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Understandable Statistics Concepts And Methods 13th Edition Charles Henry Brase, Corrinne Pellillo Brase - Solutions
4. Statistical Literacy Suppose that for x 5 3, the predicted value is yˆ 5 6. The data pair (3, 8) is part of the sample data. What is the value of the residual for x 5 3?
3. Statistical Literacy When using the least-squares line for prediction, are results usually more reliable for extrapolation or interpolation?
2. Statistical Literacy What does it mean to say that the sample correlation coefficient r is significant?
1. Statistical Literacy Suppose the scatter diagram of a random sample of data pairs (x, y) shows no linear relationship between x and y. Do you expect the value of the sample correlation coefficient r to be close to 1, 1, or 0?
5. As access to computers becomes more and more prevalent, we see the P-value reported in hypothesis testing more frequently. Review the use of the P-value in hypothesis testing. What is the difference between the level of significance of a test and the P-value? Considering both the P-value and
4. In the text, it is said that a statistical test is a package of five basic ingredients.List these ingredients, discuss them in class, and write a short description of how these ingredients relate to the above discussion questions.
3. The following statements are very important. Give them some careful thought and discuss them.(a) When we fail to reject the null hypothesis, we do not claim that it is absolutely true. We simply claim that at the given level of significance, the data were not sufficient to reject the null
2. Review and discuss the level of significance and power of a statistical test.
1. Review and discuss type I and type II errors associated with hypothesis testing.
18. Sports Car: Fuel Injection The manufacturer of a sports car claims that the fuel injection system lasts 48 months before it needs to be replaced. A consumer group tests this claim by surveying a random sample of 10 owners who had the fuel injection system replaced. The ages of the cars at the
17. Marketing: Sporting Goods A marketing consultant was hired to visit a random sample of five sporting goods stores across the state of California. Each store was part of a large franchise of sporting goods stores. The consultant taught the managers of each store better ways to advertise and
16. Psychology: Creative Thinking Six sets of identical twins were randomly selected from a population of identical twins. One child was taken at random from each pair to form an experimental group. These children participated in a program designed to promote creative thinking. The other child from
15. Vending Machines: Coffee A machine in the student lounge dispenses coffee.The average cup of coffee is supposed to contain 7.0 ounces. Eight cups of coffee from this machine show the average content to be 7.3 ounces with a standard deviation of 0.5 ounce. Do you think that the machine has
14. Civil Service: College Degrees The Congressional Budget Office reports that 36% of federal civilian employees have a bachelor’s degree or higher (The Wall Street Journal). A random sample of 120 employees in the private sector showed that 33 have a bachelor’s degree or higher. Does this
13. Archaeology: Arrowheads 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
12. Magazines: Subscriptions 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
11. Matches: Number per Box The Nero Match Company sells matchboxes that are supposed to have an average of 40 matches per box, with s 5 9. A random sample of 94 Nero matchboxes shows the average number of matches per box to be 43.1. Using a 1% level of significance, can you say that the average
10. Bus Lines: Schedules 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
9. Medical: Plasma Compress A hospital reported that the normal death rate for patients with extensive burns (more than 40% of skin area) has been significantly reduced by the use of new fluid plasma compresses. Before the new treatment, the mortality rate for extensively burned patients was about
8. Highways: Reflective Paint 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
7. Toys: Electric Trains The Toylot Company makes an electric train with a motor that it claims will draw an average of only 0.8 ampere (A) under a normal load. A sample of nine motors was tested, and it was found that the mean current was x 5 1.4 A, with a sample standard deviation of s 5 0.41 A.
6. Student Life: Employment Professor Jennings claims that only 35% of the students at Flora College work while attending school. Dean Renata thinks that the professor has underestimated the number of students with part-time or full-time jobs. A random sample of 81 students shows that 39 have
5. Vehicles: Mileage Based on information in Statistical Abstract of the United States (116th Edition), the average annual miles driven per vehicle in the United States is 11.1 thousand miles, with s < 600 miles. Suppose that a random sample of 36 vehicles owned by residents of Chicago showed that
4. Critical Thinking All other conditions being equal, does a z or t value with larger magnitude have a larger or smaller corresponding P-value?Before you solve each problem below, first categorize it by answering the following question: Are we testing a single mean, a difference of means, a paired
3. Critical Thinking All other conditions being equal, does a larger sample size increase or decrease the corresponding magnitude of the z or t value of the sample test statistic?
