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essentials of statistics
The Basic Practice Of Statistics 5th Edition David S Moore - Solutions
Are the data Normal? Fruit fly thorax lengths. Here are the lengths in millimeters of the thorax for 49 male fruit flies:11 0.64 0.64 0.64 0.68 0.68 0.68 0.72 0.72 0.72 0.72 0.74 0.76 0.76 0.76 0.76 0.76 0.76 0.76 0.76 0.78 0.80 0.80 0.80 0.80 0.80 0.82 0.82 0.84 0.84 0.84 0.84 0.84 0.84 0.84 0.84
Are the data Normal? Acidity of rainfall. Exercise 3.31 concerns the acidity(measured by pH) of rainfall. A sample of 105 rainwater specimens had mean pH 5.43, standard deviation 0.54, and five-number summary 4.33, 5.05, 5.44, 5.79, 6.81.10(a) Compare the mean and median and also the distances of
Normal is only approximate: ACT scores. Scores on the ACT test for the 2007 high school graduating class had mean 21.2 and standard deviation 5.0. In all, 1,300,599 students in this class took the test. Of these, 149,164 had scores higher than 27 and another 50,310 had scores exactly 27. ACT scores
Normal is only approximate: IQ test scores. Here are the IQ test scores of 31 seventh-grade girls in a Midwest school district:9 114 100 104 89 102 91 114 114 103 105 108 130 120 132 111 128 118 119 86 72 111 103 74 112 107 103 98 96 112 112 93(a) We expect IQ scores to be approximately Normal.
Osteoporosis. Osteoporosis is a condition in which the bones become brittle due to loss of minerals. To diagnose osteoporosis, an elaborate apparatus measures bone mineral density (BMD). BMD is usually reported in standardized form. The standardization is based on a population of healthy young
Grading managers. Some companies “grade on a bell curve” to compare the performance of their managers and professional workers. This forces the use of some low performance ratings so that not all workers are listed as “above average.”Ford Motor Company’s “performance management
A surprising calculation. Changing the mean and standard deviation of a Normal distribution by a moderate amount can greatly change the percent of observations in the tails. Suppose that a college is looking for applicants with SAT math scores 750 and above.(a) In 2007, the scores of men on the
Heights of men and women. The heights of women aged 20 to 29 follow approximately the N(64, 2.7) distribution. Men the same age have heights distributed as N(69.3, 2.8). What percent of young men are shorter than the mean height of young women?
Heights of men and women. The heights of women aged 20 to 29 follow approximately the N(64, 2.7) distribution. Men the same age have heights distributed as N(69.3, 2.8). What percent of young women are taller than the mean height of young men?
Perfect SAT scores. It is possible to score higher than 1600 on the SAT, but scores 1600 and above are reported as 1600. In 2007 the distribution of SAT scores(combining mathematics and reading) was close to Normal with mean 1021 and standard deviation 211.8 What proportion of 2007 SAT scores were
What’s your percentile? Reports on a student’s ACT or SAT usually give the percentile as well as the actual score. The percentile is just the cumulative proportion stated as a percent: the percent of all scores that were lower than this one. In 2007, composite ACT scores were close to Normal
Quintiles. The quintiles of any distribution are the values with cumulative proportions 0.20, 0.40, 0.60, and 0.80. What are the quintiles of the distribution of gas mileage?
The middle half. The quartiles of any distribution are the values with cumulative proportions 0.25 and 0.75. They span the middle half of the distribution. What are the quartiles of the distribution of gas mileage?
The top 10%. How high must a 2008 vehicle’s gas mileage be in order to fall in the top 10% of all vehicles? (The distribution omits a few high outliers, mainly hybrid gas-electric vehicles.)
In my Chevrolet. The 2008 Chevrolet Malibu with a four-cylinder engine has combined gas mileage 25 mpg. What percent of all vehicles have worse gas mileage than the Malibu?
Making tablets. A pharmaceutical manufacturer forms tablets by compressing a granular material that contains the active ingredient and various fillers. The force in kilograms (kg) applied to the tablets varies a bit, with the N(11.5, 0.2) distribution.The process specifications call for applying a
A milling machine. Automated manufacturing operations are quite precise but still vary, often with distributions that are close to Normal. The width in inches of slots cut by a milling machine follows approximately the N(0.8750, 0.0012) distribution.The specifications allow slot widths between
Runners. In a study of exercise, a large group of male runners walk on a treadmill for 6 minutes. Their heart rates in beats per minute at the end vary from runner to runner according to the N(104, 12.5) distribution. The heart rates for male nonrunners after the same exercise have the N(130, 17)
Acid rain? Emissions of sulfur dioxide by industry set off chemical changes in the atmosphere that result in “acid rain.” The acidity of liquids is measured by pH on a scale of 0 to 14. Distilled water has pH 7.0, and lower pH values indicate acidity.Normal rain is somewhat acidic, so acid rain
Running a mile. After the physical training required during World War II, the distribution of mile run times for male students at the University of Illinois was approximately Normal with mean 7.11 minutes and standard deviation 0.74 minutes.What proportion of these students could run a mile in 5
Standard Normal drill.(a) Find the number z such that the proportion of observations that are less than z in a standard Normal distribution is 0.8.(b) Find the number z such that 35% of all observations from a standard Normal distribution are greater than z.
