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Statistics 12th Edition James T. McClave, Terry T Sincich - Solutions

The Test of Knowledge about Epilepsy (KAE), which is designed to measure attitudes toward persons with epilepsy, uses 20 multiple-choice items, all of which are incorrect. For each person, two scores (ranging from 0 to 20) are obtained: an attitude score (KAE-A) and a general-knowledge score
True or False. The sampling distribution of x-bar is normally distributed, regardless of the size of the sample n.
The standard deviation (or, as it is usually called, the standard error) of the sampling distribution for the sample mean, x , is equal to the standard deviation of the population from which the sample was selected, divided by the square root of the sample size. That is, σx-bar = σ/√n a. As the
A random sample of 40 observations is to be drawn from a large population of measurements. It is known that 30% of the measurements in the population are 1’s, 20% are 2’s, 20% are 3’s, and 30% are 4’s.a. Give the mean and standard deviation of the (repeated) sampling distribution of x-bar,
Use a statistical software package to generate 100 random samples of size n = 2 from a population characterized by a normal probability distribution with a mean of 100 and a standard deviation of 10. Compute x-bar for each sample, and plot a frequency distribution for the 100 values of x-bar.
Suppose x equals the number of heads observed when a single coin is tossed; that is, x = 0 or x = 1. The population corresponding to x is the set of 0’s and 1’s generated when the coin is tossed repeatedly a large number of times. Suppose we select n = 2 observations from this population. (That
According to a Natimal Business Travel Association (NBTA) 2008 survey, the average salary of a travel management professional is $97,300. Assume that the standard deviation of such salaries is $30,000. Consider a random sample of 50 travel management professionals, and let x represent the mean
Interpersonal violence (e.g., rape) generally leads to psychological stress for the victim. Clinical Psychology Review (Vol. 15, 1995) reported on the results of all recently published studies of the relationship between interpersonal violence and psychological stress. The distribution of the time
To determine whether a metal lathe that produces machine bearings is properly adjusted, a random sample of 25 bearings is collected and the diameter of each is measured.a. If the standard deviation of the diameters of the bearings measured over a long period of time is .001 inch, what is the
Researchers at the Terry College of Business at the University of Georgia sampled 344 business students and asked them this question: “Over the course of your lifetime, what is the maximum number of years you expect to work for any one employer?” The sample resulted in x-bar = 19.1 years.
Many species of terrestrial tree frogs that hibernate at or near the ground surface can survive prolonged exposure to low winter temperatures. In freezing conditions, the frog’s body temperature, called its supercooling temperature, remains relatively higher because of an accumulation of glycerol
Over the past 20 years, the Journal of Abnormal Psychology has published numerous studies on the relationship between juvenile delinquency and poor verbal abilities. Assume that scores on a verbal IQ test have a population mean μ = 107 and a population standard deviation σ = 15. a. What shape
An article in Industrial Engineering (August 1990) discussed the importance of modeling machine downtime correctly in simulation studies. As an illustration, the researcher considered a single-machine-tool system with repair times (in minutes) that can be modeled by an exponential distribution with
A soft-drink bottler purchases glass bottles from a vendor. The bottles are required to have an internal pressure of at least 150 pounds per square inch (psi). A prospective bottle vendor claims that its production process yields bottles with a mean internal pressure of 157 psi and a standard
The state of California mandates fecal indicator bacteria monitoring at all public beaches. When the concentration of fecal bacteria in the water exceeds a certain limit (400 colony-forming units of fecal coli form per 100 milliliters), local health officials must post a sign (called surf zone
What is the confidence coefficient in a 90% confidence interval for µ?
What is the confidence level of each of the following confidence intervals for µ? a. ± 1.96(σ/√n) b. ± 1.96(σ/√n) c. ± 1.96(σ/√n) d. ± 1.96(σ/√n) e. ± 1.96(σ/√n)
A random sample of 90 observations produced a mean = 25.9 and a standard deviation s = 2.7.a. Find a 95% confidence interval for the population mean µ.b. Find a 90% confidence interval for µ.c. Find a 99% confidence interval for µ.
