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Understandable Statistics Concepts And Methods 12th Edition Charles Henry Brase, Corrinne Pellillo Brase - Solutions

Under the condition that both populations have equal standard deviations (σ1 – σ2), we can pool the standard deviations and use a Student’s t distribution with degrees of freedom d.f. – n1 + n2 – 2 to find the margin of error of a c confidence interval for µ1 – µ2. This
Consider two independent normal distributions. A random sample of size n1 = 20 from the –first distribution showed x1 = 12 and a random sample of size n2 = 25 from the second distribution showed x2 = 14.(a) Check Requirements If s1 and s2 are known, what distribution does m1 – m2 follow?
Locander et al. also studied the accuracy of responses on questions involving more sensitive material than voter registration. From public records, individuals were identified as having been charged with drunken driving not less than 6 months or more than 12 months from the starting date of the
What happens if we want several confidence intervals to hold at the same time (concurrently)? Do we still have the same level of confidence we had for each individual interval?(a) Suppose we have two independent random variables x1 and x2 with respective population means µ1 and µ2. Let us say
Athabasca Fishing Lodge is located on Lake Athabasca in northern Canada. In one of its recent brochures, the lodge advertises that 75% of its guests catch northern pike over 20 pounds. Suppose that last summer 64 out of a random sample of 83 guests did, in fact, catch northern pike weighing over 20
In the following data pairs, A represents birthrate and B represents death rate per 1000 resident population. The data are paired by counties in the Midwest. A random sample of 16 counties gave the following information (Reference: County and City Data Book, U.S. Department of Commerce).Do the data
The following data are based on information taken from the book Navajo Architecture: Forms, History, Distributions by S. C. Jett and V. E. Spencer (University of Arizona Press). A survey of houses and traditional hogans was made in a number of different regions of the modern Navajo Indian
In the following data pairs, A represents the cost of living index for utilities and B represents the cost of living index for transportation. The data are paired by metropolitan areas in the United States. A random sample of 46 metropolitan areas gave the following informationi. Let d be the
The following data are based on information from the Regis University Psychology Department. In an effort to determine if rats perform certain tasks more quickly if offered larger rewards, the following experiment was performed. On day 1, a group of three rats was given a reward of one food pellet
The same experimental design discussed in Problem 20 was used to test rats trained to climb a sequence of short ladders. Times in seconds for eight rats to perform this task are shown in the following table.Do these data indicate that rats receiving larger rewards tend to climb the ladder in less
Consider a hypothesis test of difference of means for two independent populations x1 and x2.(a) What does the null hypothesis say about the relationship between the two population means?(b) If the sample test statistic has a z distribution, give the formula for z.(c) If the sample test statistic
Based on information from The Denver Post, a random sample of n1 = 12 winter days in Denver gave a sample mean pollution index of x̅1 = 43. Previous studies show that σ1 = 21. For Englewood (a suburb of Denver), a random sample of n2 = 14 winter days gave a sample mean pollution index of x̅2 =
In the journal Mental Retardation, an article reported the results of a peer tutoring program to help mildly mentally retarded children learn to read. In the experiment, the mildly retarded children were randomly divided into two groups: the experimental group received peer tutoring along with
Consider independent random samples from two populations that are normal or approximately normal, or the case in which both sample sizes are at least 30. Then, if σ1 and σ2 are unknown but we have reason to believe that σ1 = σ2, we can pool the standard deviations. Using sample sizes n1 and n2,
This problem is based on information taken from Life in America’s Fifty States by G. S. Thomas. A random sample of n1 = 153 people ages 16 to 19 was taken from the island of Oahu, Hawaii, and 12 were found to be high school dropouts. Another random sample of n2 = 128 people ages 16 to 19 was
A random sample of n1 = 288 voters registered in the state of California showed that 141 voted in the last general election. A random sample of n2 = 216 registered voters in the state of Colorado showed that 125 voted in the most recent general election. Do these data indicate that the population
Consider use of a Student’s t distribution to test the difference of means for independent populations using random samples of sizes n1 and n2.(a) Which process gives the larger degrees of freedom, Satterthwaite’s approximation or using the smaller of n1 – 1 and n2 – 1? Which method is
When testing m or the difference of means µ1 – µ2 from independent populations, how do we decide whether to use the standard normal distribution or a Student’s t distribution?
