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mathematics
statistics

Questions and Answers of Statistics

With reference to Exercise 2.48, calculate the quartiles.In Exercise 2.48A large mail-order firm employs numerous persons to- take phone orders. Computers on which orders are entered also
The following table shows how workers in one department get to work.Mode of Transportation FrequencyDrive alone..................................25Car pool......................................
The speedy lizard data, from Exercise 2.19, are(a) Find the sample median, first quartile, and third quartile. (b) Find the sample 90th percentile.
With reference to the water quality data in Exercise 2.17:(a) Find the sample median, first quartile, and third quartile.(b) Find the sample 90th percentile.
1. If a fixed number c is added to all measurements in a data set, then the mean of the new measurements isc + (the original mean).2. If all measurements in a data set are multiplied by a fixed
On a day, the noon temperature measurements (in °F) reported by five weather stations in a state were(a) Find the mean and median temperature in °F. (b) The Celsius (°C) scale is related
Given here are the mean and median salaries of machinists employed by two competing companies A and B.Assume that the salaries are set in accordance with job competence and the overall quality of
Using the data on testosterone x4 for male alligators: (a) Make separate dot plots for the Lake Apopka and Lake Woodruff alligators. (b) Calculate the sample means for each group. (c) Do the
Refer to the alligator data in Table D.11 of the Data Bank. Using the data on testosterone x4 from Lake Apopka: (a) Make separate.dot plots for the male and female alligators. (b) Calculate the
For the data set(a) Calculate the deviations (x - ) and check to see that they add up to 0.(b) Calculate the sample variance and the standard deviation.
Repeat (a) and (b) of Exercise 2.57 for the data set
For the data set 8 6 14 4(a) Calculate the deviations (x - ) and check to see that they add up to 0.(b) Calculate the variance and the standard deviation.
Of the $207 million raised by a major university's fund drive, $117 million came from individuals and bequests, $24 million from industry and business, and $66 million from foundations and
Repeat (a) and (b) of Exercise 2.59 for the data set
For the data of Exercise 2.57, calculate s2 by using the alternative formula.In Exercise 2.57
A sample of six university students responded to the question "How much time, in minutes, did you spend on the social network site yesterday?" One student never used the site and was dropped from the
For each data set, calculate s2.(a)(b) (c)
In 2012 there were nine skyscrapers in the world over 300 meters tall. The ordered values of height are(a) Calculate the sample variance for the nine skyscrapers.(b) Calculate the sample standard
A campus area merchant recorded the number of bad checks received per month, for five monthsCalculate: (a) The sample variance. (b) The sample standard deviation.
The city of Madison regularly checks the quality of water at swimming beaches located on area lakes. Fifteen times the concentration of fecal coli forms, in number of colony forming units (CFU) per
With reference to the radiation leakage data given in Exercise 2.15, calculate: (a) The sample variance. (b) The sample standard deviation.
With reference to the data on the length of 10 major league baseball games in Exercise 2.43:(a) Find the sample mean.(b) Find the sample variance.(c) Find the sample standard deviation.
With reference to checked bags in Exercise 2.13,(a) Find the sample mean.(b) Find the sample standard deviation.
The performance time (minutes) for Beethoven's Ninth Symphony is obtained from each of seven compact discs.(a) Find the sample median.(b) Find the sample mean.(c) Find the sample standard deviation.
Recent crime reports on the number of aggravated assaults at each of the 18 largest universities reporting for the year are summarized in the computer output.(a) Locate a measure of variation and
The weights (oz) of nineteen babies born in Madison Wisconsin are summarized in the computer output.(a) Locate a measure of variation and also calculate the sample variance. (b) Calculate the
1. If a fixed number c is added to all measurements in a data set, the deviations (x - ) remain unchanged (see Exercise 2.52). Consequently, s2 and s remain unchanged.2. If all measurements in a data
For the data set of Exercise 2.22, calculate the interquartile range.In Exercise 2.22The following data represent the scores of 40 students on a college qualification test (courtesy of R. W.
For the extracurricular data of Exercise 2.3, calculate the interquartile range.In Exercise 2.3
Should you be surprised if the range is larger than twice the interquartile range? Explain.
