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Statistics The Exploration & Analysis Of Data 7th Edition Roxy Peck, Jay L. Devore - Solutions

The accompanying data represent x = amount of catalyst added to accelerate a chemical reaction and y 5 resulting reaction time:a. Calculate r. Does the value of r suggest a strong linear relationship? b. Construct a scatterplot. From the plot, does the word linear provide the most effective
The paper €œA Cross-National Relationship Between Sugar Consumption and Major Depression?€ (Depression and Anxiety [2002]: 118€“120) concluded that there was a correlation between re fined sugar consumption (calories per person per day) and annual rate of major
The following data on x = score on a measure of test anxiety and y = exam score for a sample of n = 9 students are consistent with summary quantities given in the paper €œEffects of Humor on Test Anxiety and Performance€ (Psychological Reports [1999]:
In a study of 200 Division I athletes, variables related to academic performance were examined. The paper “Noncognitive Predictors of Student Athletes’ Academic Performance” (Journal of College Reading and Learning [2000]: e167) reported that the correlation coefficient for college GPA and a
Researchers asked each child in a sample of 411 school-age children if they were more or less likely to purchase a lottery ticket at a store if lottery tickets were visible on the counter. The percentage that said that they were more likely to purchase a ticket by grade level are as follows (R&J
Percentages of public school students in fourth grade in 1996 and in eighth grade in 2000 who were at or above the proficient level in mathematics were given in the article €œMixed Progress in Math€ (USA Today, August 3, 2001) for eight western states:a. Construct a scatterplot, and comment
The following table gives the number of organ transplants performed in the United States each year from 1990 to 1999 (The Organ Procurement and Transplantation Network, 2003):a. Construct a scatterplot of these data, and then find the equation of the least-squares regression line that describes the
The paper “Effects of Canine Parvovirus (CPV) on Gray Wolves in Minnesota” (Journal of Wildlife Management [1995]: 565–570) summarized a regression of y = percentage of pups in a capture on x = percentage of CPV prevalence among adults and pups. The equation of the least-squares line, based
The paper €œAspects of Food Finding by Wintering Bald Eagles€ (The Auk [1983]: 477€“484) examined the relationship between the time that eagles spend aerially searching for food (indicated by the percentage of eagles soaring) and relative food availability. The accompanying data were
Data on salmon availability (x) and the percentage of eagles in the air (y) were given in the previous exercise. a. Calculate the correlation coefficientfor these data. b. Because the scatterplot of the original data appeared curved, transforming both the x and y values by taking square roots was
No tortilla chip lover likes soggy chips, so it is important to find characteristics of the production process that produce chips with an appealing texture. The accompanying data on x = frying time (in seconds) and y = moisture content (%) appeared in the paper, €œThermal and Physical
The article €œReduction in Soluble Protein and Chlorophyll Contents in a Few Plants as Indicators of Automobile Exhaust Pollution€ (International Journal of Environmental Studies [1983]: 239€“244) reported the following data on x = distance from a highway (in meters)
An accurate assessment of oxygen consumption provides important information for determining energy expenditure requirements for physically demanding tasks. The paper €œOxygen Consumption During Fire Suppression: Error of Heart Rate Estimation€ (Ergonomics [1991]:
Consider the four (x, y) pairs (0, 0), (1, 1), (1, -1), and (2, 0). a. What is the value of the sample correlation coefficient r? b. If a fifth observation is made at the value x = 6, find a value of y for which r = 0.5. c. If a fifth observation is made at the value x = 6, find a value of y for
Data from the U.S. Federal Reserve Board (Household Debt Service Burden, 2002) on the percentage of disposable personal income required to meet consumer loan payments and mortgage payments for selected years are shown in the following table:a. What is the value of the correlation coefficientfor
An article in the New York Times (March 2, 1994) reported that people who suffer cardiac arrest in New York City have only a 1 in 100 chance of survival. Using probability notation, an equivalent statement would be P (survival) = .01 for people who suffer a cardiac arrest in New York City (The
Approximately 30% of the calls to an airline reservation phone line result in a reservation being made. a. Suppose that an operator handles 10 calls. What is the probability that none of the 10 calls results in a reservation? b. What assumption did you make in order to calculate the probability in
The following case study is reported in the article “Parking Tickets and Missing Women,” which appears in an early edition of the book Statistics: A Guide to the Unknown. In a Swedish trial on a charge of overtime parking, a police officer testified that he had noted the position of the two air
Three friends (A, B, and C) will participate in a round-robin tournament in which each one plays both of the others. Suppose that P(A beats B) = .7, P(A beats C) = .8, and P(B beats C) = .6 and that the outcomes of the three matches are independent of one another. a. What is the probability that A
Consider a system consisting of four components, as pictured in the following diagram:Components 1 and 2 form a series subsystem, as do Components 3 and 4. The two subsystems are connected in parallel. Suppose that P(1 works) = .9, P(2 works) = .9, P(3 works) = .9, and P(4 works) = .9 and that
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
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 (€œNew Approaches to Learning Probability in the First Statistics
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:Assume that it is reasonable to consider these
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
The Los Angeles Times (June 14, 1995) reported that the U.S. Postal Service is getting speedier, with higher overnight on-time delivery rates than in the past. Postal Service standards call for overnight delivery within a zone of about 60 miles for any first-class letter deposited by the last
