Basic Statistics Understanding Conventional Methods And Modern Insights 1st Edition Rand R. Wilcox - Solutions

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Interpretation Histograms of random sample data are often used as an indication of the shape of the underlying population distribution. The histograms on the next page are based on random samples of size 30, 50, and 100 from the same population.© Cengage Learning®© Cengage Learning®Copyright
Interpretation The following histograms are based on different random samples of size 100 drawn from the same population.(a) Identify the midpoint of the class with the highest frequency in each of the three histograms.(b) Using the class midpoints, what is the range of data shown in each
Interpretation The ogives shown are based on U.S. Census data and show the average personal income per capita for each of the 50 states. The data are rounded to the nearest thousand dollars.(a) How were the percentages shown in graph (ii) computed?(b) How many states have average per capita income
Critical Thinking The following ogives come from different distributions of 50 whole numbers between 1 and 60.Labels on each point give the cumulative frequency and the cumulative percentage of data.(a) In which distribution does the most data fall below 20.5?(b) In which distribution does the most
Sports: Dog Sled Racing How long does it take to fi nish the 1161-mile Iditarod Dog Sled Race from Anchorage to Nome, Alaska (see Viewpoint)?Finish times (to the nearest hour) for 57 dogsled teams are shown below.261 271 236 244 279 296 284 299 288 288 247 256 338 360 341 333 261 266 287 296 313
Medical: Glucose Testing The following data represent glucose blood levels (mg/100 ml) after a 12-hour fast for a random sample of 70 women(Reference: American Journal of Clinical Nutrition, Vol. 19, pp. 345–351).Note: These data are also available for download at the Online Study Center.45 66 83
Medical: Tumor Recurrence Certain kinds of tumors tend to recur. The following data represent the lengths of time, in months, for a tumor to recur after chemotherapy (Reference: D. P. Byar, Journal of Urology, Vol. 10, pp. 556–561). Note: These data are also available for download at the Online
Archaeology: New Mexico The Wind Mountain excavation site in New Mexico is an important archaeological location of the ancient Native American Anasazi culture. The following data represent depths (in cm)below surface grade at which signifi cant artifacts were discovered at this site (Reference: A.
Environment: Gasoline Consumption The following data represent highway fuel consumption in miles per gallon (mpg) for a random sample of 55 models of passenger cars (Source: Environmental Protection Agency). Note: These data are also available for download at the Online Study Center.30 27 22 25 24
Advertising: Readability “Readability Levels of Magazine Ads,” by F. K.Shuptrine and D. D. McVicker, is an article in the Journal of Advertising Research. (For more information, visit the Brase/Brase statistics site at http://www.cengagebrain.com and fi nd the link to DASL, the Carnegie Mellon
Expand Your Knowledge: Decimal Data The following data represent tonnes of wheat harvested each year (1894–1925) from Plot 19 at the Rothamsted Agricultural Experiment Stations, England.2.71 1.62 2.60 1.64 2.20 2.02 1.67 1.99 2.34 1.26 1.31 1.80 2.82 2.15 2.07 1.62 1.47 2.19 0.59 1.48 0.77 2.04
Decimal Data: Batting Averages The following data represent baseball batting averages for a random sample of National League players near the end of the baseball season. The data are from the baseball statistics section of the Denver Post.0.194 0.258 0.190 0.291 0.158 0.295 0.261 0.250 0.181 0.125
Expand Your Knowledge: Dotplot Another display technique that is somewhat similar to a histogram is a dotplot. In a dotplot, the data values are displayed along the horizontal axis. A dot is then plotted over each data value in the data set.The next display shows a dotplot generated by Minitab
Dotplot: Dog Sled Racing Make a dotplot for the data in Problem 15 regarding the fi nish time (number of hours) for the Iditarod Dog Sled Race.Compare the dotplot to the histogram of Problem 15.
Dotplot: Tumor Recurrence Make a dotplot for the data in Problem 17 regarding the recurrence of tumors after chemotherapy. Compare the dotplot to the histogram of Problem 17.
Interpretation Consider graph (a) of Reasons People Like Texting on Cell Phones, based on a GfK Roper survey of 1000 adults.(a) Do you think respondents could select more than one response? Explain.(b) Could the same information be displayed in a circle graph? Explain.(c) Is graph (a) a Pareto
Interpretation Look at graph (b) of Reasons People Like Texting on Cell Phones. Is this a proper bar graph? Explain.
Critical Thinking A personnel offi ce is gathering data regarding working conditions. Employees are given a list of fi ve conditions that they might want to see improved. They are asked to select the one item that is most critical to them. Which type of graph, circle graph or Pareto chart, would be
Critical Thinking Your friend is thinking about buying shares of stock in a company. You have been tracking the closing prices of the stock shares for the past 90 trading days. Which type of graph for the data, histogram or timeseries, would be best to show your friend? Why?