Calculations with the test scores data of Exercise 2.22 give = 150.125 and s = 24.677.(a) Find the proportion of the observations in the intervals ± 2 s and ± 3 s.(b) Compare your findings in
Refer to the data on bone mineral content in Exercise 2.41.(a) Calculate and s.(b) Find the proportion of the observations that are in the intervals ± s, ± 2 s, and ± 3s.(c) Compare the
Refer to the data on lizards in Exercise 2.19.(a) Calculate and s.(b) Find the proportion of the observations that are in the intervals ± s, ± 2s, and ± 3s.(c) Compare the results of part
Refer to the data on number of returns in Example 4.(a) Calculate and s.(b) Find the proportions of the observations that are in the intervals ± s, ± 2s, and ± 3s.(c) Compare the results
When two measurements originate from different sources, converting them to the z scale helps to draw a sensible interpretation of their relative magnitudes. For instance, suppose a student scored 65
Two cities provided the following information on public school teachers' salaries.(a) Construct a boxplot for the salaries in City A. (b) Construct a boxplot, on the same graph, for the salaries in
Refer to the data on throwing speed in Exercise 2.42. Make separate boxplots to compare males and females.In Exercise 2.42
Refer to Exercise 2.27 and the data on the consumer price index for various cities. Find the increase, for each city, by subtracting the 2007 value from the 2011 value.(a) Obtain the five-number
Refer to Exercise 2.27 and the data on the consumer price index for various cities. Find the increase, for each city, by subtracting the 2007 value from the 2011 value.(a) Find the sample mean and
Refer to Example 6 and the data on hours of sleep. (a) Obtain the five-number summary: minimum, Qlʹ Q2' Q3ʹ, and maximum. (b) Make a boxplot of the hours of sleep.
Refer to Exercise 2.3 and the data on extracurricular activities. Find the sample mean and standard deviation.In Exercise 2.3
Presidents also take midterms! After two years of the president's term, members of Congress are up for election. The following table gives the number of net seats lost, by the party of the president,
With reference to Exercise 2.90:(a) Calculate the median number of lost House seats.(b) Find the maximum and minimum losses and identify these with a president.(c) Determine the range for the number
Make a time plot of the mail order phone call data in Exercise 2.48 and comment on the statistical control.In Exercise 2.48
A city department has introduced a quality improvement program and has allowed employees to get credit for overtime hours when attending meetings of their quality groups. The total numbers of
Make a control chart for the data referred to in Exercise 2.92 and comment.Make a time plot of the mail order phone call data in Exercise 2.48 and comment on the statistical control.In Exercise 2.48
Make a control chart for the data in Exercise 2.93 and comment.In Exercise 2.93
The exchange rate between the United States and Canada can be stated as the number of Canadian dollars that can be purchased with $1. The official values for the year areIs this exchange rate in
Make a control chart of the data in Exercise 2.96 and comment.In Exercise 2.96
Make a control chart for the extraordinary event overtime data in Example 23 after removing the outlier identified in that example. You need to recalculate the mean and standard deviation.
Recorded here are the numbers of civilians employed in the United States by major occupation groups for the years 2010 and 2000. (Source: Statistical Abstract of the United States, 2012.)(a) For each
Nausea from air sickness affects some travelers. A drug company, wanting to establish the effectiveness of its motion sickness pill, randomly gives either its pill or a look-alike sugar pill
A large research hospital and a community hospital are located in your area. The surgery records for the two hospitals are:The outcome is "survived" if the patient lives at least six weeks.(a)
Refer to Exercise 3.10. Not all surgery cases, even of the same type, are equally serious. Large research hospitals tend to get the most serious surgery cases, whereas community hospitals tend to get
With reference to the quit-smoking experiment: (a) Suppose the placebo trials were ignored and you were only told that 21 of 57 were abstinent after using the medicated patches. Would this now appear
Would you expect a positive, negative, or nearly zero correlation for each of the following? Give reasons for your answers. (a) The physical fitness of a dog and the physical fitness of the
In each of the following instances, would you expect a positive, negative, or zero correlation? (a) Number of salespersons and total dollar sales for real estate firms. (b) Total payroll and percent
Data since 2000 reveals a moderately strong positive correlation between the federal debt and attendance at National Football League games. Would restricting the number of persons attending games
For the data set(a) Construct a scatter diagram.(b) Guess the sign and value of the correlation coefficient.(c) Calculate the correlation coefficient.
Refer to the alligator data in Table D.11 of the Data Bank. Using the data on x3 and x4 for male and female alligators from Lake Apopka: (a) Make a scatter diagram of the pairs of concentrations for
Breakfast cereals from three leading manufacturers can be classified either above average or below average in sugar content. Data for ten cereals from each manufacturer are given below:(a) Complete
(a) Construct scatter diagrams of the data sets(b) Calculate r for the data set (i). (c) Guess the value of r for the data set (ii) and then calculate r. (The x and y values are the same for both
Calculations from a data set of it = 36 pairs of (x, y) values have provided the following results.Obtain the correlation coefficient.
