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Elementary Statistics 10th Edition Mario F. Triola - Solutions

11. BMI Values Refer to Data Set 1 in Appendix B and use the body mass index (BMI)values of males to find the 5-number summary and construct a boxplot.
10. Body Temperatures Refer to Data Set 2 in Appendix B for the 106 body temperatures for 12 A.M. on day 2. Find the 5-number summary and construct a boxplot, then determine whether the sample values support the common belief that the mean body temperature is 98.6°F.
9. Bear Lengths Refer to Data Set 6 for the lengths (in inches) of the 54 bears that were anesthetized and measured. Find the 5-number summary and construct a boxplot.Does the distribution of the lengths appear to be symmetric or does it appear to be skewed?
8. Weights of Quarters Refer to Data Set 14 and use the weights of the post-1964 quarters to find the 5-number summary and construct a boxplot. Do the results appear to be substantially different from those obtained in Exercise 7?
7. Weights of Quarters Refer to Data Set 14 and use the weights of the silver quarters(pre-1964) to find the 5-number summary and construct a boxplot.
6. Testing Corn Seeds Using the yields from the kiln-dried seed listed in Exercise 5, find the 5-number summary and construct a boxplot. Do the results appear to be substantially different from those obtained in Exercise 5?
5. Testing Corn Seeds In 1908, William Gosset published the article “The Probable Error of a Mean” under the pseudonym of “Student” (Biometrika, Vol. 6, No. 1). He included the data listed below for two different types of corn seed (regular and kiln dried) that were used on adjacent plots
4. Outliers A set of 20 sample values includes one outlier that is very far away from the other 19 values. How much of an effect does that outlier have on each of these statistics:mean, median, standard deviation, and range?
4. Draw lines extending outward from the box to the minimum and maximum data values.
3. Construct a box (rectangle) extending from to and draw a line in the box at the median value.
2. Construct a scale with values that include the minimum and maximum data values.
1. Find the 5-number summary consisting of the minimum value, the median, and the maximum value.
29. Deciles and Quintiles For a given data set, there are nine deciles, denoted by which separate the sorted data into 10 groups, with about 10% of the values in each group. There are also four quintiles, which divide the sorted data into 5 groups, with about 20% of the values in each group. (Note
28. Interpolation When finding percentiles using Figure 3-6, if the locator L is not a whole number, we round it up to the next larger whole number. An alternative to this procedure is to interpolate. For example, using interpolation with a locator of leads to a value that is 0.75 (or 3 4) of the
27. Ages of Best Actresses Use the 76 sorted ages of Best Actresses listed in Table 3-4.a. Find the interquartile range.b. Find the midquartile.c. Find the 10–90 percentile range.d. Does If so, does always equale. Does If so, does always equal
15. 25 16. 35 17. 40 18. 50 In Exercises 19–26, use the 76 sorted ages of Best Actresses listed in Table 3-4. Find the indicated percentile or quartile.19. 20. 21. 22.23. 24. 25. 26.3-4 BEYOND THE BASICS
14. Comparing Scores Three students take equivalent stress tests. Which is the highest relative score?a. A score of 144 on a test with a mean of 128 and a standard deviation of 34.b. A score of 90 on a test with a mean of 86 and a standard deviation of 18.c. A score of 18 on a test with a mean of
13. Comparing Test Scores Which is relatively better: a score of 85 on a psychology test or a score of 45 on an economics test? Scores on the psychology test have a mean of 90 and a standard deviation of 10. Scores on the economics test have a mean of 55 and a standard deviation of 5.