Education: Does College Pay Off? It is costly in both time and money to go to college. Does it pay off? According to the Bureau of the Census, the answer is yes.The average annual income (in thousands of dollars) of a household headed by a person with the stated education level is as follows: 21.6
Interpretation Consider the two graphs depicting the infl uence of advertisements on making large purchases for two different age groups, those 18–34 years old and those 45–54 years old (based on a Harris Poll of about 2500 adults aged 18 or older). Note: Other responses such as “not sure”
Commercial Fishing: Gulf of Alaska It’s not an easy life, but it’s a good life!Suppose you decide to take the summer off and sign on as a deck hand for a commercial fi shing boat in Alaska that specializes in deep-water fi shing for groundfi sh. What kind of fi sh can you expect to catch? One
Archaeology: Ireland Commercial dredging operations in ancient rivers occasionally uncover archaeological artifacts of great importance. One such artifact is Bronze Age spearheads recovered from ancient rivers in Ireland. A recent study gave the following information regarding discoveries of
Lifestyle: Hide the Mess! A survey of 1000 adults (reported in USA Today)uncovered some interesting housekeeping secrets. When unexpected company comes, where do we hide the mess? The survey showed that 68% of the respondents toss their mess into the closet, 23% shove things under the bed, 6% put
Education: College Professors’ Time How do college professors spend their time? The National Education Association Almanac of Higher Education gives the following average distribution of professional time allocation:teaching, 51%; research, 16%; professional growth, 5%; community service, 11%;
Driving: Bad Habits Driving would be more pleasant if we didn’t have to put up with the bad habits of other drivers. USA Today reported the results of a Valvoline Oil Company survey of 500 drivers, in which the drivers marked their complaints about other drivers. The top complaints turned out to
Ecology: Lakes Pyramid Lake, Nevada, is described as the pride of the Paiute Indian Nation. It is a beautiful desert lake famous for very large trout. The elevation of the lake surface (feet above sea level) varies according to the annual fl ow of the Truckee River from Lake Tahoe. The U.S.
Vital Statistics: Height How does average height for boys change as boys get older? According to Physician’s Handbook, the average heights at different ages are as follows:Make a time-series graph for average height for ages 0.5 through 14 years. Age (years) 0.5 1 2 3 4 5 6 7 Height (inches) 26
Expand Your Knowledge Donut Pie Charts The book The Wall Street Journal. Guide to Information Graphics by Dona M. Wong gives strategies for using graphs and charts to display information effectively. One popular graph discussed is the donut pie chart. The donut pie chart is simply a pie chart with
Health Care: Hospitals The American Medical Association Center for Health Policy Research, in its publication State Health Care Data:Utilization, Spending, and Characteristics, included data, by state, on the number of community hospitals and the average patient stay (in days).The data are shown in
Health Care: Hospitals Using the number of hospitals per state listed in the table in Problem 3, make a stem-and-leaf display for the number of community hospitals per state. Which states have an unusually high number of hospitals?
Expand Your Knowledge: Split Stem The Boston Marathon is the oldest and best-known U.S. marathon. It covers a route from Hopkinton, Massachusetts, to downtown Boston. The distance is approximately 26 miles. Visit the Brase/Brase statistics site at http://www.cengagebrain.com and fi nd the link to
Split Stem: Golf The U.S. Open Golf Tournament was played at Congressional Country Club, Bethesda, Maryland, with prizes ranging from$465,000 for fi rst place to $5000. Par for the course was 70.The tournament consisted of four rounds played on different days. The scores for each round of the 32
Health: Cigarette Smoke Use the data in Table 2-16 to make a stem-and-leaf display for milligrams of tar per cigarette smoked. Are there any outliers?
Health: Cigarette Smoke Use the data in Table 2-16 to make a stem-and-leaf display for milligrams of carbon monoxide per cigarette smoked. Are there any outliers?
Health: Cigarette Smoke Use the data in Table 2-16 to make a stem-and-leaf display for milligrams of nicotine per cigarette smoked. In this case, truncate the measurements at the tenths position and use two lines per stem (see Problem 5, part a).
Expand Your Knowledge: Back-to-Back Stem Plot In archaeology, the depth(below surface grade) at which artifacts are found is very important. Greater depths sometimes indicate older artifacts, perhaps from a different archaeological period. Figure 2-17 is a back-to-back stem plot showing the depths
Criminal Justice: Prisoners The time plot in Figure 2-18 gives the number of state and federal prisoners per 100,000 population (Source: Statistical Abstract of the United States, 120th Edition).(a) Estimate the number of prisoners per 100,000 people for 1980 and for 1997.(b) Interpretation During
Law: Corporation Lawsuits Many people say the civil justice system is overburdened. Many cases center on suits involving businesses. The following data are based on a Wall Street Journal report. Researchers conducted a study of lawsuits involving 1908 businesses ranked in the Fortune 1000 over a
Archaeology: Tree-Ring Data The Sand Canyon Archaeological Project, edited by W. D. Lipe and published by Crow Canyon Archaeological Center, contains the stem-and-leaf diagram shown in Figure 2-19. The study uses tree rings to accurately determine the year in which a tree was cut. The fi gure gives
Why is statistics important?
What is the nature of data?
How can you draw a random sample?
What are other sampling techniques?
How can you design ways to collect data?
What are histograms? When are they used?
What are common distribution shapes?
How can you select graphs appropriate for given data sets?
