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Statistics The Exploration And Analysis Of Data 007th Edition Roxy Peck, Ay L Devore - Solutions

In 2006, Boston Scientific sought approval for a new heart stent (a medical device used to open clogged arteries) called the Liberte. This stent was being proposed as an alternative to a stent called the Express that was already on the market. The following excerpt is from an article that appeared
Are the conclusions drawn consistent with the results of the hypothesis test?
What is the P-value associated with the test? Was a significance level reported (as opposed to simply reporting the P-value)? Is the chosen significance level reasonable?
Was the appropriate test used? Does the validity of the test depend on any assumptions about the sample or about the population from which the sample was selected? If so, are the assumptions reasonable?
What hypotheses are being tested? Are the hypotheses about a population mean, a population proportion, or some other population characteristic?
Let m denote the mean diameter for bearings of a certain type. A test of H0: m 0.5 versus Ha: m 0.5 will be based on a sample of n bearings. The diameter distribution is believed to be normal. Determine the value of b in each of the following cases:a. n 15, a .05, s 0.02, m 0.52b. n 15, a .05, s
Let m denote the true average lifetime (in hours) for a certain type of battery under controlled laboratory conditions. A test of H0: m 10 versus Ha:m 10 will be based on a sample of size 36. Suppose that s is known to be 0.6, from which sx 5 .1. The appropriate test statistic is then z 5 x 2 10
and x 152.4? What type of error might have been made in reaching this conclusion?
Water samples are taken from water used for cooling as it is being discharged from a power plant into a river. It has been determined that as long as the mean temperature of the discharged water is at most 150F, there will be no negative effects on the river’s ecosystem.To investigate whether
Much concern has been expressed regarding the practice of using nitrates as meat preservatives. In one study involving possible effects of these chemicals, bacteria cultures were grown in a medium containing nitrates.The rate of uptake of radio-labeled amino acid (in dpm, disintegrations per
Many consumers pay careful attention to stated nutritional contents on packaged foods when making purchases. It is therefore important that the information on packages be accurate. A random sample of n 12 frozen dinners of a certain type was selected from production during a particular period, and
hours.c. Explain why the null hypothesis was rejected in the test of Part (b) but not in the test of Part (a).
In a study of computer use, 1000 randomly selected Canadian Internet users were asked how much time they spend using the Internet in a typical week (Ipsos Reid, August 9, 2005). The mean of the sample observations was 12.7 hours.a. The sample standard deviation was not reported, but suppose that it
Medical research has shown that repeated wrist extension beyond 20 degrees increases the risk of wrist and hand injuries. Each of 24 students at Cornell University used a proposed new computer mouse design, and while using the mouse, each student’s wrist extension was recorded. Data consistent
The Economist collects data each year on the price of a Big Mac in various countries around the world.The price of a Big Mac for a sample of McDonald’s restaurants in Europe in May 2009 resulted in the following Big Mac prices (after conversion to U.S. dollars): 3.80 5.89 4.92 3.88 2.65 5.57 6.39
km/hour for 6 minutes is 98 beats per minute (bpm). For each of 14 boys, heart rate was measured after 15 minutes of playing Wii Bowling. The resulting sample mean and standard deviation were 101 bpm and 15 bpm, respectively. For purposes of this exercise, assume that it is reasonable to regard the
The paper “Playing Active Video Games Increases Energy Expenditure in Children” (Pediatrics[2009]: 534–539) describes an interesting investigation of the possible cardiovascular benefits of active video games. Mean heart rate for healthy boys age 10 to 13 after walking on a treadmill at
Paint used to paint lines on roads must reflect enough light to be clearly visible at night. Let m denote the mean reflectometer reading for a new type of paint under consideration. A test of H0: m 20 versus Ha: m 20 based on a sample of 15 observations gave t 3.2. What conclusion is appropriate at
