22 based on independent random samples of n1 = 100 and n2 = 200 observations from two binomial populations with probabilities of success p1 = .1 and
57 Random samples of size n1 = 50 and n2 = 60 were drawn from populations 1 and 2, respectively. The samples yielded pn 1 = .4 and pn 2 = .2. Test H0: 1p1 - p22 = .1 against Ha: 1p1 - p22 7 .1, using
56 Independent random samples, each containing 800 observations, were selected from two binomial populations. The samples from populations 1 and 2 produced 320 and 400 successes, respectively.a. Test
55 Construct a 95% confidence interval for 1p1 - p22 in each of the following situations:a. n1 = 400, pn 1 = .65; n2 = 400, pn 2 = .58b. n1 = 180, pn 1 = .31; n2 = 250, pn 2 = .25c. n1 = 100, pn 1 =
54 In each case, determine whether the sample sizes are large enough to conclude that the sampling distribution of 1pn 1 - pn 22 is approximately normal.a. n1 = 10, n2 = 12, pn 1 = .50, pn 2 = .50b.
53 Consider making an inference about p1 - p2, where there are x1 successes in n1 binomial trials and x2 successes in n2 binomial trials.a. Describe the distributions of x1 and x2.b. For large
52 What is the problem with using the z -statistic to make inferences about p1 - p2 when the sample sizes are both small?
51 What conditions are required for valid large-sample inferences about p1 - p2 ?
Use a statistical software package to conduct the test presented in Example 6 .Find and interpret the p -value of the test.
49 Homophone confusion in Alzheimer’s patients. A homophone is a word whose pronunciation is the same as that of another word having a different meaning and spelling(e.g., nun and none, doe and
48 Light-to-dark transition of genes. Synechocystis, a type of cyanobacterium that can grow and survive under a wide range of conditions, is used by scientists to model DNA behavior. In the Journal
47 Impact of red light cameras on car crashes. To combat red-light-running crashes—the phenomenon of a motorist entering an intersection after the traffic signal turns red and causing a
46 Ethical sensitivity of teachers towards racial intolerance.Many high schools have education programs that encourage teachers to embrace racial tolerance, recognize ethnic diversity, and overcome
43 Acidity of mouthwash. Acid has been found to be a primary cause of dental caries (cavities). It is theorized that oral mouthwashes contribute to the development of caries due to the antiseptic
199 Most likely coin-toss sequence. In Parade Magazine ’s(Nov. 26, 2000) column “Ask Marilyn,” the following question was posed: “I have just tossed a [balanced] coin 10 times, and I ask you
198 Flawed Pentium computer chip. In October 1994, a flaw was discovered in the Pentium microchip installed in personal computers. The chip produced an incorrect result when dividing two numbers.
197 “Let’s Make a Deal.” Marilyn vos Savant, who is listed in the Guinness Book of World Records Hall of Fame as having the “Highest IQ,” writes a weekly column in the Sunday newspaper
41 The placebo effect and pain. According to research published in Science (Feb. 20, 2004), the mere belief that you are receiving an effective treatment for pain can reduce the pain you actually
196 Odd Man Out. Three people play a game called “Odd Man Out.” In this game, each player flips a fair coin until the outcome (heads or tails) for one of the players is not the same as that for
195 The perfect bridge hand. According to a morning news program, a very rare event recently occurred in Dubuque, Iowa. Each of four women playing bridge was astounded to note that she had been dealt
194 Chance of winning at “craps.” A version of the dice game“craps” is played in the following manner. A player starts by rolling two balanced dice. If the roll (the sum of the two numbers
193 Accuracy of pregnancy tests. Seventy-five percent of all women who submit to pregnancy tests are really pregnant.A certain pregnancy test gives a false positive result with probability .02 and a
192 Language impairment in children. Children who develop unexpected difficulties with the spoken language are often diagnosed as specifically language impaired (SLI). A study published in the
191 Finding an organ transplant match. One of the problems encountered with organ transplants is the body’s rejection of the transplanted tissue. If the antigens attached to the tissue cells of the
190 Chance of winning at blackjack. Blackjack, a favorite game of gamblers, is played by a dealer and at least one opponent.At the outset of the game, 2 cards of a 52-card bridge deck are dealt to
189 Odds of winning a horse race. Handicappers for horse races express their beliefs about the probability of each horse winning a race in terms of odds . If the probability of event E is P(E) , then
186 Dream experiment in psychology. A clinical psychologist is given tapes of 20 subjects discussing their recent dreams. The psychologist is told that 10 are highanxiety individuals and 10 are
184 Monitoring the quality of power equipment. Mechanical Engineering (Feb. 2005) reported on the need for wireless networks to monitor the quality of industrial equipment. For example, consider
182 Selecting committee members. The Republican governor of a state with no income tax is appointing a committee of five members to consider changes in the income tax law.There are 15 state
181 Maize seeds. The genetic origin and properties of maize(modern-day corn) were investigated in Economic Botany .Seeds from maize ears carry either single spikelets or paired spikelets, but not
180 Lie detector test. Consider a lie detector called the Computerized Voice Stress Analyzer (CVSA). The manufacturer claims that the CVSA is 98% accurate and, unlike a polygraph machine, will not be
179 Shooting free throws. In college basketball games, a player may be afforded the opportunity to shoot two consecutive foul shots (free throws).a. Suppose a player who makes (i.e., scores on) 80%
177 Errors in estimating job costs. A construction company employs three sales engineers. Engineers 1, 2, and 3 estimate the costs of 30%, 20%, and 50%, respectively, of all jobs bid on by the
174 Chemical insect attractant. An entomologist is studying the effect of a chemical sex attractant (pheromone) on insects.Several insects are released at a site equidistant from the pheromone under
172 Herbal medicines survey. In the American Association of Nurse Anesthetists Journal (Feb. 2000) study on the use of herbal medicines before surgery, 51% of surgical patients use herbal medicines
171 Fungi in beech forest trees. Beechwood forests in East Central Europe are being threatened by dynamic changes in land ownership and economic upheaval. The current status of the beech tree species
170 Oil spill impact on seabirds. In the Journal of Agricultural, Biological, and Environmental Statistics (Sept. 2000) study of the impact of the Exxon Valdez tanker oil spill on the seabird
169 Mathematics achievement test. According to the National Center for Education Statistics, only 5% of U. S. eighth graders score above 655 on a mathematics assessment test. Find the probability
39 Healing potential of handling museum objects. Does handling a museum object have a positive impact on a sick patient’s well-being? To answer this question, researchers at the University College
168 Selecting a sample. A random sample of five students is to be selected from 50 sociology majors for participation in a special program.a. In how many different ways can the sample be drawn?b.