The mean and standard deviation of a random sample of n measurements are equal to 33.9 and 3.3, respectively. a. Find a 95% confidence interval for µ if n = 100. b. Find a 95% confidence interval for µ if n = 400. c. Find the widths of the confidence intervals you calculated in parts a and b.
Hypertension is diagnosed if a patient€™s systolic blood pressure exceeds 140 mmHg and diastolic blood pressure exceeds 90 mmHg. A study of the lipid profiles of hypertensive patients was carried out and the results published in Biology and Medicine (Vol. 2, 2010). Data on fasting blood
Refer to the American Secondary Education (Fall 2009) study of middle school students’ usage of laptop computers, Exercise 2.100 (p. 72). Recall that for a sample of 106 students, the researchers reported the following statistics on how many minutes per day each student used a laptop for taking
Refer to the Evolutionary Qi Ecology Research (July 2003) study of the patterns of extinction in the New Zealand bird population, presented in Exercise. Suppose you are interested in estimating the mean egg length (in millimeters) for the New Zealand bird population.a. What is the target
Refer to the Aquatic Biology (Vol. 9, 2010) study of green sea turtles inhabiting the Grand Cayman South Sound lagoon, Exercise. The data on curved carapace (shell) length, measured in centimeters, for 76 captured turtles are displayed in the table and saved in the TURTLES file. Environmentalists
A key statistic used by football $ coaches to evaluate players is a player€™s 40-yard sprint time. Can a drill be developed for improving a player€™s speed in the sprint? Researchers at Northern Kentucky University designed and tested a speed-training program for junior varsity and varsity
Psychologists have found that twins, in their early years, tend to have lower IQs and pick up language more slowly than non-twins. The slower intellectual growth of most twins may be caused by benign parental neglect. Suppose it is desired to estimate the mean attention time given to twins per week
According to scientists, the cockroach has had 300 million years to develop a resistance to destruction. In a study conducted by researchers for S. C. Johnson & Son, Inc. (manufacturers of Raid® and Off®), 5,000 roaches (the expected number in a roach-infested house) were released in the Raid
Suppose you have selected a random sample of n = 7 measurements from a normal distribution. Compare the standard normal z-values with the corresponding (z-values if you were forming the following confidence intervals: a. 80% confidence interval b. 90% confidence interval c. 95 % confidence
Let t0 be a particular value of t. Use Table VI of Appendix A to find t0 values such that the following statements are true: a. P(-t0 < t < t0) = .95, where df = 16 b. P(t ≤ -t0 or t ≥ t0 = .05, where df = 16 c. P(t ≤ t0) = .05, where df = 16 d. P(t ≤ -to or t ≥ t0) = .10, where df =
The following sample of 16 measurements, saved in the LM7_34 file, was selected from a population that is approximately normally distributed:a. Construct an 80% confidence interval for the population mean. b. Construct a 95% confidence interval for the population mean, and compare the width of this
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 turtles in the lagoon. These 6 turtles had a mean shell length of 52.9 cm with a standard deviation of 6.8 cm. a. Use the information on the 6
The white wood material used for the roof of an ancient Japanese temple is imported from Northern Europe. The wooden roof must withstand as much as 100 centimeters of snow in the winter. Architects at Tohoku University (in Japan) conducted a study to estimate the mean bending strength of the white
Recall that botanists randomly selected five sites in the Dry Steppe region and six sites in the Gobi Desert where ants were observed. One of the variables of interest is the annual rainfall (in millimeters) at each site. Summary statistics for the annual rainfall at each site are provided in the
Alzheimer€™s disease is a progressive disease of the brain. Much research has been conducted on how to treat Alzheimer€™s. The journal eCAM (November 2006) published an article that critiqued the quality of the methodology used in studies on Alzheimer treatment. For each in a
In planning for a new forest road to be used for tree harvesting, planners must select the location that will minimize tractor skidding distance. In the Journal of Forest Engineering (July 1999), researchers wanted to estimate the true mean skidding distance along a new road in a European forest.