Assuming a random sample from a large population, for which of the following null hypotheses and sample sizes n is the large-sample z test appropriate:a. H0: p 5 .2, n 5 25b. H0: p 5 .6, n 5 210c. H0: p 5 .9, n 5 100d. H0: p 5 .05, n 5 75
Let p denote the proportion of grocery store customers who use the store’s club card. For a largesample z test of H0: p .5 versus Ha: p .5, find the P-value associated with each of the given values of the test statistic:a. 1.40d. 2.45b. 0.93e. 0.17c. 1.96
For which of the following P-values will the null hypothesis be rejected when performing a test with a significance level of .05:a. .001d. .047b. .021e. .148c. .078
An automobile manufacturer is considering using robots for part of its assembly process. Converting to robots is an expensive process, so it will be undertaken only if there is strong evidence that the proportion of defective installations is lower for the robots than for human assemblers. Let p
The paper “MRI Evaluation of the Contralateral Breast in Women with Recently Diagnosed Breast Cancer” (New England Journal of Medicine[2007]: 1295–1303) describes a study of the use of MRI(Magnetic Resonance Imaging) exams in the diagnosis of breast cancer. The purpose of the study was to
A county commissioner must vote on a resolution that would commit substantial resources to the construction of a sewer in an outlying residential area.Her fiscal decisions have been criticized in the past, so she decides to take a survey of constituents to find out whether they favor spending money
A certain university has decided to introduce the use of plus and minus with letter grades, as long as there is evidence that more than 60% of the faculty favor the change. A random sample of faculty will be selected, and the resulting data will be used to test the relevant hypotheses. If p
For the following pairs, indicate which do not comply with the rules for setting up hypotheses, and explain why:a. H0: m 5 15, Ha: m 5 15b. H0: p 5 .4, Ha: p . .6c. H0: m 5 123, Ha: m , 123d. H0: m 5 123, Ha: m 5 125e. H0: p^ 5 .1, Ha: p^ 2 .1
The interval from 2.33 to 1.75 captures an area of .95 under the z curve. This implies that another large sample 95% confidence interval for m has lower limit x 2 2.33 s !n and upper limit x 1 1.75 s !n . Would you recommend using this 95% interval over the 95% interval x 6 1.96 s !n discussed in
When n is large, the statistic s is approximately unbiased for estimating s and has approximately a normal distribution. The standard deviation of this statistic when the population distribution is normal is ss < s!2n which can be estimated by s!2n. A large-sample confidence interval for the
to calculate the 99% upper confidence bound for the true mean wait time for bypass patients in Ontario.
The confidence intervals presented in this chapter give both lower and upper bounds on plausible values for the population characteristic being estimated. In some instances, only an upper bound or only a lower bound is appropriate. Using the same reasoning that gave the large sample interval in
The paper “The Curious Promiscuity of Queen Honey Bees (Apis mellifera): Evolutionary and Behavioral Mechanisms” (Annals of Zoology Fennici [2001]:255–265) describes a study of the mating behavior of queen honeybees. The following quote is from the paper:Queens flew for an average of 24.2
Authors of the news release titled “Major Gaps Still Exist Between the Perception and the Reality of Americans’ Internet Security Protections, Study Finds”(The National Cyber Security Alliance) estimated the proportion of Americans who claim to have a firewall installed on their computer to
Five students visiting the student health center for a free dental examination during National Dental Hygiene Month were asked how many months had passed since their last visit to a dentist. Their responses were as follows:6 17 11 22 29 Assuming that these five students can be considered a random
Fat content (in grams) for seven randomly selected hot dogs that were rated as very good by Consumer Reports (www.consumerreports.org) is shown below. Is it reasonable to use this data and the t confidence interval of this section to construct a confidence interval for the mean fat content of hot
The article “The Association Between Television Viewing and Irregular Sleep Schedules Among Children Less Than 3 Years of Age” (Pediatrics [2005]:851– 856) reported the accompanying 95% confidence intervals for average TV viewing time (in hours per day)for three different age groups.Age Group