Over the years, a traffic officer noticed that cars with fuzzy dice hanging on the rear-view mirror always seemed to be speeding. Perhaps tongue in cheek, he suggested that outlawing the sale of
The Department of Natural Resources in Wisconsin monitors air quality in the state. Ozone is a major component of smog and high temperatures also contribute. The summer maximum daily ozone (ppm) and
A zoologist collected 20 wild lizards in the southwestern United States. After measuring their total length (mm), they were placed on a treadmill and their speed (m/sec) recorded.(a) Create a scatter
An ongoing study of wolves is being conducted at the Yukon-Charley Rivers National Preserve. Table D.9 in the Data Bank gives the physical characteristics of wolves that were captured.(a) Plot length
An ongoing study of wolves is being conducted at the Yukon-Charley Rivers National Preserve. Table D.9 in the Data Bank gives the physical characteristics of wolves that were captured.(a) Plot length
Refer to Example 6 concerning spurious correlation. Replace number of cell phone subscribers with the number of registered motorcycles in millions.TABLE 10Variables Showing Spurious Correlation(a)
At the conclusion of one semester, a sample of 250 juniors was questioned about how long they studied for each of their final exams. Students were also classified as social, biological, or physical
Suppose all x measurements are changed to xÊ¹ = ax + b and all y measurements to y' = cy + d, where a, b, c, and d are fixed numbers (a ‰ 0, c ‰ 0). Then the correlation coefficient
The amount of municipal solid waste created has become a major problem. According to the Environmental Protection Agency, the yearly amounts (millions of tons) are:(a) Plot the amount of garbage
Refer to the data on garbage in Exercise 3.31.(a) Plot the amount of garbage (millions of tons) versus population (millions).(b) Does there appear to be a strong correlation? Explain.(c) How does
Refer to the data on garbage in Exercise 3.31.(a) Replace year by (year - 1960). Calculate the correlation coefficient between (year - 1960) and amount of garbage in millions of tons.(b) Based on
Refer to the data on garbage in Exercise 3.31.(a) Calculate the correlation coefficient between the amount of garbage in millions of tons and the population size in millions.(b) Based on your
Plot the line y = 2 + 3 x on graph paper by locating points for x = 1 and x = 4. What is its intercept? Its slope?
Plot the line y = 6 - 2x on graph paper by locating the points for x = 0 and x = 3. What is its intercept? Its slope?
A store manager has determined that the monthly profit y realized from selling a particular brand of car battery is given by y = l0x - 155 where x denotes the number of these batteries sold in a
Identify the predictor variable x and the response variable y in each of the following situations.(1). A training director wishes to study the relationship between the duration of training for new
Given these five pairs of (x, y) values(a) Plot the points on graph paper.(b) From a visual, draw a straight line that appears to fit the data well.
A survey was conducted to study the attitudes of the faculty, academic staff, and students in regard to a proposed measure for reducing the heating and air-conditioning expenses on campus.Compare the
For the data set(a) Construct a scatter diagram.(b) From a visual inspection, draw a straight line that appears to fit the data well.(c) Calculate the least squares estimates and draw the least
In an experiment to study the relation between the time waiting in line, y (minutes), to get to the head of the checkout line at her favorite grocery store and the number of persons ahead in line, x,
Wolves used to range over much of Michigan, Minnesota, and Wisconsin. They were reintroduced several years ago, but counts over the winter showed that the populations are expanding rapidly over the
The amount of municipal solid waste created has become a major problem. According to the Environmental Protection Agency, the yearly amount (millions of tons) are:(a) Plot the amount of garbage
Applicants for welfare are allowed an appeals process when they feel they have been unfairly treated. At the hearing, the applicant may choose self-representation or representation by an attorney.
Sugar content (g) and carbohydrate content (g) are obtained from the package of the breakfast cereals referred to in Exercise 3.2.(a) Calculate the sample mean carbohydrates for all 30 cereals.(b)
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.4 Among the lenses with only
A dealer's recent records of 80 truck sales provided the following frequency information on size of truck and type of drive.(a) Determine the marginal totals.(b) Obtain the table of relative
A high-risk group of 1083 male volunteers was included in a major clinical trial for testing a new vaccine for type B hepatitis. The vaccine was given to 549 persons randomly selected from the group,
Would you expect a positive, negative, or nearly zero correlation for each of the following? Give reasons for your answers. (a) The time a student spends playing computer games each week and the time
Groundwater from 19 wells was classified as low or high in alkalinity and low or high in dissolved iron. There were 9 wells with high alkalinity, 7 that were high in iron, and 5 that were high in
Examine each of the following situations and state whether you would expect to find a high correlation between the variables. Give reasons why an observed correlation cannot be interpreted as a
The tar yield of cigarettes is often assayed by the following method: A motorized smoking machine takes a two-second puff once every minute until a fixed butt length remains. The total tar yield is
As part of a study of the psychobiological correlates of success in athletes, the following measurements (courtesy of W. Morgan) are obtained from members of the U.S. Olympic wrestling team.(a) Plot
Given the following (x, y) values(a) Make a scatter plot.(b) Calculate r.
Given these five pairs of values(a) Plot the scatter diagram. (b) From a visual inspection, draw a straight line that appears to fit the data well.
For samples collected concerning the following pairs of variables, decide whether you should make a scatter plot or create a contingency table. (a) The amount earned and the number of weeks worked
Identify the predictor variable x and the response variable y in each of the following situations. (a) The state highway department wants to study the relationship between road roughness and a car's
The Following Exercises Require a Computer In Figure 12, we have illustrated the output from MINITAB commands for fitting a straight line. To create the scatter plot, without the fitted line,

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