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Understanding Basic Statistics 6th Edition Charles Henry Brase, Corrinne Pellillo Brase - Solutions

Allen’s hummingbird (Selasphorus sasin) has been studied by zoologist Bill Alther. A small group of 15 Allen’s hummingbirds has been under study in Arizona. The average weight for these birds is = 3.15 grams. Based on previous studies, we can assume that the weights of Allen’s hummingbirds
Overproduction of uric acid in the body can be an indication of cell breakdown. This may be an advance indication of illness such as gout, leukemia, or lymphoma. Over a period of months, an adult male patient has taken eight blood tests for uric acid. The mean concentration was = 5.35 mg/dL. The
Total plasma volume is important in determining the required plasma component in blood replacement therapy for a person undergoing surgery. Plasma volume is influenced by the overall health and physical activity of an individual. Suppose that a random sample of 45 male firefighters are tested and
What price do farmers get for their watermelon crops? In the third week of July, a random sample of 40 farming regions gave a sample mean of = $6.88 per 100 pounds of watermelons. Assume that σ is known to be $1.92 per 100 pounds. (a) Find a 90% confidence interval for the population mean price
Thirty small communities in Connecticut (population near 10,000 each) reported an average of = 138.5 cases of larceny per year. Assume that σ is known to be 42.6 cases per year. (a) Find a 90% confidence interval for the population mean annual number of reported larceny cases in such
The point estimate for the population mean μ of an x distribution is , computed from a random sample of the x distribution.
A random sample of size 36 is drawn from an x distribution. The sample mean is 100. (a) Suppose the x distribution has σ = 30. Compute a 90% confidence interval for μ. What is the value of the margin of error? (b) Suppose the x distribution has σ = 20. Compute a 90% confidence interval for μ.
A random sample is drawn from a population with σ = 12. The sample mean is 30. (a) Compute a 95% confidence interval for μ based on a sample of size 49. What is the value of the margin of error? (b) Compute a 95% confidence interval for μ based on a sample of size 100. What is the value of the
At wind speeds above 1000 centimeters per second (cm/sec), significant sand-moving events begin to occur. Wind speeds below 1000 cm/sec deposit sand, and wind speeds above 1000 cm/sec move sand to new locations. The cyclic nature of wind and moving sand determines the shape and location of large
Jobs and productivity! How do banks rate? One way to answer this question is to examine annual profits per employee. Forbes Top Companies, edited by J. T. Davis (John Wiley & Sons), gave the following data about annual profits per employee (in units of one thousand dollars per employee) for
Jobs and productivity! How do retail stores rate? One way to answer this question is to examine annual profits per employee. The following data give annual profits per employee (in units of one thousand dollars per employee) for companies in retail sales. Companies such as Gap, Nordstrom,
How hot is the air in the top (crown) of a hot air balloon? Information from Ballooning: The Complete Guide to Riding the Winds by D. Wirth and J. Young (Random House) claims that the air in the crown should be an average of 100°C for a balloon to be in a state of equilibrium. However, the
A larger sample size produces a longer confidence interval for μ.
If the original x distribution has a relatively small standard deviation, the confidence interval for μ will be relatively short.
Use Table 4 of the Appendix to find tc for a 0.95 confidence level when the sample size is 18.
A random sample of size 81 has sample mean 20 and sample standard deviation 3. (a) Is it appropriate to use a Student’s t distribution to compute a confidence interval for the population mean μ? Explain. (b) Find a 95% confidence interval for μ. (c) Explain the meaning of the confidence
At Burnt Mesa Pueblo, the method of tree-ring dating gave the following years A.D. for an archaeological excavation site (Bandelier Archaeological Excavation Project: Summer 1990 Excavations at Burnt Mesa Pueblo, edited by Kohler, Washington State University):(a) Use a calculator with mean and
How much does a sleeping bag cost? Let€™s say you want a sleeping bag that should keep you warm in temperatures from 20°F to 45°F. A random sample of prices ($) for sleeping bags in this temperature range was taken from Backpacker Magazine€™s: Gear Guide (Vol. 25, Issue 157, No. 2). Brand
How much do wild mountain lions weigh? The 77th Annual Report of the New Mexico Department of Game and Fish, edited by Bill Montoya, gave the following information. Adult wild mountain lions (18 months or older) captured and released for the first time in the San Andres Mountains gave the following
Do you want to own your own candy store? With some interest in running your own business and a decent credit rating, you can probably get a bank loan on start-up costs for franchises such as Candy Express, The Fudge Company, Karmel Korn, and Rocky Mountain Chocolate Factory. Start-up costs (in
Over the past several months, an adult patient has been treated for tetany (severe muscle spasms). This condition is associated with an average total calcium level below 6 mg/dL. Recently, the patient€™s total calcium tests gave the following readings (in mg/dL):(a) Use a calculator to verify
What percentage of hospitals provide at least some charity care? This problem is based on information taken from State Health Care Data: Utilization, Spending, and Characteristics (American Medical Association). Based on a random sample of hospital reports from eastern states, the following
The distribution of heights of 18-year-old men in the United States is approximately normal, with mean 68 inches and standard deviation 3 inches (U.S. Census Bureau). In Minitab, we can simulate the drawing of random samples of size 20 from this population (Calc ž¤ Random Data
Use Table 4 of the Appendix to find tc for a 0.99 confidence level when the sample size is 4.