12. Cholesterol Levels For men aged between 18 and 24 years, serum cholesterol levels(in mg 100 mL) have a mean of 178.1 and a standard deviation of 40.7 (based on data from the National Health Survey). Find the z score corresponding to a male, aged 18–24 years, who has a serum cholesterol level
11. Length of Pregnancy A woman wrote to Dear Abby and claimed that she gave birth 308 days after a visit from her husband, who was in the Navy. Lengths of pregnancies have a mean of 268 days and a standard deviation of 15 days. Find the z score for 308 days. Is such a length unusual? What do you
10. Heights of Women The Beanstalk Club is limited to women and men who are very tall. The minimum height requirement for women is 70 in. Women’s heights have a mean of 63.6 in. and a standard deviation of 2.5 in. Find the z score corresponding to a woman with a height of 70 in. and determine
9. Body Temperatures Human body temperatures have a mean of 98.20°F and a standard deviation of 0.62°F. Convert the given temperatures to z scores.a. 97.5°Fb. 98.60°Fc. 98.20°F
8. World’s Tallest Woman Sandy Allen is the world’s tallest woman with a height of 91.25 in. (or 7 ft, 7.25 in.). Women have heights with a mean of 63.6 in. and a standard deviation of 2.5 in.a. What is the difference between Sandy Allen’s height and the mean height of women?b. How many
7. Heights of Presidents With a height of 67 in., William McKinley was the shortest president of the past century. The presidents of the past century have a mean height of 71.5 in. and a standard deviation of 2.1 in.a. What is the difference between McKinley’s height and the mean height of
6. Einstein’s IQ Stanford Binet IQ scores have a mean of 100 and a standard deviation of 16. Albert Einstein reportedly had an IQ of 160.a. What is the difference between Einstein’s IQ and the mean?b. How many standard deviations is that [the difference found in part (a)]?c. Convert
5. Darwin’s Height Men have heights with a mean of 176 cm and a standard deviation of 7 cm. Charles Darwin had a height of 182 cm.a. What is the difference between Darwin’s height and the mean?b. How many standard deviations is that [the difference found in part (a)]?c. Convert Darwin’s
4. ZIP Codes ZIP codes are arranged from east to west. Eastern states, such as Maine, have ZIP codes beginning with 0, but western states, such as Hawaii, Alaska, and California have ZIP codes beginning with 9. If the first quartile Q1 is computed from Q1 22.3-4 Measures of Relative Standing 117
3. Quartiles For a large data set, the first quartile is found to be 15. What does it mean when we say that 15 is the first quartile?
2. z Scores A sample consists of lengths of American bald eagles, measured in centimeters.If the length of one particular eagle is converted to a z score, what units are used for the z score? Centimeters?
1. z Scores A value from a large data set is found to have a z score of Is the value above the mean or below the mean? How many standard deviations away from the mean is this value?
38. Why Divide by Let a population consist of the values 3, 6, 9. Assume that samples of 2 values are randomly selected with replacement.a. Find the variance of the population {3, 6, 9}.b. List the nine different possible samples of 2 values selected with replacement, then find the sample variance
37. Interpreting Outliers A data set consists of 20 values that are fairly close together.Another value is included, but this new value is an outlier (very far away from the other values). How is the standard deviation affected by the outlier? No effect? A small effect? A large effect?
36. Understanding Units of Measurement If a data set consists of longevity times (in days) of fruit flies, what are the units used for standard deviation? What are the units used for variance?3-3 BEYOND THE BASICS
35. Coefficient of Variation Use the sample data listed below to find the coefficient of variation for each of the two samples, then compare the results.Heights (in.) of men: 71 66 72 69 68 69 Lengths (mm) of cuckoo eggs: 19.7 21.7 21.9 22.1 22.1 22.3 22.7 22.9 23.9
34. Coefficient of Variation Refer to the data in Exercise 17. Find the coefficient of variation for each of the two samples, then compare the results.
33. Empirical Rule Heights of men have a bell-shaped distribution with a mean of 176 cm and a standard deviation of 7 cm. Using the empirical rule, what is the approximate percentage of men betweena. 169 cm and 183 cm?b. 155 cm and 197 cm?
