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statistics

Statistics 13th Edition James T. McClave - Solutions

Will the sampling distribution of x always be approximately normally distributed? Explain.
Describe how you could obtain the simulated sampling distribution of a sample statistic?
Define the target parameter.
A random sample of 100 observations from a normally distributed population possesses a mean equal to 83.2 and a standard deviation equal to 6.4.a. Find a 95% confidence interval for µ.b. What do you mean when you say that a confidence coefficient is .95?c. Find a 99% confidence interval for µ.d.
In each of the following instances, determine whether you would use a z- or t-statistic (or neither) to form a 95% confidence interval for μ; then look up the appropriate z or t value.a. Random sample of size n = 21 from a normal distribution with unknown mean m and standard deviation σb. Random
Refer to The Sport Journal (Winter 2004) study on the effectiveness of a speed-training program for football players, Exercise 7.26 (p. 326). The decreases in 40-yard sprint times (time after training minus time before training) for 38 players are saved in the SPRINT file. An athlete's sprint
Consider the following probability distribution:a. Find ( and (2.b. Find the sampling distribution of the sample mean x for a random sample of n = 2 measurements from this distribution.c. Show that xÌ… is and unbiased estimator of (.d. Find the sampling distribution of the sample variance s2 for
Alzheimer's disease is a progressive disease of the brain. The journal eCAM (Nov. 2006) published an article that critiqued the quality of the methodology used in studies on Alzheimer's treatment. For each in a sample of 13 studies, the quality of the methodology was measured on the Wong scale,
Refer to the Applied Psychology in Criminal Justice (Sept. 2009) study of the personality characteristics of drug dealers, Exercise 2.102 (p. 77). Recall that each in a sample of 100 convicted drug dealers was scored on the Wanting Recognition (WR) Scale, which provides a quantitative measure of a
Refer to the National Snow and Ice Data Center (NSIDC) collection of data on the albedo, depth, and physical characteristics of ice-melt ponds in the Canadian Arctic, presented in Exercise 2.15 (p. 40). Albedo is the ratio of the light reflected by the ice to that received by it. (High albedo
A team of university psychologists conducted a review of studies that examined the relationship between personality and aggressive behavior (Psychological Bulletin, Vol. 132, 2006). One variable of interest was the difference between the aggressive behavior level of individuals in the study who
In Alcohol & Alcoholism (Jan. /Feb. 2007), psychologists at the University of Pennsylvania compared the levels of alcohol consumption of male and female freshman students. Each student was asked to estimate the amount of alcohol (beer, wine, or liquor) they consume in a typical week. Summary
State the two problems (and corresponding solutions) that arise with using a small sample to estimate µ.
Let to be a specific value of t. Use technology or Table III in Appendix B to find to values such that the following statements are true:a. P (t ≥ to) = .025, where df = 10b. P (t ≥ to) = .01, where df = 17c. P (t ≤ to) = .005, where df = 6d. P (t ≤ to) = .05, where df = 13
Refer to the British Journal of Music Education (Mar. 2014) study of performance anxiety by music students, Exercise 2.39 (p. 40). Recall that the Performance Anxiety Inventory (PAI) was used to measure music performance anxiety on a scale from 20 to 80 points. The table below gives PAI values for
Due to habitat, giraffes travel in small groups. Hence, they require excellent vision in order to detect predators. The eyesight of giraffes was studied in African Zoology (Oct. 2013). The researchers measured a variety of eye characteristics for 27 giraffes native to Zimbabwe, Africa. One variable
Refer to the Aquatic Biology (Vol. 9, 2010) study of green sea turtles inhabiting the Grand Cayman South Sound lagoon, Exercise 7.24 (p. 326). Time-depth recorders were deployed on 6 of the 76 captured turtles. The time-depth recorders allowed the environmentalists to track the movement of the sea
What area of the United States has the least amount of daylight, on average? Having grown up in western Pennsylvania, co-author Sincich wonders if it is his hometown of Sharon, PA. Data on the number of minutes of daylight per day in Sharon, PA, for 12 randomly selected days (one each month) in a
A team of psychologists and neuroscientists tested the pitch memory of individuals diagnosed with amusia (a disorder that impacts one's perception of music) and reported their results in Advances in Cognitive Psychology (Vol. 6, 2010). Each in a sample of 17 amusiacs listened to a series of tone
Refer to the American Journal of Archaeology (Jan. 2014) study of shaft graves in ancient Greece, Exercise 2.37 (p. 50). Recall that shaft graves are named for the beautifully decorated sword shafts that are buried along with the bodies. The table on p. 336 gives the number of shafts buried at each
Ascaridia galli is a parasitic roundworm that attacks the intestines of birds, especially chickens and turkeys. Scientists are working on a synthetic vaccine (antigen) for the parasite. The success of the vaccine hinges on the characteristics of DNA in peptide (protein) produced by the antigen. In
A random sample of size n = 196 yielded p̂ = .64.a. Is the sample size large enough to use the methods of this section to construct a confidence interval for p? Explain.b. Construct a 95% confidence interval for p.c. Interpret the 95% confidence interval.d. Explain what is meant by the phrase "95%
