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mathematics
statistics

Questions and Answers of Statistics

Referring to Example 6, but using only the two conditions "signature at bottom" after filling out the form and "no signature required."(a) Conduct a x2 test. Take or = .05.(b) Does the conclusion of
Referring to Example 6, but using only the two conditions "signature at the top" and "no signature required,"(a) Make a 2 × 2 table and test H0: pT = pN versus H1 : pT < pN at a = .02.(b) Obtain
Concern over the quality of eyeglasses purchased over the Internet led to a study where many glasses were individually ordered from several different online vendors. Using only those lenses with
Osteoporosis, or a loss of bone minerals, is a common cause of broken bones in the elderly. A researcher on aging conjectures that bone mineral loss can be reduced by regular physical therapy or
Using the computer. The analysis of a contingency table can be conveniently done on a computer. For an illustration, we present here a MINITAB analysis of the data in Table 6, Example 5.(a) Compare
Recorded here is the frequency distribution of the blood types of 100 persons who have volunteered to donate blood at a plasma center.Test the goodness of fit of the model, which assumes that the
With reference to the sleep data in Table D.10 of the Data Bank, make two categories of snorers on the basis of the last variable: those who responded three or more times a week so their score is
Applicants for public assistance are allowed an appeals process when they feel unfairly treated. At such a hearing, the applicant may choose self-representation or representation by an attorney. The
A consultant to all kinds of retailers suggests that they have plenty of baskets available for customers. He bases his suggestion on data collected by watching videos from hidden cameras. Suppose
A survey was conducted by sampling 400 persons who were questioned regarding union membership and attitude toward decreased national spending on social welfare programs. The cross-tabulated frequency
Lying can have major economic and social implications. A double blind trial was conducted to study the effect of testosterone on lying. Among 91 healthy men, ni = 46 received 50 mg of testosterone on
In a study of factors that regulate behavior, three kinds of subjects are identified: over controllers, average controllers, and under controllers, with the first group being most inhibited. Each
Out of 120 members of a club who responded to a survey, 80 said that the golfing facilities were influential, 53 said the dining facilities were influential, and 25 said both were influential in
Do Exercise 13.26 on a computer. Exercise 13.26 Out of 120 members of a club who responded to a survey, 80 said that the golfing facilities were influential, 53 said the dining facilities were
To examine the quality of a random number generator, frequency counts of the individual integers are recorded from an output of 500 integers. The concept of randomness implies that the integers 0, 1,
Referring to the data in Exercise 13.2, test the null hypothesis that the probability of the blood types O, A, B, and AB is in the ratios 4:4:1:1. Use Î± = .05.
The following table records the observed number of births at a hospital in four consecutive quarterly periods.It is conjectured that twice as many babies are born during the Jan.-March quarter than
A community paper in the Spanish language was delivered to many sites in the San Francisco Bay area. As a check on the circulation numbers that are important to advertisers, a survey was conducted at
Referring to the data for site 3 and site 4 in Exercise 13.31, make a 2 x 2 table and test H0: p3 = P4 versus Hj: p3 > p4 at a = .05.(a) Is there strong evidence that the probability a paper will
Refer to Exercise 3.48 and the data concerning a vaccine for type B hepatitis.Do these data indicate that there is a different rate of incidence of hepatitis between the vaccinated and non vaccinated
Refer to the data in Exercise 13.33.(a) Use the Z test for testing the equality of two population proportions with a two-sided alternative. Verify the relation x2 = Z2 by comparing their numerical
To compare the effectiveness of four drugs in relieving postoperative pain, an experiment was done by randomly assigning 195 surgical patients to the drugs under study. Recorded here are the number
Using the data for drugs 1 and 3 in Exercise 13.35, make a 2 Ã— 2 contingency table and test Ho - p1 = P3 versus H0: p1 ‰ p3 at a = .05 employing:(a) The x2 test.(b) The Z
In a study conducted to monitor the quality of eyeglasses purchased over the Internet, 154 pairs of glasses were received from individual orders placed with several different online vendors. The
In a study on the effect of diet and lifestyle on heart disease, 96 patients with severe coronary blockage were randomly assigned, 49 to an experimental group and 47 to a control group. The patients