hours. For purposes of this exercise, assume that it is reasonable to regard this sample as representative of students taking introductory psychology at this university.a. Construct a 95% confidence interval to estimate m, the mean time spent studying for the final exam for students taking
In a study of academic procrastination, the authors of the paper “Correlates and Consequences of Behavioral Procrastination” (Procrastination, Current Issues and New Directions [2000]) reported that for a sample of 411 undergraduate students at a midsize public university preparing for a final
The formula used to compute a confidence interval for the mean of a normal population when n is small is x 6 1t critical value2 s!n What is the appropriate t critical value for each of the following confidence levels and sample sizes?a. 95% confidence, n 17b. 90% confidence, n 12c. 99% confidence,
The article “Hospitals Dispute Medtronic Data on Wires” (The Wall Street Journal, February 4, 2010)describes several studies of the failure rate of defibrillators used in the treatment of heart problems. In one study conducted by the Mayo Clinic, it was reported that failures were experienced
Discuss how each of the following factors affects the width of the confidence interval for p:a. The confidence levelb. The sample sizec. The value of p^
The use of the interval p^ 6 1z critical value2Åp^ 11 2 p^2 nrequires a large sample. For each of the following combinations of n and p^, indicate whether the sample size is large enough for use of this interval to be appropriate.a. n 50 and p^ .30b. n 50 and p^ .05c. n 15 and p^ .45d. n 100 and
The formula used to compute a large-sample confidence interval for p is p^ 6 1z critical value2Åp^ 11 2 p^2 nWhat is the appropriate z critical value for each of the following confidence levels?a. 95%d. 80%b. 90%e. 85%c. 99%
A random sample of 10 houses heated with natural gas in a particular area, is selected, and the amount of gas (in therms) used during the month of January is determined for each house. The resulting observations are as follows:103 156 118 89 125 147 122 109 138 99a. Let mJ denote the average gas
Given below are the sodium contents (in mg) for seven brands of hot dogs rated as “very good” by Consumer Reports (www.consumerreports.org):420 470 350 360 270 550 530a. Use the given data to produce a point estimate of m, the true mean sodium content for hot dogs.b. Use the given data to
Data consistent with summary quantities in the article referenced in Exercise 9.3 on total calorie consumption on a particular day are given for a sample of children who did not eat fast food on that day and for a sample of children who did eat fast food on that day.Assume that it is reasonable to
Consumption of fast food is a topic of interest to researchers in the field of nutrition. The article “Effects of Fast-Food Consumption on Energy Intake and Diet Quality Among Children” (Pediatrics [2004]: 112–118)reported that 1720 of those in a random sample of 6212 U.S. children indicated
Three different statistics are being considered for estimating a population characteristic. The sampling distributions of the three statistics are shown in the following illustration:True value of population characteristic Statistic II Statistic III Statistic I Which statistic would you recommend?
The amount of money spent by a customer at a discount store has a mean of $100 and a standard deviation of $30. What is the probability that a randomly selected group of 50 shoppers will spend a total of more than $5300? (Hint: The total will be more than $5300 when the sample mean exceeds what
A manufacturer of computer printers purchases plastic ink cartridges from a vendor. When a large shipment is received, a random sample of 200 cartridges is selected, and each cartridge is inspected. If the sample proportion of defective cartridges is more than .02, the entire shipment is returned
The article referenced in Exercise 8.25 reported that for unmarried couples living together, the proportion that are racially or ethnically mixed is .15. Answer the questions posed in Parts (a)– (e) of Exercise 8.25 for the population of unmarried couples living together.
mm. What is the probability that a problem will be detected when the next sample is taken? (Hint: This will occur if x . 2 1 3sx or x , 2 2 3sx when m 2.05.)