The paper €œPredictors of Complementary Therapy Use among Asthma Patients: Results of a Primary Care Survey€ (Health and Social Care in the Community [2008]: 155€“164) included the accompanying table. The table summarizes the responses given by 1077 asthma patients to two questions:
Five hundred first-year students at a state university were classified according to both high school grade point average (GPA) and whether they were on academic probation at the end of their first semester. The data are summarized in the accompanying table.a. Construct a table of the estimated
The table below describes (approximately) the distribution of students by gender and college at a midsize public university in the West. If we were to randomly select one student from this university: a. What is the probability that the selected student is a male? b. What is the probability that
On April 1, 2000, the Bureau of the Census in the United States attempted to count every U.S. resident. Suppose that the counts in the table on the next page are obtained for four counties in one region. a. If one person is selected at random from this region, what is the probability that the
Many cities regulate the number of taxi licenses, and there is a great deal of competition for both new and existing licenses. Suppose that a city has decided to sell 10 new licenses for $25,000 each. A lottery will be held to determine who gets the licenses, and no one may request more than three
Refer to Exercises 6.25 and 6.26. Suppose that the probabilities of timely completion are as in Exercise 6.25 for Maria, Alex, and Juan but that Jacob has a probability of completing on time of .7 if Juan is on time and .5 if Juan is late. a. Use simulation (with at least 20 trials) to estimate the
Of the 10,000 students at a certain university, 7000 have Visa cards, 6000 have MasterCards, and 5000 have both. Suppose that a student is randomly selected. a. What is the probability that the selected student has a Visa card? b. What is the probability that the selected student has both cards? c.
The Australian newspaper The Mercury (May 30, 1995) reported that, based on a survey of 600 reformed and current smokers, 11.3% of those who had attempted to quit smoking in the previous 2 years had used a nicotine aid (such as a nicotine patch). It also reported that 62% of those who quit smoking
The article €œBaseball: Pitching No-Hitters€ (Chance [Summer 1994]: 24€“ 30) gives information on the number of hits per team per game for all nine-inning major league games played between 1989 and 1993. Each game resulted in two observations, one for each team. No
Consider the five outcomes (shown in the table on the next page) for an experiment in which the type of ice cream purchased by the next customer at a certain store is noted. a. What is the probability that Dreyer’s ice cream is purchased? b. What is the probability that Von’s brand is not
A radio station that plays classical music has a “by request” program each Saturday evening. The percentages of requests for composers on a particular night are as follows: Bach........... 5% Mozart........... 21% Beethoven.......... 26% Schubert........... 12% Brahms...........
Suppose that the following information on births in the United States over a given period of time is available to you:Use this information to approximate the probability that a randomly selected pregnant woman who reaches full term a. Delivers twins b. Delivers quadruplets c. Gives birth to more
Two individuals, A and B, are finalists for a chess championship. They will play a sequence of games, each of which can result in a win for A, a win for B, or a draw. Suppose that the outcomes of successive games are independent, with P(A wins game) = .3, P(B wins game) 5 .2, and P(draw) = .5. Each
A single-elimination tournament with four players is to be held. A total of three games will be played. In Game 1, the players seeded (rated) first and fourth play. In Game 2, the players seeded second and third play. In Game 3, the winners of Games 1 and 2 play, with the winner of Game 3 declared
Many fire stations handle emergency calls for medical assistance as well as calls requesting firefighting equipment. A particular station says that the probability that an incoming call is for medical assistance is .85. This can be expressed as P(call is for medical assistance)= .85.a. Give a
“N.Y. Lottery Numbers Come Up 9-1-1 on 9/11” was the headline of an article that appeared in the San Francisco Chronicle (September 13, 2002). More than 5600 people had selected the sequence 9-1-1 on that date, many more than is typical for that sequence. A professor at the University of
In a small city, approximately 15% of those eligible are called for jury duty in any one calendar year. People are selected for jury duty at random from those eligible, and the same individual cannot be called more than once in the same year. What is the probability that an eligible person in this
Jeanie is a bit forgetful, and if she doesn’t make a “to do” list, the probability that she forgets something she is supposed to do is .1. Tomorrow she intends to run three errands, and she fails to write them on her list. a. What is the probability that Jeanie forgets all three errands? What
The paper “The Psychology of Security” (Communications of the ACM, [2008]: 36–41) states that people are more likely to gamble for a loss than to accept a guaranteed loss. For example, the authors indicate that when presented with a scenario that allows people to choose between a guaranteed
The following data are a sample of survival times (in days from diagnosis) for patients suffering from chronic leukemia of a certain type:a. Construct a relative frequency distribution for this data set, and draw the corresponding histogram. b. Would you describe this histogram as having a positive
The article €œWater 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.a. Use the given water
Red-light cameras are used in many places to deter drivers from running red lights. The following graphical display appeared in the article “Communities Put a Halt to Red-Light Cameras” (USA Today, January 18, 2010). Does this graph imply that there were fewer red-light cameras in 2009 than in
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.