The “fear of negative evaluation” (FNE) scores for 11 bulimic female students and 14 normal female students, first presented in Exercise 2.40 are reproduced at the bottom of the page. a. Construct a 95% confidence interval for the mean FNE score of the population of bulimic female students.
If p is near 0 or 1, how large a sample is needed to employ the large-sample confidence interval procedure?
A random sample of size n = 144 yielded p̂ = .76.a. Is the sample size large enough to use the methods of this section to construct a confidence interval for p̂? Explain.b. Construct a 90% confidence interval for p.c. What assumption is necessary to ensure the validity of this confidence interval?
A random sample of 50 consumers taste-tested a new ^ snack food. Their responses were coded (0: do not like; 1: like; 2: indifferent), recorded and saved in the SNACK file as follows:a. Use an 80% confidence interval to estimate the proportion of consumers who like the snack food.b. Provide a
Recall that a random sample of 501 satellite radio subscribers was asked, “Do you have a satellite radio receiver in your car?” The survey found that 396 subscribers did, in fact, have a satellite receiver in their car. a. From the sample, calculate an estimate of the true proportion of
Recall that federal law prohibits restaurants from serving a cheaper look-alike variety of fish (e.g., Vermillion snapper or lane snapper) to customers who order red snapper. In an effort to estimate the true proportion of fillets that are really red snapper, a team of University of North Carolina
Speed training in football. Refer to The Sport Journal (Winter 2004) study on the effectiveness of a speed-training program for football players, Exercise. The decreases in 40-yard sprint times (time after training minus time before training) for 38 players are saved in the SPRINT file. An
Refer to the University of Colorado study of ice-melt ponds in the Canadian Arctic, presented in Exercise. Environmental engineers are using data collected by the National Snow and Ice Data Center to learn how climate affects the sea ice. Data on 504 ice melt ponds are saved in the PONDICE file. Of
Do you think you smell? If you falsely believe you emit an unpleasant, foul, or offensive body odor, you may suffer from olfactory reference syndrome (ORS). The disorder disables patients, who often isolate themselves and consider suicide. Psychiatrists disagree over how prevalent ORS is in the
Refer to the journal eCAM (November 2006) assessment of the quality of the methodology used in studies of the treatment for Alzheimer€™s disease, presented in Exercise. Data on the quality of the methodology (using the Wong scale) for each in a sample of 13 studies are reproduced in the
In each case, find the approximate sample size required to construct a 95% confidence interval for p that has sampling error SE = .06.a. Assume that p is near .3.b. Assume that you have no prior knowledge about p, but you wish to be certain that your sample is large enough to achieve the specified
In each case, find the approximate sample size required to construct a 95% confidence interval for p that has sampling error SE = .06.a. Assume that p is near .3.b. Assume that you have no prior knowledge about p, but you wish to be certain that your sample is large enough to achieve the specified
Research published in the Journal of Quantitative Criminology (March 2010) revealed that the risk of burglaries in homes located on cul-de-sacs is lower than for homes on major roads. Suppose you want to estimate the true percentage of cul-de-sac homes in your home city that were burglarized in the
Refer to the Alaskan Lichen Radionuclide Baseline Research study, presented in Exercise. In a sample of n = 9 lichen specimens, the researchers found the mean and standard deviation of the amount of the radioactive element, cesium-137, that was present to be .009 and .005 micro curie per
A gigantic ware-house located in Tampa, Florida, stores approximately 60 million empty aluminum beer and soda cans. Recently, a fire occurred at the warehouse. The smoke from the fire contaminated many of the cans with blackspot, rendering them unusable. A University of South Florida statistician