Standard Normal drill. Use Table A to find the proportion of observations from a standard Normal distribution that falls in each of the following regions. In each case, sketch a standard Normal curve and shade the area representing the region.(a) z ≤ −2.25 (b) z ≥ −2.25 (c) z > 1.77 (d)
Low IQ test scores. Scores on the Wechsler Adult Intelligence Scale (WAIS)are approximately Normal with mean 100 and standard deviation 15. People with WAIS scores below 70 are considered mentally retarded when, for example, applying for Social Security disability benefits. According to the
Daily activity. It appears that people who are mildly obese are less active than leaner people. One study looked at the average number of minutes per day that people spend standing or walking.6 Among mildly obese people, minutes of activity varied according to the N(373, 67) distribution. Minutes
Understanding density curves. Remember that it is areas under a density curve, not the height of the curve, that give proportions in a distribution. To illustrate this, sketch a density curve that has a tall, thin peak at 0 on the horizontal axis but has most of its area close to 1 on the
The scores of adults on an IQ test are approximately Normal with mean 100 and standard deviation 15. Corinne scores 118 on such a test. She scores higher than what percent of all adults?(a) About 12% (b) About 88% (c) About 98%
The proportion of observations from a standard Normal distribution that take values larger than −0.75 is about(a) 0.2266. (b) 0.7734. (c) 0.8023.
The proportion of observations from a standard Normal distribution that take values less than 1.15 is about(a) 0.1251. (b) 0.8531. (c) 0.8749.
The scores of adults on an IQ test are approximately Normal with mean 100 and standard deviation 15. Corinne scores 118 on such a test. Her z-score is about(a) 1.2. (b) 7.87. (c) 18.
The scores of adults on an IQ test are approximately Normal with mean 100 and standard deviation 15. The organization MENSA, which calls itself “the high IQ society,” requires an IQ score of 130 or higher for membership. What percent of adults would qualify for membership?(a) 95% (b) 5% (c) 2.5%
The length of human pregnancies from conception to birth varies according to a distribution that is approximately Normal with mean 266 days and standard deviation 16 days. 95% of all pregnancies last between(a) 250 and 282 days. (b) 234 and 298 days. (c) 218 and 314 days.
The standard deviation of the Normal distribution in Figure 3.14 is(a) 2. (b) 3. (c) 5.
Figure 3.14 shows a Normal curve. The mean of this distribution is(a) 0. (b) 2. (c) 3.−8 −6 −4 −2 0 2 4 6 8 10 12 FIGURE 3.14 A Normal curve, for Exercises 3.17 and 3.18.
To completely specify the shape of a Normal distribution, you must give(a) the mean and the standard deviation.(b) the five-number summary.(c) the mean and the median.
Which of these variables is least likely to have a Normal distribution?(a) Income per person for 150 different countries(b) Lengths of 50 newly hatched pythons(c) Heights of 100 white pine trees in a forest
Returns on stocks. The returns on stocks in Exercise 2.44 vary a lot: they range from a loss of more than 27% to a gain of more than 37%. Are any of these years suspected outliers by the 1.5 × I QR rule?
Athletes’ salaries. Which members of the Boston Red Sox (Table 2.2) have salaries that are suspected outliers by the 1.5 × I QR rule?