The following data represent crime rates per 1000 population for a random sample of 46 Denver neighborhoods:(a) Use a calculator with mean and sample standard deviation keys to verify that ‰ˆ 64.2 and s ‰ˆ 27.9 crimes per 1000 population.(b) Let us say that the preceding data are
The price of a share of stock divided by a company€™s estimated future earnings per share is called the P/E ratio. High P/E ratios usually indicate €œgrowth€ stocks, or maybe stocks that are simply overpriced. Low P/E ratios indicate €œvalue€™€™ stocks or bargain stocks. A
The home run percentage is the number of home runs per 100 times at bat. A random sample of 43 professional baseball players gave the following data for home run percentages:(a) Use a calculator with mean and sample standard deviation keys to verify that ‰ˆ 2.29 and s ‰ˆ
When σ is unknown and the sample is of size n ≥ 30, there are two methods for computing confidence intervals for μ. Method 1: Use the Student’s t distribution with d.f. = n – 1. This is the method used in the text. It is widely employed in statistical studies. Also, most statistical
Use Table 4 of the Appendix to find tc for a 0.90 confidence level when the sample size is 22.
Use Table 4 of the Appendix to find tc for a 0.95 confidence level when the sample size is 12.
What is the minimal sample size needed for a 99% confidence interval to have a maximal margin of error of 0.06: (a) If a preliminary estimate for p is 0.8? (b) If there is no preliminary estimate for p?
Isabel Briggs Myers was a pioneer in the study of personality types. The following information is taken from MBTI Manual: A Guide to the Development and Use of the Myers-Briggs Type Indicator by Myers and McCaulley (Consulting Psychologists Press). In a random sample of 62 professional actors, it
In a random sample of 519 judges, it was found that 285 were introverts. (a) Let p represent the proportion of all judges who are introverts. Find a point estimate for p. (b) Find a 99% confidence interval for p. Give a brief interpretation of the meaning of the confidence interval you have
A random sample of 5222 permanent dwellings on the entire Navajo Reservation showed that 1619 were traditional Navajo hogans (Navajo Architecture: Forms, History, Distributions by Jett and Spencer, University of Arizona Press). (a) Let p be the proportion of all permanent dwellings on the entire
Santa Fe black-on-white is a type of pottery commonly found at archaeological excavations in Bandelier National Monument. At one excavation site a sample of 592 potsherds was found, of which 360 were identified as Santa Fe black-on-white (Bandelier Archaeological Excavation Project: Summer 1990
A random sample of 5792 physicians in Colorado showed that 3139 provide at least some charity care (i.e., treat poor people at no cost). These data are based on information from State Health Care Data: Utilization, Spending, and Characteristics (American Medical Association). (a) Let p represent
Case studies showed that out of 10,351 convicts who escaped from U.S. prisons, only 7867 were recaptured (The Book of Odds by Shook and Shook, Signet). (a) Let p represent the proportion of all escaped convicts who will eventually be recaptured. Find a point estimate for p. (b) Find a 99%
In a survey of a random sample of 35 households in the Cherry Creek neighborhood of Denver, it was found that 11 households turned out the lights and pretended not to be home on Halloween. (a) Compute a 90% confidence interval for p, the proportion of all housholds in Cherry Creek that pretend not
In a marketing survey, a random sample of 730 women shoppers revealed that 628 remained loyal to their favorite supermarket during the past year (i.e., did not switch stores).(a) Let p represent the proportion of all women shoppers who remain loyal to their favorite supermarket. Find a point
In a marketing survey, a random sample of 1001 supermarket shoppers revealed that 273 always stock up on an item when they find that item at a real bargain price.(a) Let p represent the proportion of all supermarket shoppers who always stock up on an item when they find a real bargain. Find a point
In a survey of 1000 large corporations, 250 said that, given a choice between a job candidate who smokes and an equally qualified nonsmoker, the nonsmoker would get the job (USA Today).(a) Let p represent the proportion of all corporations preferring a nonsmoking candidate. Find a point estimate