166 Sterile couples in Jordan. A sterile family is a couple that has no children by their deliberate choice or because they are biologically infertile. Couples who are childless by chance are not
165 Post office violence. The Wall Street Journal (Sept. 1, 2000)reported on an independent study of postal workers and violence at post offices. In a sample of 12,000 postal workers, 600 were
+ Use the applet entitled Random Numbers to generate a list of 50 numbers between 1 and 100, inclusive. Use the list to find each of the following probabilities:a. The probability that a number
163 Two events, A and B , are independent, with P1A2 = .3 and P1B2 = .1.a. Are A and B mutually exclusive? Why?b. Find P1AB2 and P1BA2 .c. Find P1A B2.
162 A balanced die is thrown once. If a 4 appears, a ball is drawn from urn 1; otherwise, a ball is drawn from urn 2.Urn 1 contains four red, three white, and three black balls.Urn 2 contains six red
161 A fair die is tossed, and the up face is noted. If the number is even, the die is tossed again; if the number is odd, a fair coin is tossed. Consider the following events:A: 5A head appears on
159 Given that P1A B2 = .4 and P1AB2 = .8, find P ( B ).
158 For two events A and B , suppose P1A2 = .7, P1B2 = .5, and P1A B2 = .4. Find P1A B2.
157 A and B are mutually exclusive events, with P1A2 = .2 and P1B2 = .3.a. Find P1AB2 .b. Are A and B independent events?
156 A sample space consists of four sample points S1, S2, S3, and S4, where P(S12 = .2, P(S22 = .1, P(S32 = .3, and P(S42 = .4.a. Show that the sample points obey the two probability rules for a
155 Use the symbols ∩ , ∪ ,| , andc, to convert the following statements into compound events involving events A and B , where A = 5You purchase a notebook computer6 and B = 5You vacation in
154 Which of the following pairs of events are mutually exclusive?a. A = 5The Tampa Bay Rays win the World Series next year.6 B = 5Evan Longoria, Rays infielder, hits 75 home runs runs next year.6b.
153 Forensic analysis of JFK assassination bullets. Following the assassination of President John F. Kennedy (JFK) in 1963, the House Select Committee on Assassinations (HSCA)conducted an official
152 Repairing a computer system. The local area network(LAN) for the College of Business computing system at a large university is temporarily shut down for repairs.Previous shutdowns have been due
151 Intrusion detection systems. Refer to the Journal of Research of the National Institute of Standards and Technology (Nov.–Dec. 2003) study of a double intrusion detection system with
150 Nondestructive evaluation. Nondestructive evaluation(NDE) describes methods that quantitatively characterize materials, tissues, and structures by noninvasive means, such as X-ray computed
149 Mining for dolomite. Dolomite is a valuable mineral that is found in sedimentary rock. During mining operations, dolomite is often confused with shale. The radioactivity features of rock can aid
148 HIV testing and false positives. Bayes’s rule was applied to the problem of HIV testing in The American Statistician(Aug. 2008). In North America, the probability of a person having HIV is
147 Tests for Down syndrome. Currently, there are three diagnostic tests available for chromosome abnormalities in a developing fetus: triple serum marker screening, ultrasound, and amniocentesis.
146 Contaminated fish. The U.S. Army Corps of Engineers’Performed a study on the DDT contamination of fish in the Tennessee River (in Alabama) . Part of the investigation focused on how far
37 A paired difference experiment yielded the following results:nd = 40, xd = 11.7, sd = 6.a. Test H0: md = 10 against Ha: md 10, where md = (m1 - m2). Use a = .05.b. Report the p -value for the
145 Drug testing in athletes. Due to inaccuracies in drug-testing procedures (e.g., false positives and false negatives), in the medical field the results of a drug test represent only one factor in

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