Refer to Exercise 6.5 and find E(x) = (. Then use the sampling distribution of xÌ… found in Exercise 6.5 to find the expected value of xÌ… . Note that E(x) = (?Refer to exercise 6.5,Consider the population described by the probability distribution shown here:The random variable x is observed
Refer to the Early Childhood Education Journal (Mar. 2014) study of interactions in a children's museum, Exercise 2.19 (p. 41). (Interactions by visitors to the museum included show and-tell, learning, teaching, refocusing, participatory play, advocating, and disciplining interactions.) Recall that
The International Nanny Association reports that in a sample of 528 in-home child care providers (nannies), 20 work for either a nationally known, a locally known, or an internationally known celebrity (2011 International Nanny Association Salary and Benefits Survey). Use Wilson's adjustment to
Refer to the Journal of Quantitative Criminology (Mar. 2014) study of a program designed to curb street gang gun violence, Exercise 2.18 (p. 41). After implementation of Boston's Operation Ceasefire program, the researchers examined 80 shootings by members of a particular Boston street gang over
Find zα/2 for each of the following: a = .10 α = .01 α = .05 α = .20
It costs you $10 to draw a sample of size n = 1 and measure the attribute of interest. You have a budget of $1,200. a. Do you have sufficient funds to estimate the population mean for the attribute of interest with a 95% confidence interval 4 units in width? Assume that ( = 12. b. If a 90%
Refer to the African Zoology (Oct. 2013) study of a giraffe's eyesight, Exercise 7.38 (p. 334). Recall that the researchers measured the eye mass for a sample of 27 giraffes native to Zimbabwe, Africa, and found x̅ = 53.4 grams and s = 8.6 grams. Suppose the objective is to sample enough giraffes
A random sample of n measurements was selected from a population with unknown mean µ and standard deviation σ = 20. Calculate a 95% confidence interval for µ for each of the following situations: a. n = 75, x̅ = 28 b. n = 200, x̅ = 102 c. n = 100, x̅ = 15 d. n = 100, x̅ = 4.05 e. Is the
Which hypothesis, the null or the alternative, is the status quo hypothesis? Which is the research hypothesis?
In a study investigating a link between walking and improved health (Social Science & Medicine, Apr. 2014), researchers reported that adults walked an average of 5.5 days in the past month for the purpose of health or recreation. Specify the null and alternative hypotheses for testing whether the
According to the Environmental Protection Agency (EPA) Fuel Economy Guide, the 2014 Honda Civic automobile obtains a mean of 36 miles per gallon (mpg) on the highway. Suppose Honda claims that the EPA has underestimated the Civic's mileage. To support its assertion, the company selects n = 50 model
Refer to the Journal of Herpetology (Dec. 2014) study of whether alligators can locate underwater sounds, Exercise 8.81 (p. 406). Recall that the researchers assumed that the proportion of alligators moving toward the underwater sound expected by chance is .5. Also, in a sample of n = 50
Refer to the Acoustical Science & Technology (Vol. 35, 2014) study of irrelevant speech effects, Exercise 8.47 (p. 392). Recall that 71 subjects performed a memorization task under two conditions: (1) with irrelevant background speech and (2) in silence. Descriptive statistics on the relative
Refer to the American Journal of Archaeology (Jan. 2014) study of sword shaft graves in ancient Greece, Exercise 2.37 (p. 50). The number of sword shafts buried at each of 13 recently discovered grave sites is reproduced in the following table. Let (represent the standard deviation of the number of
The Sloan Survey of Online Learning, "Going the Distance: Online Education in the United States, 2011," reported that 68% of college presidents believe that their online education courses are as good as or superior to courses that utilize traditional face-to-face instruction. a. Give the null
Geographical Analysis (Oct. 2006) published a study of a new method for analyzing remote-sensing data from satellite pixels in order to identify urban land cover. The method uses a numerical measure of the distribution of gaps, or the sizes of holes, in the pixel, called lacunarity. Summary
A biologist and a zoologist at the University of Florida were the first scientists to test the effectiveness of a high-tech handheld device designed to instantly identify the DNA of an animal species (PLOS Biology, Dec. 2005). They used the DNA-reading device on tissue samples collected from
When bonding teeth, orthodontists must maintain a dry field. A bonding adhesive (called "Smartbond") has been developed to eliminate the necessity of a dry field. However, there is concern that the new bonding adhesive is not as strong as the current standard, a composite adhesive (Trends in
The U.S. Department of Agriculture's National School Lunch Program mandates that for a high school to receive reimbursement for school lunches, the number of calories served at lunch must be no more than 850 calories. Suppose a nutritionist believes that the true mean number of calories served at
Suppose you are interested in conducting the statistical test of H0: μ = 200 against Ha: μ > 200, and you have decided to use the following decision rule: Reject H0 if the sample mean of a random sample of 100 items is more than 215. Assume that the standard deviation of the population is 80. a.