A New York Times/CBS poll asked the question “What do you think is the most important problem facing this country today?” Nineteen percent of the respondents answered “Crime and violence.” The margin of sampling error was plus or minus 3 percentage points. Following the convention that the
A random sample of medical files is used to estimate the proportion p of all people who have blood type B. (a) If you have no preliminary estimate for p, how many medical files should you include in a random sample in order to be 85% sure that the point estimate will be within a distance of 0.05
How hard is it to reach a businessperson by phone? Let p be the proportion of calls to businesspeople for which the caller reaches the person being called on the first try.(a) If you have no preliminary estimate for p, how many business phone calls should you include in a random sample to be 80%
What percentage of your campus student body is female? Let p be the proportion of women students on your campus.(a) If no preliminary study is made to estimate p, how large a sample is needed to be 99% sure that a point estimate will be within a distance of 0.05 from p?(b) The Statistical
The National Council of Small Businesses is interested in the proportion of small businesses that declared Chapter 11 bankruptcy last year. Since there are so many small businesses, the council intends to estimate the proportion from a random sample. Let p be the proportion of small businesses that
Why do we use 1/4 in place of p(1 – p) in formula (20) for sample size when the probability of success p is unknown? (a) Show that p(1 – p) = 1/4 – (p - 1/2)2. (b) Why is p(1 – p) never greater than 1/4?
One of the technical difficulties that arises in the computation of confidence intervals for a single proportion is that the exact formula for the maximal margin of error requires knowledge of the population proportion of success p. Since p is usually not known, we use the sample estimate = r/n
Results of a poll of a random sample of 3003 American adults showed that 20% did not know that caffeine contributes to dehydration. The poll was conducted for the Nutrition Information Center and had a margin of error of ±1.4%.(a) Does the margin of error take into account any problems with the
Jerry tested 30 laptop computers owned by classmates enrolled in a large computer-science class and discovered that 22 were infected with keystroke-tracking spyware. Is it appropriate for Jerry to use his data to estimate the proportion of all laptops infected with such spyware? Explain.
A requirement for using the normal distribution to approximate the distribution is that both np > 5 and nq > 5. Since we usually do not know p, we estimate p by and q by = 1 - . Then we require that n > 5 and n > 5. Show that the conditions n > 5 and n > 5 are equivalent to the condition
Consider n = 100 binomial trials with r = 30 successes.(a) Is it appropriate to use a normal distribution to approximate the distribution?(b) Find a 90% confidence interval for the population proportion of successes p.(c) Explain the meaning of the confidence interval you computed.
Consider n = 200 binomial trials with r = 80 successes. (a) Check Requirements Is it appropriate to use a normal distribution to approximate the distribution? (b) Find a 95% confidence interval for the population proportion of successes p. (c) Explain the meaning of the confidence interval you
What is the minimal sample size needed for a 95% confidence interval to have a maximal margin of error of 0.1: (a) If a preliminary estimate for p is 0.25? (b) If there is no preliminary estimate for p?
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.
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? Use p ≈ 0.52 as a preliminary estimate.
Three-circle, red-on-white is one distinctive pattern painted on ceramic vessels of the Anasazi period found at the Wind Mountain archaeological site. At one excavation, a sample of 167 potsherds indicated that 68 were of the three-circle, red-on-white pattern. (a) Find a point estimate for the
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 of such potsherds is within 6% of the population proportion of three-circle, red-on-white patterns found at
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 - E to + E to compute the sample mean and the maximal margin of error E.
If you have a 99% confidence interval for μ based on a simple random sample: (a) Is it correct to say that the probability that μ 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 prescribed
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 σ = $250. Find 0.90 and 0.99 confidence intervals for the mean claim payment.