How can you quickly order data and, at the same time, reveal the distribution shape?
What are commonly used measures of central tendency? What do they tell you?
How do variance and standard deviation measure data spread?Why is this important?
How do you make a box-and-whisker plot, and what does it tell about the spread of the data?
How can you use a scatter diagram to visually estimate the degree of linear correlation of two random variables?
How do you compute the correlation coeffi cient and what does it tell you about the strength of the linear relationship between two random variables?
What is the least-squares criterion? How do you fi nd the equation of the leastsquares line?
What is the coeffi cient of determination and what does it tell you about explained variation of y in a random sample of data pairs (x, y)?
Why would anyone study probability? Hint: Most big issues in life involve uncertainty.
What are the basic defi nitions and rules of probability?
What are counting techniques, trees, permutations, and combinations?
What is a random variable? How do you compute m and s for a discrete random variable? How do you compute m and s for linear combinations of independent random variables?
Many of life’s experiences consist of some successes together with some failures. Suppose you make n attempts to succeed at a certain project. How can you use the binomial probability distribution to compute the probability of r successes?
How do you compute m and s for the binomial distribution?
What are some characteristics of a normal distribution? What does the empirical rule tell you about data spread around the mean?
Can you compare apples and oranges, or maybe elephants and butterfl ies? In most cases, the answer is no—unless you fi rst standardize your measurements.What are a standard normal distribution and a standard z score?
How do you convert any normal distribution to a standard normal distribution?
How do you fi nd probabilities of “standardized events”?
As humans, our experiences are fi nite and limited. Consequently, most of the important decisions in our lives are based on sample (incomplete) information.
What is a probability sampling distribution? How will sampling distributions help us make good decisions based on incomplete information?
There is an old saying: All roads lead to Rome. In statistics, we could recast this saying: All probability distributions average out to be normal distributions (as the sample size increases). How can we take advantage of this in our study of sampling distributions?
The binomial and normal distributions are two of the most important probability distributions in statistics. Under certain limiting conditions, the binomial can be thought to evolve (or envelope) into the normal distribution. How can you apply this concept in the real world?
Many issues in life come down to success or failure. In most cases, we will not be successful all the time, so proportions of successes are very important. What is the probability sampling distribution for proportions?
How do you estimate the expected value of a random variable?
What assumptions are needed? How much confi dence should be placed in such estimates?
At the beginning design stage of a statistical project, how large a sample size should you plan to get?
What famous statistician worked for the Guinness brewing company in Ireland? What has this got to do with constructing estimates from sample data?
How do you estimate the proportion p of successes in a binomial experiment? How does the normal approximation fi t into this process?
Many of life’s questions require a yes or no answer. When you must act on incomplete(sample) information, how do you decide whether to accept or reject a proposal?
What is the P-value of a statistical test? What does this measurement have to do with performance reliability?
How do you construct statistical tests for m? Does it make a difference whether s is known or unknown?
How do you construct statistical tests for the proportion of successes in a binomial experiment?
What are the statistical advantages of paired data values?
How do we construct statistical tests?
How do we compare means from two independent populations
when we know for each population?
What if we want to compare means from two independent populations, but we do not know for each population?
How do we use sample data to compare proportions from two independent populations?
How do you decide if random variables are dependent or independent?
How do you decide if different populations share the same proportions of specifi ed characteristics?
How do you decide if two distributions are not only dependent, but actually the same distribution?
How do you construct tests for s?
How do you test a correlation coeffi cient?
What is the standard error of estimate? How do you compute it, and where is it used?
How do you compute confi dence intervals for a least-squares prediction?
The slope of the least-squares line represents rate of growth. How can you determine if the rate of growth is statistically signifi cant?
Based on a sample of 100 individuals, the values 1, 2, 3, 4, 5 are observed with relative frequencies 0.2, 0.3, 0.1, 0.25, 0.15. Compute the mean, variance and standard deviation.
Fifty individuals are rated on how open minded they are. The ratings have the values 1, 2, 3, 4 and the corresponding relative frequencies are 0.2, 0.24, 0.4, 0.16, respectively. Compute the mean, variance and standard deviation.
For the values 0, 1, 2, 3, 4, 5, 6 the corresponding relative frequencies based on a sample of 10,000 observations are 0.015625, 0.093750, 0.234375, 0.312500, 0.234375, 0.093750, 0.015625, respectively. Determine the mean, median, variance, standard deviation and mode.
For a local charity, the donations in dollars received during the last month were 5, 10, 15, 20, 25, 50 having the frequencies 20, 30, 10, 40, 50, 5.Compute the mean, variance and standard deviation.
The values 1, 5, 10, 20 have the frequencies 10, 20, 40, 30.Compute the mean, variance and standard deviation.
For the data in table 2.1, dealing with changes in cholesterol levels, suppose a histogram is to be created with bins defined as follows: −40 −30 −20 −10 0 10 20 30 40.That is, the first bin has boundaries −40 and −30, the next bin contains all values greater than −30 but less than or

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Basic Statistics Understanding Conventional Methods And Modern Insights 1st Edition Rand R. Wilcox - Solutions

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