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statistics for experimentert

Introductory Statistics 10th Global Edition Neil A. Weiss - Solutions

Venture-Capital Investments. Refer to Exercise 8.69.a. Find a 99% confidence interval for μ.b. Why is the confidence interval you found in part (a) longer than the one in Exercise 8.69?c. Draw a graph similar to that shown in Fig. 8.6 on page 365 to display both confidence intervals.d. Which
Poverty and Dietary Calcium. Refer to Exercise 8.70.a. Find a 90% confidence interval for μ.b. Why is the confidence interval you found in part (a) shorter than the one in Exercise 8.70?c. Draw a graph similar to that shown in Fig. 8.6 on page 365 to display both confidence intervals.d. Which
Medical Marijuana. An issue with legalization of medical marijuana is “diversion”, the process in which medical marijuana prescribed for one person is given, traded, or sold to someone who is not registered for medical marijuana use. The mean number of days that 116 adolescents in substance
American Alligators. Multi-sensor data loggers were attached to free-ranging American alligators in a study conducted by Y. Watanabe for the article “Behavior of American Alligators Monitored by Multi-Sensor Data Loggers” (Aquatic Biology, Vol. 18, pp. 1–8). The mean duration for a sample of
Medical Marijuana. Refer to Exercise 8.77.a. Determine the margin of error for the 95% confidence interval.b. Determine the margin of error for the 90% confidence interval.c. Compare the margins of error found in parts (a) and (b).d. What principle is being illustrated?
American Alligators. Refer to Exercise 8.78.a. Determine the margin of error for the 95% confidence interval.b. Determine the margin of error for the 99% confidence interval.c. Compare the margins of error found in parts (a) and (b).d. What principle is being illustrated?
Medical Marijuana. Refer to Exercise 8.77.a. The mean number of days that 30 adolescents in substance abuse treatment used medical marijuana in the last 6 months was 105.43.Find a 95% confidence interval for μ based on that data.b. Compare the 95% confidence intervals obtained here and in Exercise
American Alligators. Refer to Exercise 8.78.a. The mean duration for a sample of 612 dives was 322 seconds.Find a 99% confidence interval for μ based on that data.b. Compare the 99% confidence intervals obtained here and in Exercise 8.78(b) by drawing a graph similar to Fig. 8.7 on page 366.c.
Prices of New Mobile Homes. Recall that a simple random sample of 36 new mobile homes yielded the prices, in thousands of dollars, shown in Table 8.1 on page 354. We found the mean of those prices to be $63.28 thousand.a. Use this information and Procedure 8.1 on page 361 to find a 95% confidence
In a study on infants, one of the characteristics measured was head circumference. The mean head circumference of 15 infants was 34.8 centimeters (cm). Complete parts (a) through (d) below.a. Assuming that head circumferences for infants are normally distributed with standard deviation 2.1 cm,
Fuel Expenditures. In estimating the mean monthly fuel expenditure, μ, per household vehicle, the Energy Information Administration takes a sample of size 6841. Assuming that σ = $20.65, determine the margin of error in estimating μ at the 95% level of confidence.
Venture-Capital Investments. In Exercise 8.69, you found a 95% confidence interval for the mean amount of all venture-capital investments in the fiber optics business sector to be from $5.389 million to $7.274 million. Obtain the margin of error bya. taking half the length of the confidence
Smelling Out the Enemy. In Exercise 8.72, you found a 90% confidence interval for the mean number of tongue flicks per 20 minutes for all juvenile common lizards to be from 456.4 to 608.0.Obtain the margin of error bya. taking half the length of the confidence interval.b. using Formula 8.1 on page
Political Prisoners. A 95% confidence interval of 18.4 months to 48.6 months has been found for the mean duration of imprisonment,μ, of political prisoners of a certain country with chronic PTSD.a. Determine the margin of error, E.b. Explain the meaning of E in this context in terms of the
Concert Tours. In Exercise 8.74, you found a 99% confidence interval of 474515.21 tickets to 685132.79 tickets for the mean number of tickets sold of top 30 concerts.a. Determine the margin of error, E.b. Explain the meaning of E in this context in terms of the accuracy of the estimate.c. Find the
LEDs and CFLs. Light-emitting diodes (LEDs) and compact fluorescent lights (CFLs) are lightbulbs that are supposed to last up to fifty times longer than old fashioned incandescent lightbulbs and also use less energy. Consumer Reports sampled eighteen different 60-watt LED and CFL lightbulbs. The
Long Drives. The Professional Golfer’s Association of America (PGA) organizes golf tournaments for professional golfers. The following table lists the longest drives, in yards, recorded during a PGA tournament for a random sample of 26 golfers. Use the technology of your choice to decide whether
Ages of Diabetics. According to the document All About Diabetes, found on the website of the American Diabetes Association,“... diabetes is a disease in which the body does not produce or properly use insulin, a hormone that is needed to convert sugar, starches, and other food into energy needed
Civilian Labor Force. Consider again the problem of estimating the mean age, μ, of all people in the civilian labor force. In Example 8.7 on page 367, we found that a sample size of 2250 is required to have a margin of error of 0.5 year and a 95% confidence level. Suppose that, due to financial
Civilian Labor Force. Consider again the problem of estimating the mean age, μ, of all people in the civilian labor force. In Example 8.7 on page 367, we found that a sample size of 2250 is required to have a margin of error of 0.5 year and a 95% confidence level. Suppose that, due to financial
Millionaires. Professor Thomas Stanley of Georgia State University has surveyed millionaires since 1973. Among other information, Professor Stanley obtains estimates for the mean age, μ, of all U.S. millionaires. Suppose that one year’s study involved a simple random sample of 36 U.S.