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. Part of the study involved administering a “need for
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? Problem 5 Three experiments investigating the relationship between need for cognitive closure and
The Wind Mountain archaeological site is located in southwestern New Mexico. Wind Mountain was home to a culture of prehistoric Native Americans called Anasazi. A random sample of excavations at Wind Mountain gave the following depths (in centimeters) from present-day surface grade to the location
Shards of clay vessels were put together to reconstruct rim diameters of the original ceramic vessels found at the Wind Mountain archaeological site. A random sample of ceramic vessels gave the following rim diameters (in centimeters): 15.9 13.4 22.1 12.7 13.1 19.6 11.7 13.5 17.7 18.1 (a) Use a
The National Study of the Changing Workforce 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 representative sample (The Wall
Discuss each of the following topics in class or review the topics on your own. Then write a brief but complete essay in which you answer the following questions: (a) What is a null hypothesis H0? (b) What is an alternate hypothesis H1? (c) What is a type I error? a type II error? (d) What is the
Suppose you want to test the claim that a population mean equals 40.(a) State the null hypothesis.(b) State the alternate hypothesis if you have no information regarding how the population mean might differ from 40.(c) State the alternate hypothesis if you believe (based on experience or past
Suppose you want to test the claim that a population mean equals 30. (a) State the null hypothesis. (b) State the alternate hypothesis if you have no information regarding how the population mean might differ from 30. (c) State the alternate hypothesis if you believe (based on experience or past
A random sample of size 20 from a normal distribution with σ = 4 produced a sample mean of 8. (a) Is the distribution normal? Explain. (b) Compute the sample test statistic z under the null hypothesis H0: μ = 7. (c) For H1: μ ≠ 7, estimate the P-value of the test statistic. (d) For a level
A random sample of size 16 from a normal distribution with σ = 3 produced a sample mean of 4.5. (a) Is the distribution normal? Explain. (b) Compute the sample test statistic z under the null hypothesis H0: μ = 6.3. (c) For H1: μ < 6.3, estimate the P-value of the test statistic. (d) For a
The body weight of a healthy 3-month-old colt should be about μ = 60 kg. (a) If you want to set up a statistical test to challenge the claim that μ = 60 kg, what would you use for the null hypothesis H0? (b) In Nevada, there are many herds of wild horses. Suppose you want to test the claim that
How much customers buy is a direct result of how much time they spend in a store. A study of average shopping times in a large national housewares store gave the following information: Women with female companion: 8.3 minutes Women with male companion: 4.5 minutes Suppose you want to set up a
Weatherwise magazine is published in association with the American Meteorological Society. Volume 46, Number 6, has a rating system to classify nor’easter storms that frequently hit New England states and can cause much damage near the ocean coast. A severe storm has an average peak wave height
Consumer Reports stated that the mean time for a Chrysler Concorde to go from 0 to 60 miles per hour is 8.7 seconds. (a) If you want to set up a statistical test to challenge the claim of 8.7 seconds, what would you use for the null hypothesis? (b) The town of Leadville, Colorado, has an elevation
Let x be a random variable representing dividend yield of Australian bank stocks. We may assume that x has a normal distribution with σ = 2.4%. A random sample of 10 Australian bank stocks gave the following yields: 5.7 4.8 6.0 4.9 4.0 3.4 6.5 7.1 5.3 6.1 The sample mean is = 5.38%. For the
Gentle Ben is a Morgan horse at a Colorado dude ranch. Over the past 8 weeks, a veterinarian took the following glucose readings from this horse (in mg/100 mL): 93 88 82 105 99 110 84 89 The sample mean is ≈ 93.8. Let x be a random variable representing glucose readings taken from Gentle
Bill Alther is a zoologist who studies Anna’s hummingbirds (Calypte anna). Suppose that in a remote part of the Grand Canyon, a random sample of six of these birds was caught, weighed, and released. The weights (in grams) were: 3.7 2.9 3.8 4.2 4.8 3.1 The sample mean is = 3.75 grams. Let x
The price-to-earnings (P/E) ratio is an important tool in financial work. A random sample of 14 large U.S. banks (JPMorgan Chase, Bank of America, and others) gave the following P/E ratios:The sample mean is ‰ˆ 17.1. Generally speaking, a low P/E ratio indicates a
Nationally, about 11% of the total U.S. wheat crop is destroyed each year by hail. An insurance company is studying wheat hail-damage claims in Weld County, Colorado. A random sample of 16 claims in Weld County gave the following data (% wheat crop lost to hail):The sample mean is = 12.5%. Let x
Total blood volume (in mL) per body weight (in kg) is important in medical research. For healthy adults, the red-blood-cell volume mean is about μ = 28 mL/kg. Red blood cell volume that is too low or too high can indicate a medical problem (see reference). Suppose that Roger has had seven blood
If we reject the null hypothesis, does this mean that we have proved it to be false beyond all doubt? Explain your answer.