The paper €œThe 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
The article “Men, Women at Odds on Gun Control” (Cedar Rapids Gazette, September 8, 1999) included the following statement: “The survey found that 56 percent of American adults favored stricter gun control laws. Sixty-six percent of women favored the tougher laws, compared with 45 percent of
A machine that produces ball bearings has initially been set so that the mean diameter of the bearings it produces is 0.500 inch. A bearing is acceptable if its diameter is within 0.004 inch of this target value. Suppose, however, that the setting has changed during the course of production, so
Consider the variable x = time required for a college student to complete a standardized exam. Suppose that for the population of students at a particular university, the distribution of x is well approximated by a normal curve with mean 45 minutes and standard deviation 5 minutes.a. If 50 minutes
The paper €œThe 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
State whether each of the following numerical variables is discrete or continuous: a. The number of defective tires on a car b. The body temperature of a hospital patient c. The number of pages in a book d. The number of checkout lines operating at a large grocery store e. The lifetime of a
Consider the population of batteries made by a particular manufacturer. The following density curve represents the probability distribution for the variable x = lifetime (in hours):Shade the region under the curve corresponding to each of the following probabilities (draw a new curve for each
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:a. What is the
Consider the population that consists of all soft contact lenses made by a particular manufacturer, and define the variable x = thickness (in millimeters). Suppose that a reasonable model for the population distribution is the one shown in the following figure:a. Verify that the total area under
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:Use the fact that the area of a
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:a. What is the height of the density curve above x = 0?b. What is the probability that reaction time exceeds 0.5 second?c.
Determine the following standard normal (z) curve areas: a. The area under the z curve to the left of 1.75 b. The area under the z curve to the left of 20.68 c. The area under the z curve to the right of 1.20 d. The area under the z curve to the right of 22.82 e. The area under the z curve between
Determine each of the following areas under the standard normal (z) curve: a. To the left of 21.28 b. To the right of 1.28 c. Between 21 and 2 d. To the right of 0 e. To the right of 25 f. Between 21.6 and 2.5 g. To the left of 0.23
Let z denote a variable that has a standard normal distribution. Determine each of the following probabilities:
Let z denote a variable having a normal distribution with µ = 0 and Ïƒ= 1. Determine each of the following probabilities:
Let z denote a variable that has a standard normal distribution. Determine the value z* that satisfies the following conditions:
Classify each of the following numerical variables as either discrete or continuous: a. The fuel efficiency (in miles per gallon) of an automobile b. The amount of rainfall at a particular location during the next year c. The distance that a person throws a baseball d. The number of questions asked
Determine the value z* that a. Separates the largest 3% of all z values from the others b. Separates the largest 1% of all z values from the others c. Separates the smallest 4% of all z values from the others d. Separates the smallest 10% of all z values from the others
Determine the value of z* such thata.z* and 2z* separate the middle 95% of all z values from the most extreme 5%b.z* and 2z* separate the middle 90% of all z values from the most extreme 10%c.z* and 2z* separate the middle 98% of all z values from the most extreme 2%d.z* and 2z* separate the middle
Because P(z < 0.44) = .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 a. The 91st percentile b. The 77th percentile c. The 50th
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 µ = 5 ml and standard deviation Ïƒ = 0.2 ml is a reasonable model for the distribution of the variable x = amount of red dye in the paint
Consider babies born in the “normal” range of 37–43 weeks gestational age. The paper referenced in Example 7.13 (“Fetal Growth Parameters and Birth Weight: Their Relationship to Neonatal Body Compo- sition,” Ultrasound in Obstetrics and Gynecology [2009]: 441–446) suggests that a normal
Emissions of nitrogen oxides, which are major constituents of smog, can be modeled using a normal distribution. Let x denote the amount of this pollutant emitted by a randomly selected vehicle. The distribution of x can be described by a normal distribution with m = 1.6 and s 5 0.4. Suppose that
The paper referenced in Example 7.16 (“Estimating Waste Transfer Station Delays Using GPS,” Waste Management [2008]: 1742–1750) describing processing times for garbage trucks also provided information on processing times at a second facility. At this second facility, the mean total processing
The size of the left upper chamber of the heart is one measure of cardiovascular health. When the upper left chamber is enlarged, the risk of heart problems is increased The paper “Left Atrial Size Increases with Body Mass Index in Children” (International Journal of Cardiology [2009]: 1–7)
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.