Cereals. The Food and Agriculture Organization of the United Nations estimates the mean value of the production of cereals across the world. Those estimates are published on their website http://faostat.fao.org/. Suppose that an estimate, x¯, is obtained and that the margin of error is 100,000
Body Temperature. A study by researchers at the University of Maryland addressed the question of whether the mean body temperature of humans is 98.6◦F. The results of the study by P. Mackowiak et al. appeared in the article “A Critical Appraisal of 98.6◦F, the Upper Limit of the Normal Body
Malnutrition and Poverty. R. Reifen et al. studied various nutritional measures of Ethiopian school children and published their findings in the paper “Ethiopian-Born and Native Israeli School Children Have Different Growth Patterns” (Nutrition, Vol. 19, pp. 427–431). The study, conducted in
Clocking the Cheetah. The cheetah (Acinonyx jubatus) is the fastest land mammal and is highly specialized to run down prey. The cheetah often exceeds speeds of 60 mph and, according to the online document “Cheetah Conservation in Southern Africa” (Trade & Environment Database (TED) Case
Class Project: Gestation Periods of Humans. This exercise can be done individually or, better yet, as a class project.Gestation periods of humans are normally distributed with a mean of 266 days and a standard deviation of 16 days.a. Simulate 100 samples of nine human gestation periods each.b. For
For a fixed confidence level, show that (approximately) quadrupling the sample size is necessary to halve the margin of error.(Hint: Use Formula 8.2.)Another type of confidence interval is called a one-sided confidence interval. A one-sided confidence interval provides either a lower confidence
One-Sided One-Mean z-Intervals. Presuming that the assumptions for a one-mean z-interval are satisfied, we have the following formulas for (1 − α)-level confidence bounds for a population mean μ:Lower confidence bound: x¯ − zα · σ/√n Upper confidence bound: x¯ + zα · σ/√n
Poverty and Dietary Calcium. Refer to Exercise 8.70.a. Determine and interpret a 95% upper confidence bound for the mean calcium intake of all people with incomes below the poverty level.b. Compare your one-sided confidence interval in part (a) to the (twosided) confidence interval found in
Toxic Mushrooms? Refer to Exercise 8.71.a. Determine and interpret a 99% lower confidence bound for the mean cadmium level of all Boletus pinicola mushrooms.b. Compare your one-sided confidence interval in part (a) to the (twosided) confidence interval found in Exercise 8.71.
A variable has a mean of 100 and a standard deviation of 16.Four observations of this variable have a mean of 108 and a sample standard deviation of 12. Determine the observed value of thea. standardized version of x¯.b. studentized version of x¯.
Green Sea Urchins. From the paper “Effects of Chronic Nitrate Exposure on Gonad Growth in Green Sea Urchin Strongylocentrotus droebachiensis” (Aquaculture, Vol. 242, No. 1–4, pp. 357–363)by S. Siikavuopio et al., the weights, x, of adult green sea urchins are normally distributed with mean
Batting Averages. In a report by International Cricket Council revealed that batting averages, x, of a major cricket team players are normally distributed and have a mean of 52.71 and a standard deviation of 5.34. For samples of 10 batting averages, identify the distribution of each variable.a. x¯
Explain why there is more variation in the possible values of the studentized version of x¯ than in the possible values of the standardized version of x¯.
A simple random sample of size 17 is taken from a population with unknown standard deviation. A normal probability plot of the data reveals an outlier but is otherwise roughly linear. Can you reasonably apply the t-interval procedure? Explain your answer.