2. Statistical Literacy What do we mean when we say a test is significant? Does this necessarily mean the results are important?
1. Statistical Literacy When testing m or the difference of means m1 m2 from independent populations, how do we decide whether to use the standard normal distribution or a Student’s t distribution?
3. When the results of a survey or a poll are published, the sample size is usually given, as well as the margin of error. For example, suppose the Honolulu Star Bulletin reported that it surveyed 385 Honolulu residents and 78% said they favor mandatory jail sentences for people convicted of
2. Throughout Chapter 7, we have used the normal distribution, the central limit theorem, and the Student’s t distribution.(a) Give a brief outline describing how confidence intervals for means use the normal distribution or Student’s t distribution in their basic construction.(b) Give a brief
1. In this chapter, we have studied confidence intervals. Carefully read the following statements about confidence intervals:(a) Once the endpoints of the confidence interval are numerically fixed, the parameter in question (either m or p) does or does not fall inside the “fixed”interval.(b) A
1. Garrison Bay is a small bay in Washington state. A popular recreational activity in the bay is clam digging. For several years, this harvest has been monitored and the size distribution of clams recorded. Data for lengths and widths of little neck clams (Protothaca staminea) were recorded by a
19. Expand Your Knowledge: Two Confidence Intervals 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
18. Survey Response: Validity Locander et al. (see reference in Problem 17) 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
17. Survey Response: Validity The book Survey Responses: An Evaluation of Their Validity by E. J. Wentland and K. Smith (Academic Press), includes studies reporting accuracy of answers to questions from surveys. A study by Locander et al. considered the question “Are you a registered
16. Wildlife: Wolves A random sample of 17 wolf litters in Ontario, Canada, gave an average of x1 5 4.9 wolf pups per litter, with estimated sample standard deviation s1 5 1.0. Another random sample of 6 wolf litters in Finland gave an average of x2 5 2.8 wolf pups per litter, with sample standard
15. Wildlife: Wolves A random sample of 18 adult male wolves from the Canadian Northwest Territories gave an average weight x1 5 98 pounds, with estimated sample standard deviation s1 5 6.5 pounds. Another sample of 24 adult male wolves from Alaska gave an average weight x2 5 90 pounds, with
14. Stocks: Retail and Utility How profitable are different sectors of the stock market? One way to answer such a question is to examine profit as a percentage of stockholder equity. A random sample of 32 retail stocks such as Toys “ R”Us, Best Buy, and Gap was studied for x1, profit as a
13. Agriculture: Bell Peppers The following data represent soil water content(percent water by volume) for independent random samples of soil taken from two experimental fields growing bell peppers (Reference: Journal of Agricultural, Biological, and Environmental Statistics). Note: These data are
12. Archaeology: Pottery Consider the three-circle, red-on-white pattern discussed in Problem 11. How many ceramic potsherds must be found and identified if we are to be 95% confident that the sample proportion pˆ of such potsherds is within 6% of the population proportion of three-circle,
11. Archaeology: Pottery Three-circle, red-on-white is one distinctive pattern painted on ceramic vessels of the Anasazi period found at the Wind Mountain archaeological site (see source for Problem 7). At one excavation, a sample of 167 potsherds indicated that 68 were of the three-circle,
10. Telephone Interviews: Survey How large a sample is needed in Problem 9 if we wish to be 95% confident that the sample percentage of those equating success with personal satisfaction is within 1% of the population percentage?Hint: Use p < 0.52 as a preliminary estimate.