Refer to the Business and Society (Mar. 2011) study on the sustainability behaviors of CPA corporations, Exercise 7.18 (p. 324). Recall that the level of support for corporate sustainability (measured on a quantitative scale ranging from 0 to 160 points) was obtained for each in a sample of 992
Psychologists conducted a survey of 258 student drivers and their attitudes toward speeding and reported the results in the British Journal of Educational Psychology (Vol. 80, 2010). One of the variables of interest was the response to the question, "Are you confident that you can resist your
According to a theory in psychology, young female adults show more emotional empathy toward others than do males. The Journal of Moral Education (June 2010) tested this theory by examining the attitudes of a sample of 30 female college students. Each student completed the Ethic of Care Interview,
Refer to the Journal of Adolescence (Apr. 2010) study of adolescents' disclosure of their dating and romantic relationships, Exercise 1.33 (p. 23). Recall that a sample of 222 high school students was recruited to participate in the study. One of the variables of interest was the level of
An international team of economists investigated the possible link between IQ and birth order in CESifo Economic Studies (Vol. 57, 2011). The data source for the research was the Medical Birth Registry of Norway. It is known that the mean IQ (measured in stanines) for all Norway residents is 5.2
Archeologists have found that humerus bones from the same species of animal tend to have approximately the same length-to-width ratios. It is known that species A exhibits a mean ratio of 8.5.Suppose 41 fossils of humerus bones were unearthed at an archeological site in East Africa, where species A
A popular cooling method for a gas turbine engine uses high-pressure inlet fogging. The performance of a sample of 67 gas turbines augmented with high-pressure inlet fogging was investigated in the Journal of Engineering for Gas Turbines and Power (Jan. 2005). One measure of performance is heat
Refer to the Acoustical Science & Technology (Vol. 35, 2014) study of irrelevant speech effects, Exercise 7.14 (p. 323). Recall that subjects performed a memorization task under two conditions: (1) with irrelevant background speech and (2) in silence. The difference in the error rates for the
The Community Mental Health Journal (Aug. 2000) presented the results of a survey of over 6,000 clients of the Department of Mental Health and Addiction Services (DMHAS) in Connecticut. One of the many variables measured for each mental health patient was frequency of social interaction (on a
A study published in the journal Applied Linguistics (Feb. 2014) investigated the effects of implicit and explicit classroom interventions during the instruction of Japanese to English as- a-first-language (EFL) students. EFL students at a Japanese university were divided into implicit (n = 44) and
In what ways are the distributions of the z-statistic and t-statistic alike? How do they differ?
Under what circumstances should you use the t-distribution in testing a hypothesis about a population mean?
What is the problem with using the z-statistic to make inferences about p1 - p2 when the sample sizes are both small?
Refer to the British Journal of Music Education (Mar. 2014) study of performance anxiety by music students, Exercise 7.37 (p. 334). Recall that the Performance Anxiety Inventory (PAI) was used to measure music performance anxiety on a scale from 20 to 80 points. The table below gives PAI values for
Refer to the Radiation Protection Dosimetry (Dec. 2010) study of radon exposure in Egyptian tombs, Exercise 7.39 (p. 334). The radon levels-measured in becquerels per cubic meter (Bq/m3)-in the inner chambers of a sample of 12 tombs are listed in the table. For the safety of the guards and
What conditions are required for a valid large-sample test for p?
For the binomial sample sizes and null-hypothesized values of p in each part, determine whether the sample size is large enough to use the normal approximation methodology presented in this section to conduct a test of the null hypothesis H0: P = P0. a. n = 500, P0 = .05 b. n = 100, P0 = .99 c. n =
If you use the Internet, have you ever paid to access or download music? This was one of the questions of interest in a recent Pew Internet and American Life Project Survey (Oct. 2010). In a representative sample of 755 adults who use the Internet, 506 stated that they have paid to download music.