Identify the formula for the margin of error for the estimate of a population mean when the population standard deviation is unknown.
For the one-mean t-interval procedure, express the formula for the endpoints of a confidence interval in the form point estimate ± margin of error.
Northeast Commutes. According to Scarborough Research, more than 85% of working adults commute by car. Of all U.S. cities, Washington, D.C., and New York City have the longest commute times. A sample of 30 commuters in the Washington, D.C., area yielded the following commute times, in minutes.24 28
The following data represent the concentration of organic carbon (mg/L) collected from organic soil. Construct a 99% confidence interval for the mean concentration of dissolved organic carbon collected from organic soil. (Note: x¯ = 16.88 mg/L and s = 8.44 mg/L) 11.90 29.80 27.10 16.51 5.20 8.81
Sleep. In 1908, W. S. Gosset published the article “The Probable Error of a Mean” (Biometrika, Vol. 6, pp. 1–25). In this pioneering paper, written under the pseudonym “Student,” Gosset introduced what later became known as Student’s t-distribution. Gosset used the following data set,
Family Fun? Taking the family to an amusement park has become increasingly costly according to the industry publication Amusement Business, which provides figures on the cost for a family of four to spend the day at one of America’s amusement parks. A random sample of 25 families of four that
“Chips Ahoy! 1,000 Chips Challenge.” As reported by B. Warner and J. Rutledge in the paper “Checking the Chips Ahoy!Guarantee” (Chance, Vol. 12, Issue 1, pp. 10–14), a random sample of forty-two 18-ounce bags of Chips Ahoy! cookies yielded a mean of 1261.6 chips per bag with a standard
Adelie Penguin. ´ The webpage “Adelie Penguin” produced ´by the National Geographic Society provides information about the Adelie Penguin. A random sample of 50 adult Ad ´ elie Penguin can ´dive a mean depth of 575 ft with a standard deviation of 13 ft. Find and interpret a 90% confidence
Military Assistance Loans. The annual update of U.S. Overseas Loans and Grants, informally known as the “Greenbook,” contains data on U.S. government monetary economic and military assistance loans. The following table shows military assistance loans, in thousands of dollars, to a sample of 10
The following data represent the age (in weeks) at which babies first crawl based on a survey of 12 mothers.52 30 44 35 47 37 56 26 52 47 52 26 Decide whether applying the t-interval procedure to obtain a confidence interval for the population mean in question appears reasonable. Explain your
Big Bucks. In the article “The $350,000 Club” (The Business Journal, Vol. 24, Issue 14, pp. 80–82), J. Trunelle et al. examined Arizona public-company executives with salaries and bonuses totaling over $350,000. The following data provide the salaries, to the nearest thousand dollars, of a
Shoe and Apparel E-Tailers. In the special report “Mousetrap: The Most-Visited Shoe and Apparel E-tailers” (Footwear News, Vol. 58, No. 3, p. 18), we found the following data on the average time, in minutes, spent per user per month from January to June of one year for a sample of 15 shoe and
The Coruro’s Burrow. The subterranean coruro (Spalacopus cyanus) is a social rodent that lives in large colonies in underground burrows that can reach lengths of up to 600 meters.Zoologists S. Begall and M. Gallardo studied the characteristics of the burrow systems of the subterranean coruro in
Forearm Length. In 1903, K. Pearson and A. Lee published the paper “On the Laws of Inheritance in Man. I. Inheritance of Physical Characters” (Biometrika, Vol. 2, pp. 357–462). The article examined and presented data on forearm length, in inches, for a sample of 140 men, which we have
Blood Cholesterol and Heart Disease. Numerous studies have shown that high blood cholesterol leads to artery clogging and subsequent heart disease. One such study by D. Scott et al. was published in the paper “Plasma Lipids as Collateral Risk Factors in Coronary Artery Disease: A Study of 371
Bicycle Commuting Times. A city planner working on bikeways designs a questionnaire to obtain information about local bicycle commuters. One of the questions asks how long it takes the rider to pedal from home to his or her destination. A sample of local bicycle commuters yields the following
Let 0
Batting Averages. An article states that the batting averages of major cricket players are normally distributed with mean 52.12 and standard deviation 40.44.a. Simulate 1000 samples of five batting averages each.b. Determine the sample mean and sample standard deviation of each of the 1000
Northeast Commutes. Refer to Exercise 8.129.a. Determine and interpret a 90% upper confidence bound for the mean commute time of all commuters in Washington, DC.b. Compare your one-sided confidence interval in part (a) to the (twosided) confidence interval found in Exercise 8.129.