32. Range Rule of Thumb Aluminum cans with a thickness of 0.0111 in. have axial loads with a mean of 281.8 lb and a standard deviation of 27.8 lb. The axial load is measured by applying pressure to the top of the can until it collapses. (See Data Set 15 in Appendix B.) Use the range rule of thumb
31. Range Rule of Thumb The mean of electrical energy consumption amounts for the author’s home during a two-month period is 2838 kWh, and the standard deviation is 504 kWh. (The author actually tracks this stuff.) Use the range rule of thumb to identify minimum and maximum “usual” amounts of
30. Range Rule of Thumb Using the sample data in Data Set 1 from Appendix B, the sample of 40 women have upper leg lengths with a mean of 38.86 cm and a standard deviation of 3.78 cm. Use the range rule of thumb to identify the minimum and maximum“usual” upper leg lengths. Is a length of 47.0
29. Range Rule of Thumb Use the range rule of thumb to estimate the standard deviation of ages of all faculty members at your college.
28. Body Temperatures The accompanying frequency distribution summarizes a sample of human body temperatures. (See the temperatures for midnight on the second day, as listed in Data Set 2 in Appendix B.)
27. Speeding Tickets The given frequency distribution describes the speeds of drivers ticketed by the Town of Poughkeepsie police. These drivers were traveling through a 30 mi h speed zone on Creek Road, which passes the author’s college.
24. BMI and Gender Exercise 20 includes BMI values from 12 men and 12 women. Repeat Exercise 20 with the complete list of BMI values found in Data Set 1 in Appendix B. Do your conclusions change when the larger data sets are used?Finding Standard Deviation from a Frequency Distribution. In
23. Pennies Revisited Exercise 19 includes weights of pennies made before 1983 and after 1983. Repeat Exercise 19 with the complete list of weights of pennies made before 1983 and the complete list of pennies made after 1983 as listed in Data Set 14 of Appendix B. Do your conclusions change when
22. Regular Diet Coke Exercise 18 includes weights of regular Coke and Diet Coke listed in Data Set 12 in Appendix B. (The data in Exercise 18 are from the first six cans of regular Coke and the first six cans of Diet Coke.) Repeat Exercise 18 using the complete list of weights of regular Coke and
21. Weather Forecast Accuracy Exercise 15 includes temperature forecast data for 14 days. Repeat Exercise 15 after referring to Data Set 8 in Appendix B. Use the data for all 35 days to expand the list of differences shown in Exercise 15. (The data in Exercise 15 are based on the first 14 days in
20. BMI and Gender It is well known that men tend to weigh more than women, and men tend to be taller than women. The body mass index (BMI) is a measure based on weight and height. Listed below are BMI values from randomly selected men and women. Does there appear to be a difference in variation
19. Penny Thoughts U.S. pennies made before 1983 are 97% copper and 3% zinc, whereas pennies made after 1983 are 3% copper and 97% zinc. Listed below are weights (in grams) of pennies from each of those two time periods. (Data were obtained by the author.) Does there appear to be a considerable
18. Regular Diet Coke Weights (pounds) of samples of the contents in cans of regular Coke and Diet Coke are listed below. Compare the variation in the two data sets.Regular: 0.8192 0.8150 0.8163 0.8211 0.8181 0.8247 Diet: 0.7773 0.7758 0.7896 0.7868 0.7844 0.7861
17. Customer Waiting Times Waiting times (in minutes) of customers at the Jefferson Valley Bank (where all customers enter a single waiting line) and the Bank of Providence(where customers wait in individual lines at three different teller windows) are listed below. Compare the variation in the two
16. Treatment Effect Researchers at Pennsylvania State University conducted experiments with poplar trees. Listed below are weights (kg) of poplar trees given no 21 24 23 3-3 Measures of Variation 107 treatment and poplar trees treated with fertilizer and irrigation. Does there appear to be a
15. Weather Forecast Accuracy In an analysis of the accuracy of weather forecasts, the actual high temperatures are compared to the high temperatures predicted one day earlier and the high temperatures predicted five days earlier. Listed below are the errors between the predicted temperatures and