The thickness (in millimeters) of the coating applied to disk drives is one characteristic that determines the usefulness of the product. When no unusual circumstances are present, the thickness (x) has a normal distribution with a mean of 2 mm and a standard deviation of 0.05 mm. Suppose that the
An airplane with room for 100 passengers has a total baggage limit of 6000 pounds. Suppose that the total weight of the baggage checked by an individual passenger is a random variable x with a mean value of 50 pounds and a standard deviation of 20 pounds. If 100 passengers will board a flight, what
A manufacturing process is designed to produce bolts with a 0.5-inch diameter. Once each day, a random sample of 36 bolts is selected and the bolt diameters are recorded. If the resulting sample mean is less than 0.49 inches or greater than 0.51 inches, the process is shut down for adjustment. The
Explain the difference between s and sx and between m and mx.
For which of the sample sizes given in Exercise 8.10 would it be reasonable to think that the x sampling distribution is approximately normal in shape?
Consider the following population: {2, 3, 3, 4, 4}.The value of m is 3.2, but suppose that this is not known to an investigator, who therefore wants to estimate m from sample data. Three possible statistics for estimating m are Statistic 1: the sample mean, x Statistic 2: the sample median
Simulate sampling from the population of Exercise 8.7 by using four slips of paper individually marked 1, 2, 3, and 4. Select a sample of size 2 without replacement, and compute x. Repeat this process 50 times, and construct a density histogram of the 50 x values. How does this sampling
Consider the following population: {1, 2, 3, 4}.Note that the population mean is m 5 1 1 2 1 3 1 4 4 5 2.5a. Suppose that a random sample of size 2 is to be selected without replacement from this population.There are 12 possible samples (provided that the order in which observations are selected is
Select 10 additional random samples of size 5 from the population of 20 students given in Example 8.1, and compute the mean amount spent on books for each of the 10 samples. Are the x values consistent with the results of the sampling experiment summarized in Figure 8.1?
Consider a population consisting of the following five values, which represent the number of DVD rentals during the academic year for each of five housemates:8 14 16 10 11a. Compute the mean of this population.b. Select a random sample of size 2 by writing the five numbers in this population on
What is the difference between x and m? between s and s?
The following data are a sample of survival times (in days from diagnosis) for patients suffering from chronic leukemia of a certain type:7 47 58 74 177 232 273 285 317 429 440 445 455 468 495 497 532 571 579 581 650 702 715 779 881 900 930 968 1077 1109 1314 1334 1367 1534 1712 1784 1877 1886 2045
The paper “The Load-Life Relationship for M50 Bearings with Silicon Nitride Ceramic Balls” (Lubrication Engineering [1984]: 153–159) reported the following data on bearing load life (in millions of revolutions). The corresponding normal scores are also given.x Normal Score x Normal Score
The paper “The Effect of Temperature and Humidity on Size of Segregated Traffic Exhaust Particle Emissions” (Atmospheric Environment [2008]:2369–2382) gave the following summary quantities for a measure of traffic flow (vehicles/second) during peak traffic hours at a particular location
Manatees are large marine mammals found along the coast of Florida. Data on the number of manatee deaths per year reported by the Florida Marine Research Center are given in the accompanying table.Construct a time series plot of these data and comment on any trends over time.Year Number of Manatee
The article “Water Consumption in the Bay Area” (San Jose Mercury News, January 16, 2010) reported the accompanying values for water consumption(gallons per person per day) for residential customers of 27 San Francisco Bay area water agencies.49 52 53 59 59 61 69 70 70 73 79 80 85 87 89 90 92