A comparison is made between two bus lines to determine if arrival times of their regular buses from Denver to Durango are off schedule by the same amount of time. For 51 randomly selected runs, bus line A was observed to be off schedule an average time of 53 minutes, with standard deviation 19
A study is made of residents in Phoenix and its suburbs concerning the proportion of residents who subscribe to Sporting News. A random sample of 88 urban residents showed that 12 subscribed, and a random sample of 97 suburban residents showed that 18 subscribed. Does this indicate that a higher
The Wind Mountain archaeological site is in southwest New Mexico. Prehistoric Native Americans called Anasazi once lived and hunted small game in this region. A stemmed projectile point is an arrowhead that has a notch on each side of the base. Both stemmed and stemless projectile points were found
The highway department is testing two types of reflecting paint for concrete bridge end pillars. The two kinds of paint are alike in every respect except that one is orange and the other is yellow. The orange paint is applied to 12 bridges, and the yellow paint is applied to 12 bridges. After a
In Section 5.1, we studied linear combinations of independent random variables. What happens if the variables are not independent? A lot of mathematics can be used to prove the following:Let x and y be random variables with means mx and my, variances σx2 and σy2 and population correlation
Let x be a random variable that represents blood glucose level after a 12-hour fast. Let y be a random variable representing blood glucose level 1 hour after drinking sugar water (after the 12-hour fast). Units are in milligrams per 10 milliliters (mg/10 ml). A random sample of eight adults gave
There are several extensions of linear regression that apply to exponential growth and power law models. Problems 22–25 will outline some of these extensions. First of all, recall that a variable grows linearly over time if it adds a fixed increment during each equal time period. Exponential
Let x = day of observation and y = number of locusts per square meter during a locust infestation in a region of North Africa.(a) Draw a scatter diagram of the (x, y) data pairs. Do you think a straight line will be a good t to these data? Do the y values almost seem to explode as time goes
Expand Your Knowledge: Logarithmic Transformations. Power Law Model When we take measurements of the same general type, a power law of the form y = axβ often gives an excellent fit to the data. A lot of research has been conducted as to why power laws work so well in business, economics, biology,
Let x = boiler steam pressure in 100 lb/in2 and let y = critical sheer strength of boiler plate steel joints in tons/in2. We have the following data for a series of factory boilers.(a) Make the logarithmic transformations x' = log x and y' = log y. Then make a scatter plot of the 1xoe, yoe2 values.
