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nonparametric statistical inference

Questions and Answers of Nonparametric Statistical Inference

It is better for everyone involved ifthe man is the achiever outside the home and the woman takes care of the home and the family: (627, 1208)
Women should take care of running their homes and leave running the country up to men: (275,1556)
5.53. When subjectsin a recent GSS were asked whether they agreed with the following statements, the(yei1, no) counts under various conditions were as follows:
5.51. In 2006, the GSS asked about the number of hours a week spent on the World Wide Web. excluding e-mail (variable denoted WWWHR). State a research question you could address about this response
5.48. Refer to the previous exercise. Using the confidence interval for a proportion applet, let's check that the confidence interval for a proportion may work poorly with small samples. Set « = 10
5.47. You can use an applet to repeatedly generate random samples and construct confidence intervals, to
5.46. Refer to Example 5.9 (page 130). Construct a 95%confidence interval for the median time since a book was last checked out. Interpret.
5.44. You randomly sample five students at your school to estimate the proportion of students who like tofu. None of the five students say they like it.(a) Find the sample proportion who like it and
5.36. A television network plans to predict the outcome of an election between Jacalyn Levin and Roberto 5.37. A public health unit wants to sample death records for the past year in Toronto to
5.33. A study estimates the mean annual family income for families living in public housing in Chicago.For a random sample of 30 families, the annual incomes (in hundreds of dollars) are 83 90 77 100
3.50 with standard deviation 1.51?(c) What assumption are you making about the scale of measurement for political ideology when you use the sample mean and standard deviation?
5.31. The GSS asks respondents to rate their political views on a seven-point scale, where 1 = extremely liberal, 4 = moderate, and 7 = extremely conservative. A researcher analyzing data from the
5.30. For the "Florida student survey" data file mentioned in Exercise 1.11, software reportsthe results for responses on the number of times a week the subject reads a newspaper:Variable N Mean Std
5.29. The 2004 GSS asked respondents how many sex partners they had in the previous 12 months. Software reports:Variable N Mean StDev SE Mean 95.0'/. CI partners 2198 1.130 1.063 0.0227 (1.09,
5.27. The GSS has asked subjects, "How long have you lived in the city, town or community where you live now?" The responses of 1415 subjects in one
5.26. In response to the GSS question in 2006 about the number of hours daily spent watching TV. the responses by the 15 subjects who identified themselves as Buddhist were 0, 0, 0, 1, 1, 1, 2, 2, 2,
5.25. The 2004 GSS asked, "On the average day about how many hours do you personally watch television?" Software reports;Variable N Mean SE Mean 95.07. CI TVH0URS 892 2.76 0.08 (2.60, 2.93)What's
5.24. Example 5.5 (page 120) analyzed data from a study that compared therapies for anorexia. For the 17 girls who received the family therapy, the changes in weight during the study were
5.22. A GSS asked, "What do you think is the ideal number of children for a family to have?" The 497 females who responded had a median of 2, mean of 3.02, and standard deviation of 1.81.(a) Report
5.21. The 2004 GSS asked male respondents how many female partners they have had sex with since their eighteenth birthday. The median = 6 and mode = 1 (16.0% of the sample). A computer printout
5.20. Find and interpret the 95% confidence interval for jtr. ify = 70 and x = 10, based on a sample size of(a) 5(b) 20.
5.19. Report the t-score that multiplies by the standard error to form a(a) 95% confidence interval with 5 observations(b) 95% confidence interval with 15 observations(c) 95% confidence interval with
5.12. In the 2006 GSS, respondents were asked whether they favored or opposed the death penalty for people convicted of murder. Software shows results:x n Sample prop 95.0% CI 1885 2815 0.6696
5.11. State the z-score used in finding a confidence interval for a proportion with confidence level(a) 0.98(b) 0.90(c) 0.50(d) 0.9973.