Refer to the IEEE Journal of Oceanic Engineering (Apr. 2013) study of the characteristics of subcarriers-telecommunication signals carried on top of another-for underwater acoustic communications, Exercise 4.80 (p. 213). Recall that a subcarrier can be classified as either a data subcarrier (used
Settlers often chose sites to live and build communities in based on the landscape's defensibility. The defensibility of archaeological sites in the Northwest Pacific was investigated in the Journal of Anthropological Archaeology (Vol. 35, 2014). A defensibility index was calculated for each in a
Indiana University professors investigated first-year college students' knowledge of astronomy (Astronomy Education Review, Vol. 2, 2003). One concept of interest was the Big Bang theory of the creation of the universe. In a sample of 148 freshman students, 37 believed that the Big Bang theory
What is the relationship between β (the probability of committing a Type II error) and the power of the test?
Independent random samples were selected from each of two normally distributed populations, n1 = 16 from population 1 and n2 = 25 from population 2. The means and variances for the two samples are shown in the following table. Sample 1...................................Sample2 n1 =
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. Sample 1 ____________ Sample 2 3.1 ............................... 2.3 4.3 ...............................
In Kenya, human induced land-use changes and excessive resource extraction have threatened the jungle ecosystem by reducing animal grazing areas and disrupting access to water sources. In Landscape & Ecology Engineering (Jan. 2013), researchers compared hippopotamus grazing patterns in two
Refer to Exercise 9.19 (p. 449). The "fear of negative evaluation" (FNE) scores for the 11 bulimic females and 14 females with normal eating habits are saved in the BULIMIA file. The confidence interval you constructed in Exercise 9.19 requires that the variance of the FNE scores of bulimic females
Refer to the Thinking and Reasoning (Oct. 2006) study of the cognitive skills required for successful arguments, presented in Exercise 9.25 (p. 451). Recall that 52 psychology graduate students were equally divided into two groups. Group 1 was presented with arguments that always attempted to
Refer to the American Journal of Infection Control (Aug. 2014) study of the hygiene of hand greetings, Exercise 9.24 (p. 451). The number of bacteria transferred from a gloved hand dipped into a culture of bacteria to a second gloved hand contacted by either a handshake, high five, or fist bump was
Refer to the Archives of Pediatrics and Adolescent Medicine (Dec. 2007) study of honey as a children's cough remedy, Exercise 2.40 (p. 51). The data (cough improvement scores) for the 33 children in the DM dosage group and the 35 children in the honey dosage group are reproduced in the next table.
Refer to the Journal of Agricultural, Biological, and Environmental Statistics (Sept. 2000) study of the impact of a tanker oil spill on the seabird population in Alaska, presented in Exercise 2.205 (p. 111). Recall that for each of 96 shoreline locations (called transects), the number of seabirds
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 critically. The subjects of the experiment were five males who took part in an American expedition climbing Mount Everest. At the base camp,
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 it takes to read silently? To answer this question, 42 undergraduate psychology students participated in a reading experiment (Memory &
Chance (Fall 2002) described a lawsuit charging Intel Corp. with infringing on a patent for an invention used in the automatic manufacture of computer chips. In response, Intel accused the inventor of adding material to his patent notebook after the patent was witnessed and granted. The case rested
Refer to the Journal of Biogeography (Dec. 2003) study of ants in Mongolia (central Asia), presented in Exercise 2.68 (p. 63). Recall that botanists placed seed baits at 5 sites in the Dry Steppe region and 6 sites in the Gobi Desert and observed the number of ant species attracted to each site.