Ocean currents are important in studies of climate change, as well as ecology studies of dispersal of plankton. Drift bottles are used to study ocean currents in the Pacific near Hawaii, the Solomon Islands, New Guinea, and other islands. Let x represent the number of days to recovery of a drift
Wolf packs tend to be large extended family groups that have a well-defined hunting territory. Wolves not in the pack are driven out of the territory or killed. In ecologically similar regions, is the size of an extended wolf pack related to size of hunting region? Using radio collars on wolves,
Refer to the Minitab printout regarding prehistoric pottery.(a) The standard error Se of the linear regression model is given in the print out as “S.” What is the value of Se?(b) The standard error of the coefficient of the predictor variable is found under “SE Coef.” Recall that the
Given the linear regression equationx1 = 1.6 + 3.5x2 – 7.9x3 + 2.0x4(a) Which variable is the response variable? Which variables are the explanatory variables?(b) Which number is the constant term? List the coefficients with their corresponding explanatory variables.(c) If x2 = 2, x3 = 1, and
Given the linear regression equationx3 = –16.5+ 4.0x1 +9.2x4 –1.1x7(a) Which variable is the response variable? Which variables are the explanatory variables?(b) Which number is the constant term? List the coefficients with their corresponding explanatory variables.(c) If x1 = 10, x4 = 1,
The systolic blood pressure of individuals is thought to be related to both age and weight. For a random sample of 11 men, the following data were obtained:(a) Generate summary statistics, including the mean and standard deviation of each variable compute the coefficient of variation for each
Professor Gill has taught general psychology for many years. During the semester, she gives three multiple-choice exams, each worth 100 points. At the end of the course, Dr. Gill gives a comprehensive final worth 200 points. Let x1, x2, and x3 represent a student’s scores on exams 1, 2, and 3,
A motion picture industry analyst is studying movies based on epic novels. The following data were obtained for 10 Hollywood movies made in the past 5 years. Each movie was based on an epic novel. For these data, x1 = first-year box office receipts of the movie, x2 = total production costs of
All Greens is a franchise store that sells house plants and lawn and garden supplies. Although All Greens is a franchise, each store is owned and managed by private individuals. Some friends have asked you to go into business with them to open a new All Greens store in the suburbs of San Diego. The
Let x be a random variable representing percentage change in neighborhood population in the past few years, and let y be a random variable representing crime rate (crimes per 1000 population). A random sample of six Denver neighborhoods gave the following information (Source: Neighborhood Facts,
Bighorn sheep are beautiful wild animals found throughout the western United States. Data for this problem are based on information taken from The Desert Bighorn, edited by Monson and Sumner (University of Arizona Press). Let x be the age of a bighorn sheep (in years), and let y be the mortality
A sociologist is interested in the relation between x = number of job changes and y = annual salary (in thousands of dollars) for people living in the Nashville area. A random sample of 10 people employed in Nashville provided the following information:Σx = 60; Σy = 359; Σx2 = 442; Σy2 =
Modern medical practice tells us not to encourage babies to become too fat. Is there a positive correlation between the weight x of a 1-year-old baby and the weight y of the mature adult (30 years old)? A random sample of medical les produced the following information for 14 females:Σx = 300;
Dorothy Kelly sells life insurance for the Prudence Insurance Company. She sells insurance by making visits to her clients homes. Dorothy believes that the number of sales should depend, to some degree, on the number of visits made. For the past several years, she has kept careful records of the
Each box of Healthy Crunch breakfast cereal contains a coupon entitling you to a free package of garden seeds. At the Healthy Crunch home office, they use the weight of incoming mail to determine how many of their employees are to be assigned to collecting coupons and mailing out seed packages on a
For Problems 9–19, please provide the following information.(a) What is the level of significance? State the null and alternate hypotheses.(b) Find the value of the chi-square statistic for the sample. Are all the expected frequencies greater than 5? What sampling distribution will you use?
For Problems 5–16, please provide the following information.(a) What is the level of significance? State the null and alternate hypotheses.(b) Find the value of the chi-square statistic for the sample. Are all the expected frequencies greater than 5? What sampling distribution will you use?
For Problems 5–16, please provide the following information.(a) What is the level of significance? State the null and alternate hypotheses.(b) Find the value of the chi-square statistic for the sample. Are all the expected frequencies greater than 5? What sampling distribution will you use?