5.9. In 2006, the Florida Poll conducted by Florida International University asked whether current environmental regulations arc too strict or not too strict. Of 1200 respondents, 229 said they were
5.4. A national survey conducted in July 2006 by Pew Forum on Religion & Public Life asked whether the subject favored allowing homosexual couples to enter into civil unions—legal agreements that
5.2. In response to the GSS question in 2006 about the number of hours daily spent watching TV, the responses by the seven subjects who identified themselves as Hindus were 2, 3, 2,1,0,1, 4, 3.(a)
5.1. Of 577,006 people involved in motor vehicle accidents in Florida in a recent year, 412,878 were wearing scat belts (Source: Florida Department of Highway Safety and Motor Vehicles). Find a point
4.57. The standard error formula ay = a/Jn treats the population size N as infinitely large relative to the sample size n. The formula for ay for a finite population size N is IN - n (
4.56. The curve for a normal distribution with mean p and standard deviation a has mathematical formula f(y) = (>'-M)2/(2^2)_•J2tti ira Show that this curve is symmetric, by showing that for any
4.55. The standard deviation of a discrete probability distribution is" = VSCv - m) P{y)-(a) Suppose y = 1 with probability 0.50 and y = 0 with probability 0.50, such as in Example 4.8(page 91). Show
4.54. Lake Wobegon Junior College admits students only if they score above 400 on a standardized achievement test. Applicants from group A have a mean of 500 and a standard deviation of 100 on this
4.50. For an election exit poll for a Senatorial election, find the standard error of the sample proportion voting for a candidate for whom the population proportion is 0.50, when n = 100,1000, and
4.49. In an exit poll of 1336 voters in the 2006 Senatorial election in New York State, 67% said they voted for Hillary Clinton. Based on this information, would you be willing to predict the winner
4.48. For a normal distribution, show that(a) The upper quartile equals /x + 0.67a.(b) According to the 1.5(IQR) criterion, an outlier is an observation falling more than 2.7 standard deviations
4.47. The Palestinian Central Bureau of Statistics(www.pcbs.gov.ps) asked mothers of age 20-24 about the ideal number of children. For those living on the Gaza Strip, the probability distribution is
4.46. (a) Which distribution docs the sample data distribution tend to resemble more closely—the sampling distribution or the population distribution? Explain.(b) Explain carefully the difference
4.45. (Class Exercise) For a single toss of a coin, let y = 1 for a head and y = 0 for a tail. This simulates the vote in an election with two equally-preferred candidates.(a) Construct the
4.44. (Class Exercise) Table 4.5 provides the ages of all 50 heads of households in a small Nova Scotian fishing village. The distribution of these ages is characterized by/x = 47.18 and a =
4.43. (Class Exercise) Refer to Exercises 1.11 and 1.12(page 8). Using the population defined by your class or using the studentsurvey, the instructor will select a variable,such as weekly time
4.41. You can use an applet on a computer or on the Internet to repeatedly generate random samples from artificial populations and analyze them to study the properties of statistical methods. To try
4.40. Refer to the previous exercise.(a) Describe the sampling distribution of y for a random sample of size n -(b) Describe the sampling distribution of y if you sample all 50,000 residents.
4.39. Sunshine City was designed to attract retired people. Its current population of 50,000 residents has a mean age of 60 years and a standard deviation of 16 years. The distribution of ages is
4.36. The distribution of family size in a particular tribal society is skewed to the right, with /x = 5.2 and a - 3.0. These values are unknown to an anthropologist, who samples families to estimate
4.34. A study plans to sample randomly 100 government records of farms in Ontario to estimate the mean 4.35. According to the U.S. Census Bureau, in 2000 the number of people in a household had a
4.33. The scores on the Psychomotor Development Index (PD1), a scale of infant development, are approximately normal with mean 100 and standard deviation 15.(a) An infant is selected at random. Find
4.32. According to recent General Social Surveys (variable PARTNERS), in the United States the distribution ofy = number ofsex partners you have had in the past 12 months has a mean of about 1.1 and
4.31. Referto Exercise 4.6. The mean and standard deviation of the probability distribution for the lottery winnings y arc p, = 0.10 and a = 316.23. Suppose you play the lottery 1 million times. Let
4.29. An exit poll of 2293 voters in the 2006 Ohio Senatorial election indicated that 44% voted for the Republican candidate, Mike DeWine, and 56% voted for the Democratic candidate, Sherrod
4.28. The probability distribution associated with the outcome of rolling a balanced die has probability 1/6 attached to each integer, {1,2,3,4,5,6}. Let(yi^yi) denote the outcomes for rolling the
4.26. Five students, Ann, Betty, Clint, Douglas, and Edward, arc rated equally qualified for admission to law school, ahead of other applicants. However, all but two positions have been filled for
4.25. An energy study in Gainesville, Florida, found that in March 2006, household use of electricity had a mean of 673 and a standard deviation of 556 kWh(kilowatt-hours).(a) If the distribution
4.23. For an SAT distribution (/x = 500, rr = 100) and an ACT distribution (/x = 21, cr = 4.7), which score is relatively higher, SAT = 600 or ACT = 29?Explain.