9. Telephone Interviews: Survey The National Study of the Changing Work Force conducted an extensive survey of 2958 wage and salaried workers on issues ranging from relationships with their bosses to household chores. The data were gathered through hour-long telephone interviews with a nationally
8. Archaeology: Pottery Shards of clay vessels were put together to reconstruct rim diameters of the original ceramic vessels found at the Wind Mountain archaeological site (see source in Problem 7). A random sample of ceramic vessels gave the following rim diameters (in centimeters):15.9 13.4 22.1
7. Archaeology: Excavations The Wind Mountain archaeological site is located in southwestern New Mexico. Wind Mountain was home to an ancient culture of prehistoric Native Americans called Anasazi. A random sample of excavations at Wind Mountain gave the following depths (in centimeters)from
6. Psychology: Closure How large a sample is needed in Problem 5 if we wish to be 99% confident that the sample mean score is within 2 points of the population mean score for students who are high on the need for closure?
5. Psychology: Closure Three experiments investigating the relationship between need for cognitive closure and persuasion were reported in “Motivated Resistance and Openness to Persuasion in the Presence or Absence of Prior Information” by A. W. Kruglanski (Journal of Personality and Social
4. Auto Insurance: Claims Anystate Auto Insurance Company took a random sample of 370 insurance claims paid out during a 1-year period. The average claim paid was $1570. Assume s 5 $250. Find 0.90 and 0.99 confidence intervals for the mean claim payment.
3. Critical Thinking If you have a 99% confidence interval for m based on a simple random sample,(a) is it correct to say that the probability that m is in the specified interval is 99%? Explain.(b) is it correct to say that in the long run, if you computed many, many confidence intervals using the
2. Critical Thinking Suppose you are told that a 95% confidence interval for the average price of a gallon of regular gasoline in your state is from $3.15 to$3.45. Use the fact that the confidence interval for the mean has the form x E to x 1 E to compute the sample mean and the maximal margin of
1. Statistical Literacy In your own words, carefully explain the meanings of the following terms: point estimate, critical value, maximal margin of error, confidence level, and confidence interval.
Green Behavior: Purchasing Habits A recent Harris Poll on green behavior showed that 25% of adults often purchase used items instead of new ones. Consider a random sample of 75 adults. Let ˆp be the sample proportion of adults who often purchase used instead of new items.(a) Is it appropriate to
5. In a way, the central limit theorem can be thought of as a kind of “grand central station.” It is a connecting hub or center for a great deal of statistical work. We will use it extensively in Chapters 7, 8, and 9. Put in a very elementary way, the central limit theorem states that as the
4. Most people would agree that increased information should give better predictions.Discuss how sampling distributions actually enable better predictions by providing more information. Examine Theorem 6.1 again. Suppose that x is a random variable with a normal distribution. Then x, the sample
3. Most companies that manufacture a product have a division responsible for quality control or quality assurance. The purpose of the quality-control division is to make reasonably certain that the products manufactured are up to company standards. Write a brief essay in which you describe how the
Basic Computation: pˆ Distribution Suppose we have a binomial distribution with n 5 24 trials and probability of success p 5 0.4 on each trial. The sample proportion of successes is pˆ 5r /n.(a) Is it appropriate to approximate the ˆp distribution with a normal distribution? Explain.(b) What are
Hatchery Fish: Length A large tank of fish from a hatchery is being delivered to a lake. The hatchery claims that the mean length of fish in the tank is 15 inches, and the standard deviation is 2 inches. A random sample of 36 fish is taken from the tank. Let x be the mean sample length of these
Psychology: IQ Scores Assume that IQ scores are normally distributed, with a standard deviation of 15 points and a mean of 100 points. If 100 people are chosen at random, what is the probability that the sample mean of IQ scores will not differ from the population mean by more than 2
Drugs: Effects A new muscle relaxant is available.Researchers from the firm developing the relaxant have done studies that indicate that the time lapse between administration of the drug and beginning effects of the drug is normally distributed, with mean m 5 38 minutes and standard deviation s 5 5
Job Interview: Length The personnel office at a large electronics firm regularly schedules job interviews and maintains records of the interviews. From the past records, they have found that the length of a first interview is normally distributed, with mean m 5 35 minutes and standard deviation s 5
Control Chart: Landing Gear Hydraulic pressure in the main cylinder of the landing gear of a commercial jet is very important for a safe landing. If the pressure is not high enough, the landing gear may not lower properly. If it is too high, the connectors in the hydraulic line may spring a
2. Why are standard z values so important? Is it true that z values have no units of measurement? Why would this be desirable for comparing data sets with different units of measurement? How can we assess differences in quality or performance by simply comparing z values under a standard normal