A civil engineer has been studying the frequency of vehicle accidents on a certain stretch of interstate highway. Long-term history indicates that there has been an average of 1.72 accidents per day on this section of the interstate. Let r be a random variable that represents number of accidents
A pathologist has been studying the frequency of bacterial colonies within the field of a microscope using samples of throat cultures from healthy adults. Long-term history indicates that there is an average of 2.80 bacteria colonies per field. Let r be a random variable that represents the
A factor in determining the usefulness of an examination as a measure of demonstrated ability is the amount of spread that occurs in the grades. If the spread or variation of examination scores is very small, it usually means that the examination was either too hard or too easy. However, if the
A set of solar batteries is used in a research satellite. The satellite can run on only one battery, but it runs best if more than one battery is used. The variance s2 of lifetimes of these batteries affects the useful lifetime of the satellite before it goes dead. If the variance is too small, all
The following problem is based on information from Archaeological Surveys of Chaco Canyon, New Mexico, by A. Hayes, D. Brugge, and W. Judge, University of New Mexico Press. A transect is an archaeological study area that is 1/5 mile wide and 1 mile long. A site in a transect is the location of a
The following problem is based on information from an article by N. Keytz in the American Journal of Sociology (Vol. 53, pp. 470–480). Let x 5 age in years of a rural Quebec woman at the time of her first marriage. In the year 1941, the population variance of x was approximately s2 = 5.1.
The following problem is based on information taken from Accidents in North American Mountaineering (jointly published by The American Alpine Club and The Alpine Club of Canada). Let x represent the number of mountain climbers killed each year. The long-term variance of x is approximately s2 =
The following problem is based on information taken from Academe, Bulletin of the American Association of University Professors. Let x represent the average annual salary of college and university professors (in thousands of dollars) in the United States. For all colleges and universities in the
A new kind of typhoid shot is being developed by a medical research team. The old typhoid shot was known to protect the population for a mean time of 36 months, with a standard deviation of 3 months. To test the time variability of the new shot, a random sample of 23 people were given the new shot.
Jim Mead is a veterinarian who visits a Vermont farm to examine prize bulls. In order to examine a bull, Jim first gives the animal a tranquilizer shot. The effect of the shot is supposed to last an average of 65 minutes, and it usually does. However, Jim sometimes gets chased out of the pasture
The fan blades on commercial jet engines must be replaced when wear on these parts indicates too much variability to pass inspection. If a single fan blade broke during operation, it could severely endanger a flight. A large engine contains thousands of fan blades, and safety regulations require
How reliable are mutual funds that invest in bonds? Again, this depends on the bond fund you buy (see reference in Problem 9). A random sample of annual percentage returns for mutual funds holding short-term U.S. government bonds is shown next.Use a calculator to verify that s2 ≈ 13.59 for the
A new fuel injection system has been engineered for pickup trucks. The new system and the old system both produce about the same average miles per gallon. However, engineers question which system (old or new) will give better consistency in fuel consumption (miles per gallon) under a variety of
A new thermostat has been engineered for the frozen food cases in large supermarkets. Both the old and the new thermostats hold temperatures at an average of 25oF. However, it is hoped that the new thermostat might be more dependable in the sense that it will hold temperatures closer to 25oF. One
Rothamsted Experimental Station (England) has studied wheat production since 1852. Each year, many small plots of equal size but different soil/fertilizer conditions are planted with wheat. At the end of the growing season, the yield (in pounds) of the wheat on the plot is measured. The following
Two plots at Rothamsted Experimental Station (see reference in Problem 5) were studied for production of wheat straw. For a random sample of years, the annual wheat straw production (in pounds) from one plot was as follows:Use a calculator to verify that, for the preceding data, s2 ≈
An economist wonders if corporate productivity in some countries is more volatile than that in other countries. One measure of a company’s productivity is annual percentage yield based on total company assets. Data for this problem are based on information taken from Forbes Top Companies, edited
A random sample of leading companies in South Korea gave the following percentage yields based on assets (see reference in Problem 7):Use a calculator to verify that s2 = 2.247 for these South Korean companies.Another random sample of leading companies in Sweden gave the following percentage yields
You don’t need to be rich to buy a few shares in a mutual fund. The question is, “How reliable are mutual funds as investments?”That depends on the type of fund you buy. The following data are based on information taken from Morningstar, a mutual fund guide available in most libraries. A
Wind Mountain is an archaeological study area located in southwestern New Mexico. Pot sherds are broken pieces of prehistoric Native American clay vessels. One type of painted ceramic vessel is called Mimbres classic black-on-white. At three different sites, the number of such sherds was counted in
Another type of painted ceramic vessel is called three-circle red-on-white (see reference in Problem 1). At four different sites in the Wind Mountain archaeological region, the number of such sherds was counted in local dwelling excavations.Shall we reject or not reject the claim that there is no
How productive are U.S. workers? One way to answer this question is to study annual prots per employee. A random sample of companies in computers (I), aerospace (II), heavy equipment (III), and broadcasting (IV) gave the following data regarding annual prots per employee (units in thousands of
A random sample of companies in electric utilities (I), financial services (II), and food processing (III) gave the following information regarding annual prots per employee (units in thousands of dollars).Shall we reject or not reject the claim that there is no difference in population mean
Where are the deer? Random samples of square-kilometer plots were taken in different ecological locations of Mesa Verde National Park. The deer counts per square kilometer were recorded and are shown in the following table (The Mule Deer of Mesa Verde National Park, edited by G. W. Mierau and J. L.