4.21. Suppose that the weekly use of gasoline for motor travel by adults in North America is approximately normally distributed, with a mean of 16 gallons and a standard deviation of 5 gallons.(a)
4.20. For 5459 pregnant women using Aarhus University Hospital in Denmark in a two-year period who reported information on length of gestation until birth, the mean was 281.9 days, with standard
4.19. The Mental Development Index (MDI) ofthe Bayley Scales of Infant Development is a standardized measure used in studies with high-risk infants. It has approximately a normal distribution with a
4.17. Mensa is a society of high-lQ people whose members have a score on an IQ test atthe 98th percentile or higher.(a) How many standard deviations above the mean is the 98th percentile?(b) For the
4.15. What proportion of a normal distribution falls in the following ranges?(a) Above a z-score of 2.10(b) Below a z-score of-2.10(c) Above a z-score of —2.10(d) Between z-scores of -2.10 and 2.10
4.14. If z is the positive number such that the interval from fx - zo-\o fx + z
4.13. Show that if z is the number such that the interval from fx - zcr Xo ix + zu contains 90% of a normal distribution, then ^ + zcr equals the 95th percentile.
4.12. Find the z-values corresponding to the(a) 90th.(b) 95th,(c) 98th, and
4.11. Find the z-value such that for a normal distribution the interval from /t - zcr to jtx + zo- contains(a) 50%(b) 90%(c) 95%(d) 98%(e) 99% of the probability.
4.10. Find the z-value for which the probability that a normal variable exceeds fx + zo- equals(a) 0.01(b) 0.025(c) 0.05(d) 0.10(e) 0.25(f) 0.50
4.9. For a normally distributed variable, verify that the probability between:(a) fi - a and /x + a equals 0.68(b) fx — 1.96(r and/x + L96(t equals 0.95(c) /x — 3o- and /x + 3(r equals 0.997(d)
4.8. For a normal distribution, find the probability that an observation falls(a) At least one standard deviation above the mean(b) At least one standard deviation below the mean(c) At least 0.67
4.7. Let y be the outcome of selecting a single digit from a random number table.(a) Construct the probability distribution for y.(This type of distribution is called a uniform distribution because
4.5. Let y denote the number of people known personally who were victims of homicide within the past 12 months. According to results from recent General Social Surveys,for a randomly chosen person in
4.4. Let y — number of languages in which a person is fluent. According to Statistics Canada, for residents of Canada this has probability distribution P(0) = 0.02, P(l) = 0.81, P{2) =0.17, with
4.3. In 2000, the GSS asked subjects whether they are a member of an environmental group (variable GRNGROUP) and whether they would be very willing to pay much higher prices to protect the
3.81. The leastsquares property of the mean states that the data fall closer to y than to any other numberc, in the sense that the sum of squares of deviations of the data about their mean is smaller
3.80. The Russian mathematician Tchebysheff proved that for any A: > 1, the proportion of observations that fall more than k standard deviations from the mean can be no greater than \/k~. This holds
- >y«-
3.79. Showthat S(y,- — y) must equal 0 for any collection of observations yi,y2^
3.78. For a sample with mean y, adding a constant c to each observation changes the mean to y +c, and the standard deviation s is unchanged. Multiplying each observation by c changes the mean to cy
3.77. Refer to Table 3.2 (page 34). Explain why the mean of these 50 observations is not necessarily the same as the violent crime rate for the entire U.S. population.