Guarantee: Package Delivery Express Courier Service has found that the delivery time for packages is normally distributed, with mean 14 hours and standard deviation 2 hours.(a) For a package selected at random, what is the probability that it will be delivered in 18 hours or less?(b) Inverse Normal
Guarantee: Battery Life Many people consider their smart phone to be essential! Communication, news, Internet, entertainment, photos, and just keeping current are all conveniently possible with a smart phone. However, the battery better be charged or the phone is useless. Battery life of course
1. If you look up the word empirical in a dictionary, you will find that it means“relying on experiment and observation rather than on theory.” Discuss the empirical rule in this context. The empirical rule certainly applies to the normal distribution, but does it also apply to a wide variety
Recycling: Aluminum Cans One environmental group did a study of recycling habits in a California community. It found that 70% of the aluminum cans sold in the area were recycled.(a) If 400 cans are sold today, what is the probability that 300 or more will be recycled?(b) Of the 400 cans sold, what
Customer Complaints: Time The Customer Service Center in a large New York department store has determined that the amount of time spent with a customer about a complaint is normally distributed, with a mean of 9.3 minutes and a standard deviation of 2.5 minutes. What is the probability that for a
Medical: Blood Type Blood type AB is found in only 3% of the population (Reference: Textbook of Medical Physiology, by A. Guyton, M.D.). If 250 people are chosen at random, what is the probability that(a) 5 or more will have this blood type?(b) between 5 and 10 will have this blood type?AppendixLO1
Basic Computation: Inverse Normal Find z such that 99% of the area under the standard normal curve lies between 2z and z.AppendixLO1
Basic Computation: Inverse Normal Find z such that 5% of the area under the standard normal curve lies to the right of z.AppendixLO1
26. Green Behavior: Purchasing Habits A recent Harris Poll on green behavior showed that 25% of adults often purchase used items instead of new ones.Consider a random sample of 75 adults. Let pˆ be the sample proportion of adults who often purchase used instead of new items.(a) Is it appropriate
Basic Computation: Probability Given that x is a normal variable with mean m 5110 and standard deviation s 512, find(a) P(x # 120)(b) P(x $ 80)(c) P(108 # x # 117)AppendixLO1
Basic Computation: Probability Given that x is a normal variable with mean m 5 47 and standard deviation s 5 6.2, find (a) P(x # 60)(b) P(x $ 50)(c) P(50 # x # 60)AppendixLO1
Critical Thinking If x has a normal distribution with mean m 515 and standard deviation s 5 3, describe the distribution of x values for sample size n, where n 5 4, n 516, and n 5100. How do the x distributions compare for the various sample sizes?AppendixLO1
Critical Thinking Let x be a random variable representing the amount of sleep each adult in New York City got last night. Consider a sampling distribution of sample means x .(a) As the sample size becomes increasingly large, what distribution does the x distribution approach?(b) As the sample size
Statistical Literacy Give the formula for the standard error of the sample proportion pˆ distribution, based on n binomial trials with probability of success p on each trial.AppendixLO1
25. Basic Computation: pˆ Distribution Suppose we have a binomial distribution with n 5 24 trials and probability of success p 5 0.4 on each trial. The sample proportion of successes is pˆ 5 r/n.(a) Is it appropriate to approximate the pˆ distribution with a normal distribution?Explain.(b) What
Statistical Literacy Give the formula for the standard error of the sample mean x distribution, based on samples of size n from a distribution with standard deviation s .AppendixLO1
Statistical Literacy For a normal distribution, is it likely that a data value selected at random is more than 2 standard deviations above the mean?AppendixLO1
Statistical Literacy What characteristic of a normal quantile plot indicates that the data follow a distribution that is approximately normal?AppendixLO1
Statistical Literacy Can a normal distribution always be used to approximate a binomial distribution?Explain.AppendixLO1
24. Hatchery Fish: Length A large tank of fish from a hatchery is being delivered to a lake. The hatchery claims that the mean length of fish in the tank is 15 inches, and the standard deviation is 2 inches. A random sample of 36 fish is taken from the tank. Let x be the mean sample length of these
Statistical Literacy Is a process in control if the corresponding control chart for data having a normal distribution shows a value beyond 3 standard deviations of the mean?AppendixLO1
Statistical Literacy According to the empirical rule, approximately what percentage of the area under a normal distribution lies within 1 standard deviation of the mean? within 2 standard deviations? within 3 standard deviations?AppendixLO1
Statistical Literacy Describe a normal probability distribution.AppendixLO1
Basic Computation: pˆ Distribution Suppose we have a binomial experiment in which success is defined to be a particular quality or attribute that interests us.(a) Suppose n 5100 and p 5 0.23. Can we safely approximate the pˆ distribution by a normal distribution? Why? Compute p mˆ and p s ˆ
23. Psychology: IQ Scores Assume that IQ scores are normally distributed, with a standard deviation of 15 points and a mean of 100 points. If 100 people are chosen at random, what is the probability that the sample mean of IQ scores will not differ from the population mean by more than 2 points?