Carbon dioxide emissions. Table 1.6 (page 34) gives carbon dioxide (CO2) emissions per person for countries with population at least 20 million. A stemplot or histogram shows that the distribution is strongly skewed to the right. The United States and several other countries appear to be high
Older Americans. The stemplot in Exercise 1.19 (page 26) displays the distribution of the percents of residents aged 65 and older in the states. Stemplots help you find the five-number summary because they arrange the observations in increasing order.(a) Give the five-number summary of this
Does breast-feeding weaken bones? Breast-feeding mothers secrete calcium into their milk. Some of the calcium may come from their bones, so mothers may lose bone mineral. Researchers compared 47 breast-feeding women with 22 women of similar age who were neither pregnant nor lactating. They measured
Compressing soil. Farmers know that driving heavy equipment on wet soil com-presses the soil and hinders the growth of crops. Table 2.5 gives data on the “penetrability”of the same soil at three levels of compression.17 Penetrability is a measure of the resistance plant roots meet when they
Daily activity and obesity. People gain weight when they take in more energy from ST EP food than they expend. Table 2.4 compares volunteer subjects who were lean with others who were mildly obese. None of the subjects followed an exercise program.TABLE 2.4 Time (minutes per day) active and lying
Do good smells bring good business? Businesses know that customers often respond to background music. Do they also respond to odors? Nicolas Gu´eguen and his colleagues studied this question in a small pizza restaurant in France on Saturday evenings in May. On one evening, a relaxing lavender odor
Returns on stocks. How well have stocks done over the past generation? The ST EP Wilshire 5000 index describes the average performance of all U.S. stocks. The average is weighted by the total market value of each company’s stock, so think of the index as measuring the performance of the average
Athletes’ salaries. In 2007, the Boston Red Sox won the World Series for the ST EP second time in 4 years. Table 2.2 gives the salaries of the 25 players on the Red Sox World Series roster. Provide the team owner with a full description of the distribution of salaries and a brief summary of its
You create the data. Give an example of a small set of data for which the mean is larger than the third quartile.Exercises 2.43 to 2.48 ask you to analyze data without having the details outlined for you.The exercise statements give you the State step of the four-step process. In your work, follow
You create the data. Create a set of 5 positive numbers (repeats allowed) that have median 10 and mean 7. What thought process did you use to create your numbers?
Test your technology. This exercise requires a calculator with a standard deviation button or statistical software on a computer. The observations 10, 001 10, 002 10, 003 have mean x = 10,002 and standard deviation s = 1. Adding a 0 in the center of each number, the next set becomes 100, 001 100,
A standard deviation contest. This is a standard deviation contest. You must choose four numbers from the whole numbers 0 to 10, with repeats allowed.(a) Choose four numbers that have the smallest possible standard deviation.(b) Choose four numbers that have the largest possible standard
Thinking about medians.Areport says that “the median credit card debt of American households is zero.”We know that many households have large amounts of credit card debt. Explain how the median debt can nonetheless be zero.
Thinking about means. Table 1.1 (page 12) gives the percent of foreign-born residents in each of the states. For the nation as a whole, 12.5% of residents are foreign-born. Find the mean of the 51 entries in Table 1.1. It is not 12.5%.Explain carefully why this happens. (Hint: The states with the
Never on Sunday: also in Canada? Exercise 1.5 (page 11) gives the number of births in the United States on each day of the week during an entire year. The boxplots in Figure 2.6 are based on more detailed data from Toronto, Canada: the number of births on each of the 365 days in a year, grouped by
Guinea pig survival times. Here are the survival times in days of 72 guinea pigs after they were injected with infectious bacteria in a medical experiment.13 Survival times, whether of machines under stress or cancer patients after treatment, usually have distributions that are skewed to the
Behavior of the median. Place five observations on the line in the Mean and Median APPLET •••applet by clicking below it.(a) Add one additional observation without changing the median. Where is your new point?(b) Use the applet to convince yourself that when you add yet another
Making resistance visible. In the Mean and Median applet, place three observa- APPLET •••tions on the line by clicking below it: two close together near the center of the line, and one somewhat to the right of these two.(a) Pull the single rightmost observation out to the right. (Place the
More on study times. In Exercise 1.38 (page 35) you examined the nightly study time claimed by first-year college men and women. The most common methods for formal comparison of two groups use x and s to summarize the data.(a) What kinds of distributions are best summarized by x and s ?(b) One
Weight of newborns. Here is the distribution of the weight at birth for all babies born in the United States in 2005:12 Weight (grams) Count Weight (grams) Count Less than 500 6,599 3,000 to 3,499 1,596,944 500 to 999 23,864 3,500 to 3,999 1,114,887 1,000 to 1,499 31,325 4,000 to 4,499 289,098
How much fruit do adolescent girls eat? Figure 1.14 (page 30) is a histogram of the number of servings of fruit per day claimed by 74 seventeen-year-old girls.With a little care, you can find the median and the quartiles from the histogram. What are these numbers? How did you find them?Photodisc
Comparing tropical flowers. An alternative presentation of the flower length data in Table 2.1 reports the five-number summary and uses boxplots to display the distributions.Do this. Do the boxplots fail to reveal any important information visible in the stemplots in Figure 2.5?