Let x denote the systolic blood pressure of an individual selected at random from a certain population.Suppose that the normal distribution with mean m 5 120 mm Hg and standard deviation s 5 10 mm Hg is a reasonable model for describing the population distribution of x. (The article “Oral
The following figure appeared in the paper“EDTA-Extractable Copper, Zinc, and Manganese in oils of the Canterbury Plains” (New Zealand Journal of Agricultural Research [1984]: 207–217): A large number of topsoil samples were analyzed for manganese (Mn), zinc (Zn), and copper (Cu), and the
Ecologists have long been interested in factors that might explain how far north or south particular animal species are found. As part of one such study, the paper“Temperature and the Northern Distributions of Wintering Birds” (Ecology [1991]: 2274–2285) gave the following body masses (in
The article “The Distribution of Buying Frequency Rates” (Journal of Marketing Research [1980]:210–216) reported the results of a 3 1 2-year study of toothpaste purchases. The investigators conducted their research using a national sample of 2071 households and recorded the number of
Example 7.19 examined rainfall data for Minneapolis- St. Paul. The square-root transformation was used to obtain a distribution of values that was more symmetric than the distribution of the original data. Another transformation that has been suggested by meteorologists is the cube root:
Consider the following sample of 25 observations on the diameter x (in centimeters) of a disk used in a certain system. 16.01 16.08 16.13 15.94 16.13 16.11 The 13 largest normal scores for a sample of size 25 are 1.965, 1.524, 1.263, 1.067, 0.905, 0.764, 0.637, 0.519, 0.409, 0.303, 0.200, 0.100,
Consider the following 10 observations on the lifetime (in hours) for a certain type of component: 152.7 172. 172.5 173.3 193.0 204.7 216.5 234.9 262.6 422.6 Construct a normal probability plot, and comment on the plausibility of a normal distribution as a model for component lifetime.
Macular degeneration is the most common cause of blindness is people older than 60 years. One variable thought to be related to a type of inflammation associated with this disease is level of a substance called soluble Fas ligand (sFasL) in the blood. The accompanying table contains representative
Measures of nerve conductivity are used in the diagnosis of certain medical conditions. The paper “Effects of Age, Gender, Height, and Weight on Late Responses and Nerve Conduction Study Parameters”(Acta Neurologica Taiwanica [2009]: 242–249) describes a study where the ulnar nerve was
The paper “Risk Behavior, Decision Making, and Music Genre in Adolescent Males” (Marshall University, May 2009) examined the effect of type of music playing and performance on a risky, decision-making task.a. Participants in the study responded to a questionnaire that was used to assign a risk
The authors of the paper “Development of Nutritionally At-Risk Young Children Is Predicted by Malaria, Anemia, and Stunting in Pemba, Zanzibar”(The Journal of Nutrition [2009]: 763–772) studied factors that might be related to dietary deficiencies in children. Children were observed for a
Suppose that the distribution of typing speed in words per minute (wpm) for typists using a new type of split keyboard can be approximated by a normal curve with mean 60 wpm and standard deviation 15 wpm(The effects of Split Keyboard Geometry on Upper Body Postures,” Ergonomics [2009]”
Refer to Exercise 7.30. Suppose that there are two machines available for cutting corks. The machine described in the preceding problem produces corks with diameters that are approximately normally distributed with mean 3 centimeters and standard deviation 0.1 centimeter. The second machine
The paper referenced in the previous exercise also included data on left atrial diameter for children who were considered overweight. For these children, left atrial diameter was approximately normally distributed with a mean of 28 millimeters and a standard deviation of 4.7 millimeters.a.
Consider the population of all 1-gallon cans of dusty rose paint manufactured by a particular paint company. Suppose that a normal distribution with mean m 5 5 ml and standard deviation s 5 0.2 ml is a reasonable model for the distribution of the variable x 5 amount of red dye in the paint mixture.