Refer to the Naval Oceanography Portal data on number of minutes of daylight per day in Sharon, PA, Exercise. An estimate of the mean number of minutes of daylight per day was obtained using data collected for 12 randomly selected days (one each month) in 2009. a. Determine the number of days in
Refer to The Sport Journal (Winter 2004) study on the effectiveness of a speed training program for football players, Exercise. The confidence interval for the population proportion of athletes who improve their sprint times after participating in the speed-training program was fairly wide due to
The chemical benzalkonium chloride (BAC) is an antibacterial agent that is added to some asthma medications to prevent contamination. Researchers at the University Of Florida College Of Pharmacy have discovered that adding BAC to asthma drugs can cause airway constriction in patients. In a sample
According to a Food and Drug Administration (FDA) study, a cup of coffee contains an average of 115 milligrams (mg) of caffeine, with the amount per cup ranging from 60 to 180 mg. Suppose you want to repeat the FDA experiment in order to obtain an estimate of the mean caffeine content in a cup of
It costs more to produce defective items—since they must be scrapped or reworked—than it does to produce non-defective items. This simple fact suggests that manufacturers should ensure the quality of their products by perfecting their production processes instead of depending on inspection of
For each of the following combinations of a and degrees of freedom (df), use Table VII in Appendix B to find the values of x2α/2 and, x2(1-α/2) that would be used to form a confidence interval for σ2. a. α = .05, df = 7 b. α = .10, df = 16 c. α = .01, df = 20 d. α = .05, df = 20
Refer to Exercise 7.97. For each part, a-d, form a 90% confidence interval for σ.In Exercise 7.97Given the following values of x , s , and n , form a 90% confidence interval for s2 .a. x̅ = 21, s = 2.5, n = 50b. x̅ = 1.3, s = .02, n = 15c. x̅ = 167, s = 31.6, n = 22d. x̅ = 9.4, s = 1.5, n = 5
Refer to the Applied Psychology in Criminal Justice (Sept. 2009) study of the personality characteristics of convicted drug dealers, Exercise. A random sample of 100 drug dealers had a mean Wanting Recognition (WR) score of 39 points, with a standard deviation of 6 points. The researchers also are
Refer to the Gene Therapy and Molecular Biology (June 2009) study of DNA in peptide (protein) produced by antigens for a parasitic roundworm in birds, Exercise. Recall that scientists tested each in a sample of 4 alleles of antigen-produced protein for level of peptide. The results were: = 1.43
Jitter in a water power system. Jitter is a term used to describe the variation in conduction time of a water power system. Low throughput jitter is critical to successful waterline technology. An investigation of throughput jitter in the opening switch of a prototype system (Journal of Applied
Shell lengths of sea turtles. Refer to the Aquatic Biology JQf (Vol. 9, 2010) study of green sea turtles inhabiting the Grand Cayman South Sound lagoon, Exercise. Recall that the data on shell length, measured in centimeters, for 76 captured turtles are saved in the TURTLES file. Use the sample
Is honey a cough remedy? Refer to the Archives of Pediatrics and Adolescent Medicine (Dec. 2007) study of honey as a remedy for coughing, Exercise. Recall that the 105 ill children in the sample were randomly divided into groups. One group received a dosage of an over-the-counter cough medicine
Let t0 represent a particular value of t from Table VI of Appendix A. Find the table values such that the following statements are true: a. P(t ≤ t0) = .05, where df = 17 b. P(t ≥ t0) = .005, where df = 14 c. P(t ≤ -t0 or t ≥ t0) = .10, where df = 6 d. P(t ≤ t0 or t ≥ t0) = .01, where
A random sample of 225 measurements is selected from a population, and the sample mean and standard deviation are = 32.5 and s = 30.0, respectively. a. Use a 99% confidence interval to estimate the mean of the population, µ. b. How large a sample would be needed to estimate µ to within .5 with
In sociology, a personal network is defined as the people with whom you make frequent contact. The Living Arrangements and Social Networks of Older Adults (LSN) research program used a stratified random sample of men and women born between 1908 and 1937 to gauge the size of the personal network of