Wild irises are beautiful flowers found throughout the United States, Canada, and northern Europe. This problem concerns the length of the sepal (leaf-like part covering the flower) of different species of wild iris. Data are based on information taken from an article by R. A. Fisher in Annals of
An executive at the home office of Big Rock Life Insurance is considering three branch managers as candidates for promotion to vice president. The branch reports include records showing sales volume for each salesperson in the branch (in hundreds of thousands of dollars). A random sample of these
The quantity of dissolved oxygen is a measure of water pollution in lakes, rivers, and streams. Water samples were taken at four different locations in a river in an effort to determine if water pollution varied from location to location. Location I was 500 meters above an industrial plant water
A sociologist studying New York City ethnic groups wants to determine if there is a difference in income for immigrants from four different countries during their first year in the city. She obtained the data in the following table from a random sample of immigrants from these countries (incomes
In a study of media usage versus education level (American Demographics, Vol. 17, No. 6), an index was used to measure media usage, where a measurement of 100 represents the U.S. average. Values above 100 represent above-average media usage.(a) List the factors and the number of levels of each
In the same study described in Problem 4, media usage versus household income also was considered. The media usage indices for the various media and income levels follow.(a) List the factors and the number of levels of each factor.(b) Assume there is no interaction between the factors. Use two-way
Does college grade point average (GPA) depend on gender? Does it depend on class (freshman, sophomore, junior, senior)? In a study, the following GPA data were obtained for random samples of college students in each of the cells.(a) List the factors and the number of levels of each factor.(b) Use
A researcher forms three blocks of students interested in taking a history course. The groups are based on grade point average (GPA). The first group consists of students with a GPA less than 2.5, the second group consists of students with a GPA between 2.5 and 3.1, and the last group consists of
A machine that puts corn flakes into boxes is adjusted to put an average of 15 ounces into each box, with standard deviation of 0.25 ounce. If a random sample of 12 boxes gave a sample standard deviation of 0.38 ounce, do these data support the claim that the variance has increased and the machine
Two processes for manufacturing large roller bearings are under study. In both cases, the diameters (in centimeters) are being examined. A random sample of 21 roller bearings from the old manufacturing process showed the sample variance of diameters to be s2 = 0.235. Another random sample of 26
Two processes for manufacturing 60-watt light bulbs are under study. In both cases, the life (in hours) of the bulb before it burns out is being examined. A random sample of 18 light bulbs manufactured using the old process showed the sample variance of lifetimes to be s2 = 51.87. Another random
Does the newspaper section in which an ad is placed make a difference in the average daily number of people responding to the ad? Is there a difference in average daily number of people responding to the ad if it is placed in the Sunday newspaper as compared with the Wednesday newspaper? Disk
The makers of Country Boy Corn Flakes are thinking about changing the packaging of the cereal in the hope of improving sales. In an experiment, ve stores of similar size in the same region sold Country Boy Corn Flakes in different-shaped containers for 2 weeks. Total packages sold are given in
A consumer agency is investigating the blowout pressures of Soap Stone tires. A Soap Stone tire is said to blow out when it separates from the wheel rim due to impact forces usually caused by hitting a rock or a pothole in the road. A random sample of 30 Soap Stone tires were inflated to the
Anela is a computer scientist who is formulating a large and complicated program for a type of data processing. She has three ways of storing and retrieving data: cloud storage, disk, or hard drive. As an experiment, she sets up her program in three different ways: one using cloud storage, one