A random sample has 49 values. The sample mean is 8.5 and the sample standard deviation is 1.5. Use a level of significance of 0.01 to conduct a left-tailed test of the claim that the population mean is 9.2. (a) Is it appropriate to use a Student’s t distribution? Explain. How many degrees of
Weatherwise is a magazine published by the American Meteorological Society. One issue gives a rating system used to classify nor’easter storms that frequently hit New England and can cause much damage near the ocean. A severe storm has an average peak wave height of μ = 16.4 feet for waves
Let x be a random variable that represents the pH of arterial plasma (i.e., acidity of the blood). For healthy adults, the mean of the x distribution is μ = 7.4. A new drug for arthritis has been developed; however, it is thought that this drug may change blood pH. A random sample of 31 patients
A random sample of 46 adult coyotes in a region of northern Minnesota showed the average age to be = 2.05 years, with sample standard deviation s = 0.82 years (based on information from the book Coyotes: Biology, Behavior, and Management, edited by M. Bekoff, Academic Press). However, it is
Pyramid Lake is on the Paiute Indian Nation in Nevada. The lake is famous for cutthroat trout. Suppose a friend tells you that the average length of trout caught in Pyramid Lake is μ = 19 inches. However, a creel survey published by the Pyramid Lake Fisheries reported that for a random sample of
Socially conscious investors screen out stocks of alcohol and tobacco makers, firms with poor environmental records, and companies with poor labor practices. Some examples of “good,” socially conscious companies are Johnson and Johnson, Dell, Bank of America, and Home Depot. The question is,
Unfortunately, arsenic occurs naturally in some groundwater. A mean arsenic level of μ = 8.0 parts per billion (ppb) is considered safe for agricultural use. A well in Texas is used to water cotton crops. This well is tested on a regular basis for arsenic. A random sample of 37 tests gave a sample
Let x be a random variable that represents red blood cell (RBC) count in millions of cells per cubic millimeter of whole blood. Then x has a distribution that is approximately normal. For the population of healthy female adults, the mean of the x distribution is about 4.8 (based on information from
Let x be a random variable that represents hemoglobin count (HC) in grams per 100 milliliters of whole blood. Then x has a distribution that is approximately normal, with population mean of about 14 for healthy adult women. Suppose that a female patient has taken 10 laboratory blood tests during
Snow avalanches can be a real problem for travelers in the western United States and Canada. A very common type of avalanche is called the slab avalanche. These have been studied extensively by David McClung, a professor of civil engineering at the University of British Columbia. Slab avalanches
USA Today reported that the state with the longest mean life span is Hawaii, where the population mean life span is 77 years. A random sample of 20 obituary notices in the Honolulu Advertiser gave the following information about life span (in years) of Honolulu residents:i. Use a calculator with
Hosmer Lake, Oregon, has an Atlantic salmon catch-and-release program that has been very successful. The average fisherman€™s catch has been Î¼ = 8.8 Atlantic salmon per day. Suppose that a new quota system restricting the number of fishermen has been put into effect this
Tree-ring dating from archaeological excavation sites is used in conjunction with other chronologic evidence to estimate occupation dates of ancient Indian ruins in the southwestern United States. It is thought that Burnt Mesa Pueblo was occupied around ad 1300 (based on evidence from potsherds and
(a) For the same data and null hypothesis, is the P-value of a one-tailed test (right or left) larger or smaller than that of a two-tailed test? Explain. (b) For the same data, null hypothesis, and level of significance, is it possible that a one-tailed test results in the conclusion to reject H0
Is there a relationship between confidence intervals and two-tailed hypothesis tests? Let c be the level of confidence used to construct a confidence interval from sample data. Let α be the level of significance for a two-tailed hypothesis test. The following statement applies to hypothesis tests
Change the null hypothesis of Problem 25 to H0: μ = 21. Repeat parts (a) and (b). Problem 25 (a) What is the value of c = 1 - α? Using the methods of Chapter 8, construct a 1 - α confidence interval for m from the sample data. What is the value of μ given in the null hypothesis (i.e., what is
Solve Problem 11 using the critical region method of testing (i.e., traditional method). Compare your conclusion with the conclusion obtained by using the P-value method. Are they the same?
Table 4 of the Appendix gives critical values for the Student’s t distribution. Use an appropriate d.f. as the row header. For a right-tailed test, the column header is the value of α found in the one-tail area row. For a left-tailed test, the column header is the value of α found in the

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