3.76. Ten people are randomly selected in Florida and another ten people are randomly selected in Alabama. Table 3.18 provides summary information on mean income. The mean is higher in Alabama both
3.75. A teacher summarizes grades on the midterm exam by Min = 26,01 - 67, Median - 80.Q3 = 87, Max = 100, Mean = 76. Mode = 100, Standard dev. = 76, IOR = 20.She incorrectly recorded one of these.
3.71. Answer true or false to the following:(a) The mean, median, and mode can never all be the same.(b) The mean is always one of the data points.(c) The median is the same as the second quartile
3.70. To measure variability, why is(a) The standard deviation s usually preferred over the range?(b) The 1QR sometimes preferred to .v?
3.65. The fertility rate (mean number of children per adult woman) varies in Western European?
3.64. A U.S. Federal Reserve study in 2000 indicated that for those families with annual incomes above $100,000, their median net worth was about$500,000 both in 1995 and in 1998, but their mean net
3.53. What is the difference between the descriptive measures symbolized by(a) y and /x?(b) s and rr?
3.51. For the data for OECD nations in Table 3.11 in Exercise 3.6, use software to construct a scatterplot relating y - carbon dioxide emissions and x = GDP.(a) Based on this plot, would you expect
3.46. The United Nations publication Energy Statistics Yearbook (unstats.un.org/unsd/energy) lists consumption of energy. For the 25 nations that made up the EU in 2006, the energy values (in
3.41. In 2004, the five-numbersummary forthe statewide percentage ofpeople without health insurance had a minimum of 8.9% (Minnesota), Ql = 11.6, Med = 14.2, (93 = 17.0, and maximum of 25.0%(Texas)
3.40. Infant mortality rates (number of infant deaths, per 1000 live births) are reported by the UN.In their 2006 report, the values for Africa had a five-number summary of min — 54,Q1 - 76, median
3.39. For the student survey data on number of times a week reading a newspaper, referred to in Exercise 1.11, Figure 3.20 shows a computer printout of the stem-and-leaf plot and the box plot.(a)
3.38. The January 2007 unemployment rates of the 27 countries in the European Union ranged from 3.2 (Denmark) to 12.6 (Poland), with lower quartile = 5.0, median = 6.7, upper quartile =7.9, mean =
3.36. For each of the following variables, indicate whether you would expect its relative frequency histogram to be bell shaped, U shaped, skewed to the right, or skewed to the left.(a) Exam score of
3.34. During a recent semester at the University of Florida, computer usage3 of students having accounts on a mainframe computer was summarized by a mean of 1921 and a standard deviation of 11,495
3.29. For all homes in Gainesville, Florida, the residential electrical consumption2 for the year 2006 had a mean of 10,449 and a standard deviation of 7489 kilowatt-hours (kWh). The maximum usage
3.28. According to the U.S. Census Bureau, the U.S.nationwide median selling price of homes sold in 2005 was $184,100. Which of the following is the most plausible value for the standard
3.26. The first exam in your Statistics course is graded on a scale of 0 to 100, and the mean is 76. Which value is most plausible for the standard deviation:-20, 0, 10, or 50? Why?
3.16. According to the U.S. Bureau of the Census, 2005 American Community Survey, the median earnings in the past 12 months was $32,168 for females and$41,965 for males, whereas the mean was $39,890
3.14. Table 3.13 summarizes responses of 2333 subjects in the 2006 General Social Survey to the question,"About how often did you have sex during the last 12 months?"(a) Report the median and the
3.8. Global warming seems largely a result of human activity that produces carbon dioxide emissions and other greenhouse gases. The Human DevelopmentReport2005, published by the United Nations
3.6. The OECD (Organization for Economic Cooperation and Development) consists of advanced, industrialized countries that accept the principles of representative democracy and a free market economy.
3.3. A teacher shows her class the scores on the midterm exam in the stem-and-leaf plot:6 15 8 8 7101136779 8 I 1223334677789 91011234458(a) Identify the number of students and the minimum and
2.40. An interval scale for which ratios are valid is called a ratio scale. Such scales have a well-defined 0 point, so, for instance, one can regard the value 20 as twice the quantity of the value
2.38. An interviewer stands at an entrance to a popular shopping mall and conducts interviews. True or false: Because we cannot predict who will be interviewed, the sample obtained is an example of a

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