Digital Viewing Times. Refer to Exercise 8.130.a. Find and interpret a 90% lower confidence bound for last year’s mean time spent per day with digital media by American adults.b. Compare your one-sided confidence interval in part (a) to the (twosided) confidence interval found in Exercise 8.130.
M&Ms. In the article “Sweetening Statistics—What M&M’s Can Teach Us” (Minitab Inc., August 2008), M. Paret and E. Martz discussed several statistical analyses that they performed on bags of M&Ms. The authors took a random sample of 30 small bags of peanut M&Ms and obtained the following
Christmas Spending. In a national poll of 1039 U.S. adults, conducted November 7–10, 2013, Gallup asked “Roughly how much money do you think you personally will spend on Christmas gifts this year?”. The data provided on the WeissStats site are based on the results of the poll.a. Determine a
Bootstrap Confidence Intervals. With the advent of highspeed computing, new procedures have been developed that permit statistical inferences to be performed under less restrictive conditions than those of classical procedures. Bootstrap confidence intervals constitute one such collection of new
use and understand the formulas in this chapter.
obtain a point estimate for a population mean.
find and interpret a confidence interval for a population mean when the population standard deviation is known.
compute and interpret the margin of error for the estimate of μ.
understand the relationship between sample size, standard deviation, confidence level, and margin of error for a confidence interval for μ.
determine the sample size required for a specified confidence level and margin of error for the estimate of μ.
understand the difference between the standardized and studentized versions of x¯.
state the basic properties of t-curves.
use Table IV to find tα/2 for df = n − 1 and selected values of α.
find and interpret a confidence interval for a population mean when the population standard deviation is unknown.
decide whether it is appropriate to use the z-interval procedure, the t-interval procedure, or neither.
Suppose that you intend to find a 95% confidence interval for a population mean by applying the one-mean z-interval procedure to a sample of size 100.a. What would happen to the accuracy of the estimate if you used a sample of size 50 instead but kept the same confidence level of 0.95?b. What would
A confidence interval for a population mean has a margin of error of 10.7.a. Obtain the length of the confidence interval.b. If the mean of the sample is 75.2, determine the confidence interval.c. Express the confidence interval in the form “point estimate ±margin of error.”
A variable of a population has a mean of 159.58 and a standard deviation of 27.67. Ten observations of this variable have a mean of 145.13 and a sample standard deviation of 28.40. Obtain the observed value of thea. standardized version of x¯.b. studentized version of x¯.
Baby Weight. The paper “Are Babies Normal?” by T. Clemons and M. Pagano (The American Statistician, Vol. 53, No. 4, pp. 298–302) focused on birth weights of babies. According to the article, for babies born within the “normal” gestational range of 37–43 weeks, birth weights are normally
The following figure shows the standard normal curve and two t-curves. Which of the two t-curves has the larger degrees of freedom? Explain your answer.Standard normal curve−3 −2 −1 0 1 2 3 In each of Problems 12–17, we have provided a scenario for a confidence interval. Decide, in each
A random sample of size 17 is taken from a population. A normal probability plot of the sample data is found to be very close to linear (straight line). The population standard deviation is unknown.
A random sample of size 50 is taken from a population. A boxplot of the sample data reveals no outliers. The population standard deviation is known.
A random sample of size 25 is taken from a population. A normal probability plot of the sample data shows three outliers but is otherwise roughly linear. Checking reveals that the outliers are due to recording errors and are really not outliers. The population standard deviation is known.
A random sample of size 20 is taken from a population. A normal probability plot of the sample data shows three outliers but is otherwise roughly linear. Removal of the outliers is questionable.The population standard deviation is unknown.
A random sample of size 128 is taken from a population. A normal probability plot of the sample data shows no outliers but has significant curvature. The population standard deviation is known.
A random sample of size 13 is taken from a population. A normal probability plot of the sample data shows no outliers but has significant curvature. The population standard deviation is unknown.