Pulling wood apart. Example 1.9 (page 20) gives the breaking strengths of 20 pieces of Douglas fir.(a) Give the five-number summary of the distribution of breaking strengths. (The stemplot, Figure 1.11, helps because it arranges the data in order, but you should use the unrounded values in
University endowments. The National Association of College and University Business Officers collects data on college endowments. In 2007, 785 colleges and universities reported the value of their endowments. When the endowment values are arranged in order, what are the positions of the median and
Saving for retirement. Retirement seems a long way off and we need money now, so saving for retirement is hard. Among households with an employed person aged 21 to 64, only 63% own a retirement account. The mean value in these accounts is$112,300, but the median value is just $31,600. For people 55
Incomes of college grads. According to the Census Bureau’s 2007 Current Population Survey, the mean and median 2006 income of people at least 25 years old who had a bachelor’s degree but no higher degree were $46,453 and $58,886.Which of these numbers is the mean and which is the median?
Which of the following is least affected if an extreme high outlier is added to your data?(a) The median (b) The mean (c) The standard deviation
You have data on the weights in grams of 5 baby pythons. The mean weight is 31.8 and the standard deviation of the weights is 2.39. The correct units for the standard deviation are(a) no units—it’s just a number. (b) grams. (c) grams squared.
What are all the values that a standard deviation s can possibly take?(a) 0 ≤ s (b) 0 ≤ s ≤ 1 (c) −1 ≤ s ≤ 1
The standard deviation of the 10 amounts of money in Exercise 2.15 (use your calculator)is(a) 35.3. (b) 37.2. (c) 43.3.
To make a boxplot of a distribution, you must know(a) all of the individual observations.(b) the mean and the standard deviation.(c) the five-number summary.
What percent of the observations in a distribution lie between the first quartile and the third quartile?(a) 25% (b) 50% (c) 75%
If a distribution is skewed to the right,(a) the mean is less than the median.(b) the mean and median are equal.(c) the mean is greater than the median.
The five-number summary of the data in Exercise 2.15 is(a) 0, 0, 42.5, 76, 97.(b) 0, 29, 57.5, 81.5, 97.(c) 0, 29, 42.5, 75, 97.
The median of the data in Exercise 2.15 is(a) 35. (b) 42.5. (c) 57.5.
Here are the amounts of money (cents) in coins carried by 10 students in a statistics class:50 35 0 97 76 0 0 87 23 65 The mean of these data is(a) 37.2. (b) 42.5. (c) 43.3.
Watch those scales! The impression that a time plot gives depends on the scales you use on the two axes. If you stretch the vertical axis and compress the time axis, change appears to be more rapid. Compressing the vertical axis and stretching the time axis make change appear slower. Make two more
El Nin˜o and the monsoon. The earth is interconnected. For example, it appears that El Ni˜no, the periodic warming of the Pacific Ocean west of South America, affects the monsoon rains that are essential for agriculture in India. Here are the monsoon rains (in millimeters) for the 23 strong El
Dates on coins. Sketch a histogram for a distribution that is skewed to the left.Suppose that you and your friends emptied your pockets of coins and recorded the year marked on each coin. The distribution of dates would be skewed to the left.Explain why.
Marijuana and traffic accidents. Researchers in New Zealand interviewed 907 drivers at age 21. They had data on traffic accidents and they asked the drivers about marijuana use. Here are data on the numbers of accidents caused by these drivers at age 19, broken down by marijuana use at the same
Rock sole in the Bering Sea. Make a time plot of the rock sole recruitment data in Exercise 1.37. What does the time plot show that your stemplot in Exercise 1.37 did not show? When you have time series data, a time plot is often needed to understand what is happening.