Refer to the Journal of Agricultural, Biological, and Environmental Statistics (Sept. 2000) study of the mortality of rice weevils exposed to low oxygen, presented in Exercise 8.92 (p. 408). Recall that 31,386 of 31,421 rice weevils were found dead after exposure to nitrogen gas for 4 days. In a
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 a possible link between jet lag and memory impairment, a University of Bristol (England) neurologist recruited 20 female flight
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 instruments that are available to measure the paper specimens are subject to error, but they can be adjusted so that the mean readings
Each year, the state of Kentucky invites bids from dairies to supply half-pint containers of fluid milk products for its school districts. In several school districts in northern Kentucky (called the "tri-county" market), two suppliers-Meyer Dairy and Trauth Dairy-were accused of price fixing, that
Taste testers of new food products are presented with several competing food samples and asked to rate the taste of each on a 9-point scale (where 1 = "dislike extremely" and 9 = "like extremely"). In the Journal of Sensory Studies (June 2014), food scientists compared two different taste testing
Researchers at Griffin University (Australia) conducted a study to determine whether video game players have superior visual attention skills compared to non-video game players (Journal of Articles in Support of the Null Hypothesis, Vol. 6, 2009). Two groups of male psychology students-32 video
Health professionals warn that transmission of infectious diseases may occur during the traditional handshake greeting. Two alternative methods of greeting (popularized in sports) are the "high five" and the "fist bump." Researchers compared the hygiene of these alternative greetings in a designed
A study in the Academy of Management Journal (Oct. 2007) investigated how rude behaviors influence a victim's task performance. College students enrolled in a management course were randomly assigned to one of two experimental conditions: rudeness condition (45 students) and control group (53
Two populations are described in each of the cases that follow. In which cases would it be appropriate to apply the small-sample t-test to investigate the difference between the population means? a. Population 1: Normal distribution with variance σ21 Population 2: Skewed to the right with variance
Refer to the Minerals Engineering (Vol. 46-47, 2013) study of the impact of calcium and gypsum on the flotation properties of silica in water, Exercise 2.48 (p. 53). Fifty solutions of deionized water were prepared both with and without calcium/ gypsum, and the level of flotation of silica in the
What are the advantages of using a paired difference experiment over an independent samples design?
Structures built on a shallow foundation (e.g., a concrete slab-on-grade foundation) are susceptible to settlement. Consequently, accurate settlement prediction is essential in the design of the foundation. Several methods for predicting settlement of shallow foundations on cohesive soil were
Scale deposits can cause a serious reduction in the flow performance of a well. A study published in the Journal of Petroleum and Gas Engineering (Apr. 2013) compared two methods of estimating the damage from scale deposits (called skin factor). One method of estimating the well skin factor uses a
To combat red light- running crashes, many states are adopting photo-red enforcement programs. In these programs, red light cameras installed at dangerous intersections photograph the license plates of vehicles that run the red light. How effective are photo-red enforcement programs in reducing red
A classic psychological test involves adding a set of numbers (e.g., 1,000 + 40 + 1,000 + 30 + 1,000 + 20 + 1,000 + 10) to evaluate cognitive behavior. In a study published in Advances in Cognitive Psychology (Jan. 2013), undergraduate students were all given the serial addition task, with the
Response rates to Web surveys are typically low, partially due to users starting but not finishing the survey. The factors that influence response rates were investigated in Survey Methodology (Dec. 2013). In a designed study, Web users were directed to participate in one of several surveys with
A study was conducted to determine the effectiveness of pheromones produced by two different strains of fall armyworms: the corn-strain and the rice-strain (Journal of Chemical Ecology, Mar. 2013). Both corn-strain and rice-strain male armyworms were released into a field containing a synthetic
When you sign on to your Facebook account, you are granted access to more than 1 million relying party (RP) Web sites. This single sign-on (SSO) scheme is enabled by OAuth 2.0, an open and standardized Web resource authorization protocol. Although the protocol claims to be secure, there is
Linear enamel hypoplasia (LEH) defects are pits or grooves on the tooth surface that are typically caused by malnutrition, chronic infection, stress, and trauma. A study of LEH defects in prehistoric Japanese cultures was published in the American Journal of Physical Anthropology (May 2010). Three
In determining the sample sizes for estimating (1 - (2, how do you obtain estimates of the population variances ((2)2 and ((2)2 used in the calculations?
Refer to the Advances in Cognitive Psychology (Jan. 2013) study of influencing performance in a classic psychological test that involved adding a set of numbers, Exercise 9.66 (p. 471). Recall that one group of students saw each of the numbers for 2 seconds on the screen while a second group saw
Refer to the Journal of Articles in Support of the Null Hypothesis (Vol. 6, 2009) study comparing the visual attention skill of video game and non-video game players, Exercise 9.22 (p. 450). Recall that there was no significant difference between the mean score on the attentional blink test of
A field experiment was conducted to compare the effectiveness of different traps for catching beetles (Journal of Chemical Ecology, Vol. 94, 2011). Paraffin traps were baited either with or without linalool. Also, the color of the trap was varied as green or yellow. Seven traps for each combination
Refer to the Tropical Journal of Pharmaceutical Research (June 2003) study of the impact of binding agent, binding concentration, and relative density on the mean dissolution time of pain-relief tablets, presented in Exercise 10.16 (p. 510). Recall that binding agent was set at two levels (khaya

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