Donations to tax-exempt organizations such as the Red Cross, the Salvation Army, the YMCA, and the American Cancer Society not only go to the stated charitable purpose, but are used to cover fundraising expenses and overhead. The CHARITY file (see table on p. 341) contains the charitable
Refer to Exercise and the Journal of Global Business (Spring 2002) survey to determine what “Made in the USA” means to consumers. Recall that 106 shoppers at a shopping mall in Muncie, Indiana, responded to the question ‘“Made in the USA’ means what percentage of U.S. labor and
The EPA wants to test a randomly selected sample of n water specimens and estimate µ, the mean daily rate of pollution produced by a mining operation. If the EPA wants a 95% confidence interval estimate with a sampling error of 1 milligram per liter (mg/L), how many water specimens are required in
Refer to the Environmental Science & Technology (September 1, 2000) study on the ammonia levels near the exit ramp of a San Francisco highway tunnel, presented in Exercise 2.184 (p. 100). The ammonia concentration (parts per million) data for eight randomly selected days during the afternoon drive
According to a University of Michigan study, many adults have experienced lingering “fright” effects from a scary movie or TV show they saw as a teenager (Tampa Tribune, March 10, 1999). In a survey of 150 college students, 39 said they still experience “residual anxiety” from a scary TV
In Exercise, you learned that the postmortem interval (PMI) is the elapsed time between death and the performance of an autopsy on the cadaver. Brain and Language (June 1995) reported on the PMIs of 22 randomly selected human brain specimens obtained at autopsy. The data, reproduced in the
Researchers at the University of Florida’s Department of Exercise and Sport Sciences conducted a study of variety in exercise workouts. A sample of 120 men and women were randomly divided into three groups, with 40 people per group. Group 1 members varied their exercise routine in workouts, group
Refer to the Applied Psycholinguistics (June 1998) study of language skills of low-income children, presented in Exercise. Each in a sample of 65 low-income children was administered the Communicative Development Inventory (CDI) exam. The sentence complexity scores had a mean of 7.62 and a standard
Refer to Exercise 2.65 (p. 59) and the Teaching of Psychology (May 1998) study in which students assisted in the training of zoo animals. A sample of 15 psychology students rated “The Training Game” as a “great” method of understanding the animal’s perspective during training on a 7-1
Suppose it is now 1 year after the poisoning was traced to ice cream bars. The manufacturer wishes to estimate the proportion who still will not purchase bars to within .02, using a 95% confidence interval. How many consumers should be sampled?
For over 20 years, the Occupational Safety & Health Administration has required companies that handle hazardous chemicals to complete material safety data sheets (MSDSs). These sheets have been criticized for being too hard to understand and complete by workers. Although improvements were
By law, all new cars must be equipped with both driver-side and passenger- side safety air bags. There is concern, however, over whether air bags pose a danger for children sitting on the passenger side. In a National Highway Traffic Safety Administration (NHTSA) study of 55 people killed by the
What is the difference between Type I and Type II errors in hypothesis testing? How do a and b relate to Type I and Type II errors?
We (generally) reject the null hypothesis when the test statistic falls into the rejection region, but we do not accept the null hypothesis when the test statistic does not fall into the rejection region. Why?
Consider a test of H0: μ = 4. In each of the following cases, give the rejection region for the test in terms of the z-statistic: a. Ha: μ >,4 a = .05 b. Ha: μ > 4, a = .10 c. Ha: μ < 4, a = .05 d. Ha: μ ≠ 4, a = .05
Researchers writing in Analysis of Verbal Behavior (Dec. 2007) reported that the mean listening time of 16-month-old infants exposed to non-meaningful monosyllabic words (e.g., “giff,” “cham,” “gack”) is 8 seconds. Set up the null and alternative hypotheses for testing the claim.