Do women study more than men? We asked the students in a large first-year college class how many minutes they studied on a typical weeknight. Here are the responses of random samples of 30 women and 30 men from the class:Women Men 180 120 180 360 240 90 120 30 90 200 120 180 120 240 170 90 45 30
Rock sole in the Bering Sea. “Recruitment,” the addition of new members to a fish population, is an important measure of the health of ocean ecosystems. The table gives data on the recruitment of rock sole in the Bering Sea from 1973 to 2000.25 Make a stemplot to display the distribution of
Carbon dioxide emissions. Burning fuels in power plants or motor vehicles emits carbon dioxide (CO2), which contributes to global warming. Table 1.6 displays CO2 emissions per person from countries with populations of at least 20 million.24(a) Why do you think we choose to measure emissions per
Where are the doctors? Table 1.5 gives the number of active medical doctors per 100,000 people in each state.23(a) Why is the number of doctors per 100,000 people a better measure of the availability of health care than a simple count of the number of doctors in a state?(b) Make a histogram that
Food oils and health. Fatty acids, despite their unpleasant name, are necessary for human health. Two types of essential fatty acids, called omega-3 and omega-6, are not produced by our bodies and so must be obtained from our food. Food oils, widely used in food processing and cooking, are major
Name that variable. A survey of a large college class asked the following questions:1. Are you female or male? (In the data, male = 0, female = 1.)2. Are you right-handed or left-handed? (In the data, right = 0, left = 1.)3. What is your height in inches?4. How many minutes do you study on a
Returns on common stocks. The return on a stock is the change in its market price plus any dividend payments made. Total return is usually expressed as a percent of the beginning price. Figure 1.16 is a histogram of the distribution of the monthly returns for all stocks listed on U.S. markets from
IQ test scores. Figure 1.15 is a stemplot of the IQ test scores of 78 seventh-grade students in a rural midwestern school.20(a) Four students had low scores that might be considered outliers. Ignoring these, describe the shape, center, and spread of the distribution. (Notice that it looks roughly
Do adolescent girls eat fruit? We all know that fruit is good for us. Many of us don’t eat enough. Figure 1.14 is a histogram of the number of servings of fruit per day claimed by 74 seventeen-year-old girls in a study in Pennsylvania.19 Describe the shape, center, and spread of this
Spam. Email spam is the curse of the Internet. Here is a compilation of the most common types of spam:18 Type of spam Percent Adult 19 Financial 20 Health 7 Internet 7 Leisure 6 Products 25 Scams 9 Make two bar graphs of these percents, one with bars ordered as in the table (alphabetically)and the
Hispanic origins. Figure 1.13 is a pie chart prepared by the Census Bureau to show the origin of the more than 43 million Hispanics in the United States in 2006.17 About what percent of Hispanics are Mexican? Puerto Rican? You see that it is hard to determine numbers from a pie chart. Bar graphs
Deaths among young people. Among persons aged 15 to 24 years in the United States, the leading causes of death and the number of deaths in 2005 were: accidents, 15,567; homicide, 5359; suicide, 4139; cancer, 1717; heart disease, 1067; congenital defects, 483.16(a) Make a bar graph to display these
Buying music online. Young people are more likely than older folk to buy music online.Here are the percents of people in several age groups who bought music online in 2006:15 Age group Bought music online 12 to 17 years 24%18 to 24 years 21%25 to 34 years 20%35 to 44 years 16%45 to 54 years 10%55
What color is your car? The most popular colors for cars and light trucks change over time. Silver passed green in 2000 to become the most popular color worldwide, then gave way to shades of white in 2007. Here is the distribution of colors for vehicles sold in North America in 2007:14 Color
Protecting wood. How can we help wood surfaces resist weathering, especially when restoring historic wooden buildings? In a study of this question, researchers prepared wooden panels and then exposed them to the weather. Here are some of the variables recorded. Which of these variables are
Medical students. Students who have finished medical school are assigned to residencies in hospitals to receive further training in a medical specialty. Here is part of a hypothetical database of students seeking residency positions. USMLE is the student’s score on Step 1 of the national medical
You look at real estate ads for houses in Naples, Florida. There are many houses ranging from $200,000 to $500,000 in price. The few houses on the water, however, have prices up to $15 million. The distribution of house prices will be(a) skewed to the left.(b) roughly symmetric.(c) skewed to the
The center of the distribution in Exercise 1.19 is close to(a) 12.8%. (b) 12.0%. (c) 6.8% to 16.8%.
Ignoring the outlier, the shape of the distribution in Exercise 1.19 is(a) clearly skewed to the right.(b) roughly symmetric.(c) clearly skewed to the left.
The population of the United States is aging, though less rapidly than in other developed countries. Here is a stemplot of the percents of residents aged 65 and older in the 50 states and the District of Columbia. The stems are whole percents and the leaves are tenths of a percent.67 89 10 11 12 13
Here are the amounts of money (cents) in coins carried by 10 students in a statistics class:50 35 0 97 76 0 0 87 23 65 To make a stemplot of these data, you would use stems(a) 0, 1, 2, 3, 4, 5, 6, 7, 8, 9.(b) 0, 2, 3, 5, 6, 7, 8, 9.(c) 00, 10, 20, 30, 40, 50, 60, 70, 80, 90.
Figure 1.9 (page 19) is a histogram of the percent of women in each state aged 15 and over who have never been married. The leftmost bar in the histogram covers percents of never-married women ranging from about(a) 20% to 24%. (b) 20% to 22%. (c) 0% to 20%.
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