Based on interviews of couples seeking divorces, a social worker compiles the following data related to the period of acquaintanceship before marriage and the duration of marriage.Test the null
A market researcher wishes to assess consumers' preference among three different colors available on name-brand dishwashers. The following frequencies were observed from a random sample of 150 recent
By polling a random sample of 350 undergraduate students, a campus press obtains the following frequency counts regarding student attitude toward a proposed change in dormitory regulations.Are
In a genetic study of chromosome structures, 132 individuals are classified according to the type of structural chromosome aberration and carriers in their parents. The following counts are
A random sample of 130 business executives was classified according to age and the degree of risk aversion as measured by a psychological test.Do these data demonstrate an association between risk
Pooling contingency tables can produce spurious association. A large organization is being investigated to determine if its recruitment is sex-biased. Tables 15 and 16, respectively, show the
A shipment of assorted nuts is labeled as having 45% walnuts, 20% hazelnuts, 20% almonds, and 15% pistachios. By randomly picking several scoops of nuts from this shipment, an inspector finds the
Cross-fertilizing a pure strain of red flowers with a pure strain of white flowers produces pink hybrids that have one gene of each type. Crossing these hybrids can lead to any one of four possible
According to the records of the National Safety Council, accidental deaths in the United States during a recent year had the following distribution according to the principal types of accidents.In a
The following table, based on government data, shows the frequency distribution of births by day of the week for all registered births in the United States in a recent year. Test the null hypothesis,
Observations of 80 litters, each containing 3 rabbits, reveal the following frequency distribution of the number of male rabbits per litter.Under the model of Bernoulli trials for the sex of rabbits,
Independent random samples of sizes nA = 4 and nB = 2 are taken from two continuous populations. (a) Enumerate all possible collections of ranks associated with the smaller sample in the combined
Morphologic measurements of a particular type of fossil excavated from two geological sites provided the following data: Site A....................Site B 1.49 ................... 1.31 1.32
IfnA = landnB = 9, find (a) The rank configuration that most strongly supports H1: Population A is shifted to the right of population B. (b) The null probability of WA = 10. (c) Is it possible to
In a taste test of two chocolate chip cookie recipes, 13 out of 18 subjects favored recipe A. Using the sign test, find the significance probability when H1 states that recipe A is preferable.
wo critics rate the service at six a ward-winning restaurants on a continuous 0 to 10 scale. Is there a difference between the critics' ratings?(a) Use the sign test with a below .05.(b) Find the
A social researcher interviews 25 newly married couples. Each husband and wife are independently asked the question: "How many children would you like to have?" The following data are obtained.Do the
Use Appendix B, Table 9, to find: (a)P[T+ ≥54 ] when n = 11. (b)P [T+ ≤ 32] when n = 15. (c)The value of c so that P [T+ ≥ c ] is nearly .05 when n = 14.
Use Appendix B, Table 9, to find: (a) P[T+ > 65] when n = 12. (b) P [ T+ < 10 ] when n = 10. (c) The value c such that P [T+ > c ] = .039 when n = 8. (d) The values c, and c2 such that P [T+ < c, ] =
Referring to Exercise 15.14, apply the Wilcoxon signed-rank test with or near .05.
The null distribution of the Wilcoxon signed-rank statistic T+ is determined from the fact that under the null hypothesis of a symmetric distribution about zero, each of the ranks 1, 2, . . . , n is
Independent samples of sizes nA = 2 and nB = 2 are taken from two continuous populations. (a) Enumerate all possible collections of ranks associated with population A. Also attach probabilities to
A married couple's monthly credit charges are divided into his and hers and the difference, husband's minus wife's, is calculated. A random sample of 30 married couples yielded the Wilcoxon
In Example 14 of Chapter 10, we presented data on the blood pressure of 15 persons before and after they took a pill.(a) Perform a sign test, with a near .05, to determine if blood pressure has
Charles Darwin performed an experiment to determine if self-fertilized and cross-fertilized plants have different growth rates. Pairs of Zea mays plants, one self- and the other cross-fertilized,
Refer to Exercise 11.31 and the first four countries in Table 7. The number of Internet users per one hundred residents and the human development index (HDI) are
Refer to Exercise 11.67 and the height and speed of the four tallest roller coasters. Given the data
The following scores are obtained on a test of dexterity and aggression administered to a random sample of 10 high school seniors.Evaluate Spearman's statistic.