Professor Stone complains that students’ teacher ratings depend on the grade students receive. In other words, according to Professor Stone, a teacher who gives good grades gets good ratings, and a teacher who gives bad grades gets bad ratings. To test this claim, the Student Assembly took a
How do the average weekly incomes of lawyers and architects compare? A random sample of 18 regions in the United States gave the following information about average weekly incomes (in dollars)Does this information indicate that architects tend to have a larger average weekly income? Use a =
Is the high school dropout rate higher for males or females? A random sample of population regions gave the following information about percentage of 15- to 19-year-olds who are high school dropoutsDoes this information indicate that the dropout rates for males and females are different (either
The Focus Problem at the beginning of this chapter asks you to use a sign test with a 5% level of significance to test the claim that the overall temperature distribution of Madison, Wisconsin, is different (either way) from that of Juneau, Alaska. The monthly average data (in °F) are as
Asian economies impact some of the world’s largest populations. The growth of an economy has a big influence on the everyday lives of ordinary people. Are Asian economies changing? A random sample of 15 Asian economies gave the following information about annual percentage growth rate(a) What is
Borrowing money may be necessary for business expansion. However, too much borrowed money can also mean trouble. Are developing countries tending to borrow more? A random sample of 20 developing countries gave the following information regarding foreign debt per capita (in U.S. dollars, inflation
A high school science teacher decided to give a series of lectures on current events. To determine if the lectures had any effect on student awareness of current events, an exam was given to the class before the lectures, and a similar exam was given after the lectures. The scores follow. Use a
With an ever-increasing world population, grain yields are extremely important. A random sample of 16 large grain producing regions in the world gave the following information about grain production (in kg/hectare)Does this information indicate that modern grain production is higher? Use a 5% level
To compare two elementary schools regarding teaching of reading skills, 12 sets of identical twins were used. In each case, one child was selected at random and sent to school A, and his or her twin was sent to school B. Near the end of fifth grade, an achievement test was given to each child. The
How do the average weekly incomes of electricians and carpenters compare? A random sample of 17 regions in the United States gave the following information about average weekly income (in dollars)Does this information indicate a difference (either way) in the average weekly incomes of electricians
One program to help people stop smoking cigarettes uses the method of posthypnotic suggestion to remind subjects to avoid smoking. A random sample of 18 subjects agreed to test the program. All subjects counted the number of cigarettes they usually smoke a day; then they counted the number of
This cumulative review problem uses material from Chapters 3, 5, and 10. Recall that the Poisson distribution deals with rare events. Death from the kick of a horse is a rare event, even in the Prussian army. The following data are a classic example of a Poisson application to rare events.A
Random samples of two species of iris gave the following petal lengths (in cm).(a) Use a 5% level of significance to test the claim that the population standard deviation of x1 is larger than 0.55.(b) Find a 90% confidence interval for the population standard deviation of x1.(c) Use a 1% level
The following data are paired by date. Let x and y be random variables representing wind direction at 5 A.M. and 5 P.M., respectively (units are degrees on a compass, with 0° representing true north). The readings were taken at seeding level in a cloud seeding experiment.A random sample of days
Commercial apple trees usually consist of two parts grafted together. The upper part, or graft, determines the character of the fruit, while the root stock determines the size of the tree. The following data are from two root stocks A and B. The data represent total extension growth (in meters) of

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