For a t-curve with df = 18, obtain the t-value and illustrate your results graphically.a. The t-value having area 0.025 to its rightb. t0.05c. The t-value having area 0.10 to its leftd. The two t-values that divide the area under the curve into a middle 0.99 area and two outside 0.005 areas
Millionaires. Dr. Thomas Stanley of Georgia State University has surveyed millionaires since 1973. Among other information, Stanley obtains estimates for the mean age, μ, of all U.S. millionaires.Suppose that 36 randomly selected U.S. millionaires are the following ages, in years.31 45 79 64 48 38
Millionaires. From Problem 19, we know that “a 95% confidence interval for the mean age of all U.S. millionaires is from 54.3 years to 62.8 years.” Decide which of the following sentences provide a correct interpretation of the statement in quotes.Justify your answers.a. Ninety-five percent of
Prison Sentences. Researcher Sudhinta Sinha discussed how people adjust to prison life in the article “Adjustment and mental health problem in prisoners” (Industrial Psychiatry Journal, Vol. 19, No. 2, pp. 101–104). A sample of 37 sentenced adult male prisoners had an average age of 36.7
Prison Sentences. Refer to Problem 21.a. Find the margin of error, E.b. Explain the meaning of E as far as the accuracy of the estimate is concerned.c. Determine the sample size required to have a margin of error of 1.2 year and a 90% confidence level.d. Find a 90% confidence interval for μ if a
Children of Diabetic Mothers. The paper “Correlations between the Intrauterine Metabolic Environment and Blood Pressure in Adolescent Offspring of Diabetic Mothers” (Journal of Pediatrics, Vol. 136, Issue 5, pp. 587–592) by N. Cho et al. presented findings of research on children of diabetic
Diamond Pricing. In a Singapore edition of Business Times, diamond pricing was explored. The price of a diamond is based on the diamond’s weight, color, and clarity. A simple random sample of 18 one-half-carat diamonds had the following prices, in dollars.1676 1442 1995 1718 1826 2071 1947 1983
Wildfires. Wildfires are uncontrolled fires that usually spread quickly and are common in wilderness areas that have long and dry summers. The Insurance Information Institute reports statistics on wildfires on their website www.iii.org. The following data lists the size, in thousands of acres, of a
Delaying Adulthood. The convict surgeonfish is a common tropical reef fish that has been found to delay metamorphosis into adult by extending its larval phase. This delay often leads to enhanced survivorship in the species by increasing the chances of finding suitable habitat. In the paper
Fuel Economy. The U.S. Department of Energy collects fueleconomy information on new motor vehicles and publishes its findings in Fuel Economy Guide. The data included are the result of vehicle testing done at the Environmental Protection Agency’s National Vehicle and Fuel Emissions Laboratory in
Old Faithful Geyser. In the online article “Old Faithful at Yellowstone, a Bimodal Distribution,” D. Howell examined various aspects of the Old Faithful Geyser at Yellowstone National Park.Despite its name, there is considerable variation in both the length of the eruptions and in the time
Booted Eagles. The rare booted eagle of western Europe was the focus of a study by S. Suarez et al. to identify optimal nesting habitat for this raptor. According to their paper “Nesting Habitat Selection by Booted Eagles (Hieraaetus pennatus) and Implications for Management” (Journal of
What is the relation between the significance level of a hypothesis test and the probability of making a Type I error?
Approving Bills in Parliament. Suppose that you are performing a statistical test to decide whether a bill should be approved in parliament. Further suppose that failing to reject the null hypothesis corresponds to approval. What property would you want the Type II error probability, β, to have?
Guilty or Innocent? In the U.S. court system, a defendant is assumed innocent until proven guilty. Suppose that you regard a court trial as a hypothesis test with null and alternative hypotheses H0: Defendant is innocent Ha: Defendant is guilty.a. Explain the meaning of a Type I error.b. Explain
Toxic Mushrooms? Cadmium, a heavy metal, is toxic to animals. Mushrooms, however, are able to absorb and accumulate cadmium at high concentrations. The Czech and Slovak governments have set a safety limit for cadmium in dry vegetables at 0.5 part per million (ppm). M. Melgar et al. measured the
Body Weight. Quail chicks, after hatching, can be either stable or unstable depending upon the social environment. The average body weight of a stable chick after 4 weeks is 202.56 grams. The body weight of such chicks has been studied by F. Guibert et al. in the article “Social Instability in
Iron Content of the Body. Iron is essential to most life forms and to normal human physiology. It is an integral part of many proteins and enzymes that maintain good health. Recommendations for iron are provided in Nutrient Reference Values for Australia and New Zealand, developed by the Ministry
Early-Onset Dementia. Dementia is the loss of the intellectual and social abilities severe enough to interfere with judgment, behavior, and daily functioning. Alzheimer’s disease is the most common type of dementia. In the article “Living with Early Onset Dementia: Exploring the Experience and
Fraud/Deception. According to the NSW Bureau of Crime Statistics and Research of Australia and New Zealand, the mean length of imprisonment for ‘committing fraud and deception’ offenders in Australia is 208.3 days. You want to perform a hypothesis test to decide whether the mean length of

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