Because P(z , 0.44) 5 .67, 67% of all z values are less than 0.44, and 0.44 is the 67th percentile of the standard normal distribution. Determine the value of each of the following percentiles for the standard normal distribution (Hint: If the cumulative area that you must look for does not appear
Let z denote a variable that has a standard normal distribution. Determine the value z* that satisfies the following conditions:a. P(z , z*) 5 .025b. P(z , z*) 5 .01c. P(z , z*) 5 .05d. P(z . z*) 5 .02e. P(z . z*) 5 .01f. P(z . z* or z , 2z*) 5 .20
Let z denote a variable having a normal distribution with m 5 0 and s 5 1. Determine each of the following probabilities:a. P(z , 0.10)b. P(z , 20.10)c. P(0.40 , z , 0.85)d. P(20.85 , z , 20.40)e. P(20.40 , z , 0.85)f. P(z . 21.25)g. P(z 21.50 or z . 2.50)
Let z denote a variable that has a standard normal distribution. Determine each of the following probabilities:a. P(z , 2.36)b. P(z # 2.36)c. P(z , 21.23)d. P(1.14 , z , 3.35)e. P(20.77 # z # 0.55)f. P(z . 2)g. P(z $ 23.38) h. P(z , 4.98)
Let x denote the time (in seconds) necessary for an individual to react to a certain stimulus. The probability distribution of x is specified by the following density curve:Density x1a. What is the height of the density curve above x 5 0?(Hint: Total area under the curve 5 1.)b. What is the
A delivery service charges a special rate for any package that weighs less than 1 pound. Let x denote the weight of a randomly selected parcel that qualifies for this special rate. The probability distribution of x is specified by the following density curve:1 0.5 xDensity Density = 0.5+ x 1.0 1.5
Consider the population that consists of all soft contact lenses made by a particular manufacturer, and define the variable x 5 thickness (in millimeters). Suppose that a reasonable model for the population distribution is the one shown in the following figure:Density 0 0.20 Thickness 50.40a.
A particular professor never dismisses class early.Let x denote the amount of time past the hour (in minutes) that elapses before the professor dismisses class.Suppose that the density curve shown in the following figure is an appropriate model for the probability distribution of x:1 10 0 10
Consider the population of batteries made by a particular manufacturer. The following density curve represents the probability distribution for the variable x 5 lifetime (in hours):0 25 50 Shade the region under the curve corresponding to each of the following probabilities (draw a new curve for
Homicide rate (homicides per 100,000 population) for each of the 50 states appeared in the 2010 Statistical Abstract (www.census.gov). A frequency distribution constructed from the 50 observations is shown in the following table:Homicide Rate Frequency 0 to ,30 14 3 to ,60 18 6 to ,90 16 9 to ,12 1
Airlines sometimes overbook flights. Suppose that for a plane with 100 seats, an airline takes 110 reservations.Define the variable x as the number of people who actually show up for a sold-out flight. From past experience, the population distribution of x is given in the following table:x
A pizza shop sells pizzas in four different sizes. The 1000 most recent orders for a single pizza gave the following proportions for the various sizes:Size 12 in. 14 in. 16 in. 18 in.Proportion .20 .25 .50 .05 With x denoting the size of a pizza in a single-pizza order, the given table is an
Suppose that fund-raisers at a university call recent graduates to request donations for campus outreach programs. They report the following information for last year’s graduates:Size of donation $0 $10 $25 $50 Proportion of calls .45 .30 .20 .05 Three attempts were made to contact each graduate;
USA Today (March 15, 2001) introduced a measure of racial and ethnic diversity called the Diversity Index. The Diversity Index is supposed to approximate the probability that two randomly selected individuals are racially or ethnically different. The equation used to compute the Diversity Index
Is ultrasound a reliable method for determining the gender of an unborn baby? Consider the following data on 1000 births, which are consistent with summary values that appeared in the online Journal of Statistics Education (“New Approaches to Learning Probability in the First Statistics Course”
Researchers at UCLA were interested in whether working mothers were more likely to suffer workplace injuries than women without children. They studied 1400 working women, and a summary of their findings was reported in the San Luis Obispo Telegram-Tribune(February 28, 1995). The information in the
A Gallup Poll conducted in November 2002 examined how people perceived the risks associated with smoking. The following table summarizes data on smoking status and perceived risk of smoking that is consistent with summary quantities published by Gallup:Perceived Risk Smoking Status Very Harmful
Students at a particular university use an online registration system to select their courses for the next term.There are four different priority groups, with students in Group 1 registering first, followed by those in Group 2, and so on. Suppose that the university provided the accompanying

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