Referring to Example 10, determine the significance probability of rSp = .4, using the one-sided test, when n = 40.
Three male and three female students recorded the number of times they used a credit card in one week.Designate males as population A. Evaluate WA.
Using Appendix B, Table 8, find:(a) P[WS ≥ 42 ] when n1 = 5, n2 = 7.(b) P [ Ws ≤ 25 ] when n1 = 6, n2 = 6.(c) P [ Ws ≥ 81 or Ws ≤ 45 ] when n1 = 10, n2 = 7.(d) The point c such that P [ Ws
(a) Evaluate all possible rank configurations associated with treatment A when nA = 3 and nB = 2. (b) Determine the null distribution of WA.
Using Appendix B, Table 8, find: (a) P[WS ≥ 39 ] when nA = 5, nB = 6. (b) P[WS ≤ 15] when nA = 6, nB = 4. (c) The point c such that P [ Ws ≥ c ] is close to .05 when nA = 7, nB = 7.
Five finalists in a figure-skating contest are rated by two judges on a 10-point scale as follows:Calculate the Spearman's rank correlation between the two ratings.
Using Appendix B, Table 9, find: (a) P[T+ ≥28 ] when n = 8. (b) P [ T+ ≤ 5 ] when n = 7. (c) The point c such that P (T+ < c ) is approximately .05 when n = 13.
Referring to Exercise 15.30, calculate:(a) The sign test statistic.(b) The significance probability when the alternative is that Judge 2 gives higher scores than Judge 1.
In a study of the cognitive capacities of non-human primates, 19 monkeys of the same age are randomly divided into two groups of 10 and 9. The groups are trained by two different teaching methods to
A mixture of compounds called phenolics occurs in wood waste products. It has been found that when phenolics are present in large quantities that waste become unsuitable for use as a livestock feed.
(a) Calculate Spearman's rank correlation for the data on Chester Whites in Exercise 15.6.(b) Test for independence of calcium and phosphate levels using the rejection region(c) What is the
In the study described in Exercise 1.23, golfers were asked to estimate the size of the hole (cm) in the green by selecting among nine in a board. The size selected and their score for the day for
Refer to Exercise 10.76. Evaluate: (a) Sign test statistic. (b) Signed-rank statistic.
Let X1, . . . , Xn" be a random sample from a continuous population whose median is denoted by M. For testing H0: M = M0, we can use the sign test statistic S = No. of Xi > M0,i = 1, . . . , n. H0 is
Using Appendix B, Table 8, find: (a) P [ Ws ≥ 57] when nA = 6, nB = 8. (b) P [ Ws ≤ 31] when nA = 8, nB = 6. (c) P [Ws ≥ 38 or Ws < 22 ] when nA = 5 and nB = 6. (d) The point c such that P [ Ws
See Table D.10 in the Data Bank. The number of breathing pauses per hour (BPH) helps determine a sleeping disorder. We took a random sample of 3 males, population A, and a random sample of 2 females
The following data pertain to the serum calcium measurements in units of IU/L and the serum alkaline phosphate measurements in units of Î¼g/ml for two breeds of pigs, Chester White and
Referring to the data in Exercise 15.6, is there strong evidence of a difference in the serum phosphate level between the two breeds?