A University of Florida economist conducted a study of Virginia elementary school lunch menus. During the state-mandated testing period, school lunches averaged 863 calories (National Bureau of Economic Research, November 2002). The economist claimed that after the testing period end, the average
The Sloan Survey of Online Learning, “Making the Grade: Online Education in the United States, 2006,” reported that 60% of college presidents believe that their online education courses are as good as or superior to courses that utilize traditional face-to-face instruction ( Inside Higher Ed ,
The International Journal of Clinical and Experimental Hypnosis (Vol. 58, 2010) investigated using virtual reality hypnosis (VRH) to reduce the pain of trauma patients. Patients reported their pain intensity on the Graphic Rating Scale (GRS) both prior to and one hour after a VRH session. The
Sometimes, the outcome of a jury trial defies the “commonsense” expectations of the general public (e.g., the 1995 O. J. Simpson verdict and the 2011 Casey Anthony verdict). Such a verdict is more acceptable if we understand that the jury trial of an accused murderer is analogous to the
Explain the difference between a one-tailed and a two tailed test.
For what values of the test statistic do you reject H0? fail to reject H0?
A random sample of 64 observations produced the following summary statistics: = .323 and s2 = .034. a. Test the null hypothesis that µ = .36 against the alternative hypothesis that µ ≠ .36, using a = .10. b. Test the null hypothesis that µ = .36 against the alternative hypothesis that µ
Teenage drivers will inevitably be tempted to drive faster, even to exceed the speed limit, by their friends. Did you resist such temptations when you first began to drive? To gain insight into this phenomenon, psychologists from the United Kingdom conducted a survey of 258 student drivers and
Refer to the Current Allergy & Clinical Immunology (March 2004) study of n = 46 hospital employees who were diagnosed with a latex allergy from exposure to the powder on latex gloves, presented in Exercise. The number of latex gloves used per week by the sampled workers is summarized as
Laughter is often called “the best medicine,” since studies have shown that laughter can reduce muscle tension and increase oxygenation of the blood. In the International Journal of Obesity (Jan. 2007), researchers at Vanderbilt University investigated the physiological changes that accompany
Geographers use remote-sensing data from satellite pictures to identify urban land cover as either grassland, commercial, or residential. In Geographical Analysis (Oct. 2006), researchers from Arizona State, Florida State, and Louisiana State Universities collaborated on a new method for analyzing
During periods of high demand for electricity-especially in the hot summer months-the power output from a gas turbine engine can drop dramatically. One way to counter this drop in power is by cooling the inlet air to the turbine. An increasingly popular cooling method uses high-pressure inlet
The level of dissolved oxygen in the surface water of a lake is vital to maintaining the lake's ecosystem. Environmentalists from the University of Wisconsin monitored the dissolved oxygen levels over time for a sample of 25 lakes in the state (Aquatic Biology, May 2010). To ensure a representative
How does the observed significance level (p -alue) of a test differ from the value of a?
If a hypothesis test using α = .05 were conducted, for which of the following p -values would the null hypothesis be rejected? a. .06 b. .10 c. .01 d. .001 e. .251 f. .042
In a test of the hypothesis H0:µ= 10 versus Ha: µ ≠ 10, a sample of n = 50 observations possessed mean x = 10.7 and standard deviation s = 3.1. Find and interpret the p -value for this test.
Refer to the British Journal of Educational Psychology (Vol. 80, 2010) study of teenage drivers' temptation to exceed the speed limit, Exercise. Recall that in a survey of 258 student drivers taken 5 months after the students had attended a safe-driver presentation, responses (measured on a 7-point
Refer to the Current Allergy & Clinical Immunology (March 2004) study of latex allergy in health care workers, presented in Exercise 8.28 (p. 365). Recall that you tested H0: µ = 20 against Ha: µ < 20, where µ is the mean number of latex gloves used per week by all hospital employees, based on
According to a theory in psychology, young female adults show more emotional empathy towards 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 Applied Animal Behaviour Science (October 2000) study of domestic chickens exposed to a pecking stimulus, presented in Exercise. Recall that the average number of pecks a chicken takes at a white string over a specified time interval is known to beµ= 7.5 pecks. In an experiment in

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