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statistics for experimentert

Questions and Answers of Statistics For Experimentert

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
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
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
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
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 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
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
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
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.
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
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
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
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
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
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
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
“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
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
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
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
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
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,
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.
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
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
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
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
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
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
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
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
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
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
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.
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
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,
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
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
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
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
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. 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
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,
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
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.
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
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
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
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
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
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
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
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:
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
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
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
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
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
Worker Fatigue. A study by M. Chen et al. titled “Heat Stress Evaluation and Worker Fatigue in a Steel Plant” (American Industrial Hygiene Association, Vol. 64, pp. 352–359) assessed fatigue in
A study by researchers at a university addressed the question of whether the mean body temperature of an animal is 101.3◦F.Among other data, the researchers obtained the body temperatures of 106
Teacher Salaries. Data on salaries in the public school system are published annually in Ranking of the States and Estimates of School Statistics by the National Education Association. The mean
Toxic Mushrooms? Refer to Exercise 9.15. Explain what each of the following would mean.a. Type I errorb. Type II errorc. Correct decision Now suppose that the results of carrying out the hypothesis
Body Weight. Refer to Exercise 9.16. Explain what each of the following would mean.a. Type I errorb. Type II errorc. Correct decision Now suppose that the results of carrying out the hypothesis test
Iron Content of the Body. Refer to Exercise 9.17. Explain what each of the following would mean.a. Type I errorb. Type II errorc. Correct decision Now suppose that the results of carrying out the
Early-Onset Dementia. Refer to Exercise 9.18. Explain what each of the following would mean.a. Type I errorb. Type II errorc. Correct decision Now suppose that the results of carrying out the
Motor-Vehicle Theft. The mean length of imprisonment for motor-vehicle theft offenders in this country is 21.5 months. A hypothesis test is to be performed to decide whether the mean length of
Worker Fatigue. Refer to Exercise 9.20. Explain what each of the following would mean.a. Type I errorb. Type II errorc. Correct decision Now suppose that the results of carrying out the hypothesis
Body Temperature. Refer to Exercise 9.21. Explain what each of the following would mean.a. Type I errorb. Type II errorc. Correct decision Now suppose that the results of carrying out the hypothesis
Teacher Salaries. Refer to Exercise 9.22. Explain what each of the following would mean.a. Type I errorb. Type II errorc. Correct decision Now suppose that the results of carrying out the hypothesis
The P-value for a hypothesis test is 0.105. For each of the following significance levels, decide whether the null hypothesis should be rejected.a. α = 0.05b. α = 0.10c. α = 0.01
Obtaining the P-value. Let x denote the test statistic for a hypothesis test and x0 its observed value. Then the P-value of the hypothesis test equalsa. P(x ≥ x0) for a right-tailed test,b. P(x ≤
Explain why considering outliers is important when you are conducting a one-mean z-test.In each of Exercises 9.73–9.76, we have provided a scenario for a hypothesis test for a population mean.
Preliminary data analyses reveal that the sample data contain no outliers but that the distribution of the variable under consideration is probably highly skewed. The sample size is 24.
A normal probability plot of the sample data shows no outliers and is quite linear. The sample size is 12.
Preliminary data analyses reveal that the sample data contain no outliers but that the distribution of the variable under consideration is probably mildly skewed. The sample size is 70.
Preliminary data analyses reveal that the sample data contain an outlier. It is determined that the outlier is a legitimate observation and should not be removed. The sample size is 12.
Cadmium, a heavy metal, is toxic to animals. Mushrooms, however, are able to absorb and accumulate cadmium at high concentrations. A government set a safety limit for cadmium in dry vegetables at 0.5
Grey-Seal Nursing. The average lactation (nursing) period of all earless seals is 23 days. Grey seals are one of several types of earless seals. The length of time that a female grey seal nurses her
Iron Content. The recommended dietary allowance (RDA) of iron for adult females is 18 milligrams (mg) per day. The given iron intakes (mg) were obtained for 45 random adult females. At the
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

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