A project (courtesy of Howard Garber) is constructed to prevent the decline of intellectual performance in children who have a high risk of the most common type of mental retardation, called
The possible synergetic effect of insecticides and herbicides is a matter of concern to many environmentalists. It is feared that farmers who apply both herbicides and insecticides to a crop may
Fluoridation of drinking water has long been a controversial issue in the United States. One of the first communities to add fluoride to their water was Newburgh, New York. In March 1944, a plan was
Researchers studied 300,818 golfers in Sweden and found that the "standardized mortality ratios" for golfers, adjusting for age, sex, and socioeconomic status, were lower than for non golfers,
Olestra is a no-calorie, no-fat additive that is used in the production of some potato chips. After the Food and Drug Administration approved the use of olestra, some consumers complained that
In a study of acupuncture, patients with headaches are randomly divided into two groups. One group is given acupuncture and the other group is given aspirin. The acupuncturist evaluates the
Randomized, controlled experiments have found that vitamin C is not effective in treating terminal cancer patients. However, a 1976 research paper reported that terminal cancer patients given vitamin
On 3 November 2009, the blog lifehacker.com contained a posting by an individual with chronic toenail fungus. He remarked that after many years of suffering and trying all sorts of cures, he resorted
For each of the following cases [(a) (b)], (I) State whether the study should be observational or experimental. (II) State whether the study should be run blind, double-blind, or neither. If the
For each of the following cases [(a) and (b)], (I) State whether the study should be observational or experimental. (II) State whether the study should be run blind, double-blind, or neither. If the
In order to assess the effectiveness of a new fertilizer, researchers applied the fertilizer to the tomato plants on the west side of a garden but did not fertilize the plants on the east side of the
Researchers studied 1,718 persons over age 65 living in North Carolina. They found that those who attended religious services regularly were more likely to have strong immune systems (as determined
In each of the following studies, identify which sampling technique best describes the way the data were collected (or could be treated as if they were collected): simple random sampling, random
For each of the following studies, identify the source(s) of sampling bias and describe (i) how it might affect the study conclusions and (ii) how you might alter the sampling method to avoid the
For each of the following studies, identify the source(s) of sampling bias and describe (i) how it might affect the study conclusions and (ii) how you might alter the sampling method to avoid the
Write the digits 1,2,3,4 in order on an index card. Bring this card to a busy place (e.g., dining hall, library, university union) and ask at least 30 people to look at the card and select one of the
Consider a population consisting of 600 individuals with unique IDs: 001, 002, . . . , 600. Use the following string of random digits to select a simple random sample of 5 individuals. List the IDs
(a) A paleontologist measured the width (in mm) of the-last upper molar in 36 specimens of the extinct mammal Acropithecits rigidus. (b) The birth-weight, date of birth, and the mother's race were
(a) A physician measured the height and weight of each of 37 children. (b) During a blood drive, a blood bank offered to check the cholesterol of anyone who donated blood. A total of 129 persons
(a) A biologist measured the number of leaves on each of 25 plants. (b) A physician recorded the number of seizures that each of 20 patients with severe epilepsy had during an eight-week period.
(a) A conservationist recorded the weather (clear, partly cloudy, cloudy, rainy) and number of cars parked at noon at a trailhead on each of 18 days. (b) An enologist measured the pH and residual
(a) A biologist measured the body mass (g) and sex of each of 123 blue jays. (b) A biologist measured the lifespan (in days), the thorax length (in mm), and the percent of time spent sleeping for
A paleontologist measured the width (in mm) of the last upper molar in 36 specimens of the extinct mammal Acropithecus rigidus. The results were as follows:(a) Construct a frequency distribution and
In a study of schizophrenia, researchers measured the activity of the enzyme monoamine oxidase (MAO) in the blood platelets of 18 patients. The results (expressed as nmoles benzylaldehyde product per
Consider the data presented in Exercise 2.2.2. Construct a frequency distribution and display it as a table and as a histogram.Exercise 2.2.2.In a study of schizophrenia, researchers measured the
A dendritic tree is a branched structure that emanates from the body of a nerve cell. As part of a study of brain development, 36 nerve cells were taken from the brains of newborn guinea pigs. The
Consider the data presented in Exercise 2.2.4. Construct a frequency distribution and display it as a table and as a histogram.Exercise 2.2.4A dendritic tree is a branched structure that emanates
The total amount of protein produced by a dairy cow can be estimated from periodic testing of her milk. The following are the total annual protein production values (lb) for twenty-eight 2-year-old
For each of 31 healthy dogs, a veterinarian measured the glucose concentration in the anterior chamber of the right eye and also in the blood serum. The following data are the anterior chamber

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