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statistics informed decisions using data

Questions and Answers of Statistics Informed Decisions Using Data

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
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
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
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
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
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,
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
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
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
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
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
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
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
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?
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
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
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
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
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
Archaeology: Ireland Commercial dredging operations in ancient rivers occasionally uncover archaeological artifacts of great importance. One such artifact is Bronze Age spearheads recovered from
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
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
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,
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
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
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.
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
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
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
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
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
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
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)
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.
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.
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
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
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
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)
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
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,
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,
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

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