Basic Computation: pˆ Distribution Suppose we have a binomial experiment in which success is defined to be a particular quality or attribute that interests us.(a) Suppose n 5 33 and p 5 0.21. Can we approximate the pˆ distribution by a normal distribution? Why? What are the values of p mˆ and p
22. Drugs: Effects A new muscle relaxant is available. Researchers from the firm developing the relaxant have done studies that indicate that the time lapse between administration of the drug and beginning effects of the drug is normally distributed, with mean m 5 38 minutes and standard deviation
Statistical Literacy Is pˆ an unbiased estimator for p when np . 5 and nq . 5? Recall that a statistic is an unbiased estimator of the corresponding parameter if the mean of the sampling distribution equals the parameter in question.AppendixLO1
Statistical Literacy What is the formula for the standard error of the normal approximation to the pˆdistribution? What is the mean of the pˆ distribution?AppendixLO1
Statistical Literacy Under what conditions is it appropriate to use a normal distribution to approximate the pˆ distribution?AppendixLO1
21. Job Interview: Length The personnel office at a large electronics firm regularly schedules job interviews and maintains records of the interviews. From the past records, they have found that the length of a first interview is normally distributed, with mean m 5 35 minutes and standard deviation
General: Approximations We have studied two approximations to the binomial, the normal approximation and the Poisson approximation (See Section 5.4). Write a brief but complete essay in which you discuss and summarize the conditions under which each approximation would be used, the formulas
Airline Flights: No-Shows Based on long experience, an airline has found that about 6% of the people making reservations on a flight from Miami to Denver do not show up for the flight. Suppose the airline overbooks this flight by selling 267 ticket reservations for an airplane with only 255
Ice Cream: Flavors What’s your favorite ice cream flavor? For people who buy ice cream, the all-time favorite is still vanilla. About 25% of ice cream sales are vanilla. Chocolate accounts for only 9% of ice cream sales. (See reference in Problem 8.) Suppose that 175 customers go to a grocery
Supermarkets: Free Samples Do you take the free samples offered in supermarkets? About 60% of all customers will take free samples. Furthermore, of those who take the free samples, about 37% will buy what they have sampled. (See reference in Problem 8.) Suppose you set up a counter in a supermarket
20. Control Chart: Landing Gear Hydraulic pressure in the main cylinder of the landing gear of a commercial jet is very important for a safe landing. If the pressure is not high enough, the landing gear may not lower properly. If it is too high, the connectors in the hydraulic line may spring a
Health: Blood Type According to the American Red Cross, type O-positive blood is the most common blood type in America, and as a result it is in very high demand. Approximately 38% of all Americans have blood type O-positive. Suppose the 63 blood donors at a given clinic represent a random sample
Grocery Stores: New Products The Denver Post stated that 80% of all new products introduced in grocery stores fail (are taken off the market) within 2 years. If a grocery store chain introduces 66 new products, what is the probability that within 2 years(a) 47 or more fail?(b) 58 or fewer fail?(c)
Fishing: Billfish Ocean fishing for billfish is very popular in the Cozumel region of Mexico. In World Record Game Fishes (published by the International Game Fish Association), it was stated that in the Cozumel region, about 44% of strikes (while trolling)result in a catch. Suppose that on a given
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