According to the paper “Commuters’ Exposure to Particulate Matter and Carbon Monoxide in Hanoi, Vietnam” (Transportation Research [2008]: 206–211), the carbon monoxide exposure of someone riding a motorbike for = km on a highway in Hanoi is approximately normally distributed with a mean of
Consider the variable x = earthquake insurance status for the population of homeowners in an earthquake- prone California county. This variable associates a category (insured or not insured) with each individual in the population. a. Construct a relative frequency bar chart that represents the
A machine that cuts corks for wine bottles operates in such a way that the distribution of the diameter of the corks produced is well approximated by a normal distribution with mean 3 centimeters and standard deviation 0.1 centimeters. The specifications call for corks with diameters between 2.9
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
A gasoline tank for a certain car is designed to hold 15 gallons of gas. Suppose that the variable x 5 actual capacity of a randomly selected tank has a distribution that is well approximated by a normal curve with mean 15.0 gallons and standard deviation 0.1 gallon.a. What is the probability that
The time that it takes a randomly selected job applicant to perform a certain task has a distribution that can be approximated by a normal distribution with a mean value of 120 seconds and a standard deviation of 20 seconds. The fastest 10% are to be given advanced training. What task times qualify
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]”
The authors of the paper €œDevelopment 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.
The paper €œRisk 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
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
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
Based on past history, a fire station reports that 25% of the calls to the station are false alarms, 60% are for small fires that can be handled by station personnel without outside assistance, and 15% are for major fires that require outside help.a. Construct a relative frequency bar chart that
Consider the following 10 observations on the lifetime (in hours) for a certain type of component:Construct a normal probability plot, and comment on the plausibility of a normal distribution as a model for component lifetime.
Consider the following sample of 25 observations on the diameter x (in centimeters) of a disk used in a certain system.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, and 0. The 12 smallest scores result
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:
The article €œThe Distribution of Buying Frequency Rates€ ( Journal of Marketing Research [1980]: 210€“216) reported the results of a 312 -year study of toothpaste purchases. The investigators conducted their research using a national sample of 2071 households and
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
A machine producing vitamin E capsules operates in such a way that the distribution of x = actual amount of vitamin E in a capsule can be modeled by a normal curve with a mean of = mg and standard deviation 0.05 mg. What is the probability that a randomly selected capsule contains less than 4.9 mg
The Wall Street Journal (February 15, 1972) reported that General Electric was being sued in Texas for sex discrimination because of a minimum height requirement of = ft. 7 in. The suit claimed that this restriction eliminated more than 94% of adult females from consideration. Let x represent the
Suppose that your statistics professor tells you that the distribution of scores on a midterm exam was approximately normal with a mean of 78 and a standard deviation of7. The top 15% of all scores have been designated A’s. Your score was 89. Did you receive an A? Explain.
Suppose that the distribution of pH readings for soil samples taken in a certain geographic region can be approximated by a normal distribution with mean 6.00 and standard deviation 0.10. The pH of a randomly selected soil sample from this region is to be determined.a. What is the probability that
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:Three attempts were made to contact each graduate; a donation of $0 was recorded both for those who were contacted
The light bulbs used to provide exterior lighting for a large office building have an average lifetime of 700 hours. If the distribution of the variable x = length of bulb life can be modeled as a normal distribution with a standard deviation of 50 hours, how often should all the bulbs be replaced
Let x denote the duration of a randomly selected pregnancy (the time elapsed between conception and birth). Accepted values for the mean value and standard deviation of x are 266 days and 16 days, respectively. Suppose that a normal distribution is an appropriate model for the probability
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 Ïƒ = 10 mm Hg is a reasonable model for describing the population distribution of x. (The article €œOral

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