14. Ages of Stowaways The Queen Mary sailed between England and the United States, and stowaways were sometimes found on board. The ages (in years) of stowaways from eastbound crossings and westbound crossings are given below (data from the Cunard Steamship Co., Ltd.). Compare the variation in the
13. It’s Raining Cats Statistics are sometimes used to compare or identify authors of different works. The lengths of the first 20 words in the foreword written by Tennessee Williams in Cat on a Hot Tin Roof are listed along with the first 20 words in The Cat in the Hat by Dr. Seuss. Does there
12. Personal Income Listed below are the amounts of personal income per capita (in dollars)for the first five states listed in alphabetical order: Alabama, Alaska, Arizona, Arkansas, and California (data from the U.S. Bureau of Economic Analysis). Assume that the 45 amounts from the other states
11. Fruit Flies Listed below are the thorax lengths (in millimeters) of a sample of male fruit flies. If we learn that the listed measurements were obtained from fruit flies hovering over an apple sitting on a kitchen table in Pocatello, does the standard deviation serve as a reasonable estimate of
10. Body Temperatures Researchers at the University of Maryland collected body temperature readings from a sample of adults, and eight of those temperatures are listed below (in degrees Fahrenheit). Based on these results, is a body temperature of 21, 62.”106 Chapter 3 Statistics for Describing,
9. Blood Pressure Measurements Fourteen different second-year medical students at Bellevue Hospital measured the blood pressure of the same person. The systolic readings(in mmHg) are listed below. If the subject’s blood pressure remains constant and the medical students correctly apply the same
8. Old Faithful Geyser Listed below are intervals (in minutes) between eruptions of the Old Faithful geyser in Yellowstone National Park. Based on the results, is an interval of 100 minutes unusual?98 92 95 87 96 90 65 92 95 93 98 94
7. Phenotypes of Peas An experiment was conducted to determine whether a deficiency of carbon dioxide in the soil affects the phenotypes of peas. Listed below are the phenotype codes, where 1 smooth-yellow, 2 smooth-green, 3 wrinkled-yellow, and 4 wrinkled-green. Can the measures of
6. Cereal A dietician obtains the amounts of sugar (in centigrams) from 100 centigrams(or 1 gram) in each of 10 different cereals, including Cheerios, Corn Flakes, Fruit Loops, and 7 others. Those values are listed below. Is the standard deviation of those values likely to be a good estimate of the
5. Perception of Time Statistics students participated in an experiment to tests their ability to determine when 1 minute (or 60 seconds) has passed. The results are given below in seconds. Identify at least one good reason why the standard deviation from this sample might not be a good estimate of
3, and the low the standard deviation is Is that statement correct? Why or why not?In Exercises 5–12, find the range, variance, and standard deviation for the given sample data. (The same data were used in Section 3-2 where we found measures of center. Here we find measures of variation.) Also,
4. Correct Statement? In the book How to Lie with Charts, Gerald E. Jones writes that“the standard deviation is usually shown as plus or minus the difference between the high and the mean, and the low and the mean. For example, if the mean is 1, the high
3. Unusual Value? A statistics professor gives a test that has a mean of 50 and a standard deviation of 10. (She is not using a typical test with a maximum score of 100, and she promises to curve the scores.) One student earns a score of 85 on this test. In this context, is the score of 85
2. Comparing Variation Which do you think has more variation: the IQ scores of 30 students in a statistics class or the IQ scores of 30 patrons watching a movie? Why?SOLUTION Because we have sample statistics, we find the two coefficients of variation as follows:Heights:Weights:Although the
1. Variation Why is the standard deviation considered a measure of variation? In your own words, describe the characteristic of a data set that is measured by the standard deviation.
36. Median When data are summarized in a frequency distribution, the median can be found by first identifying the median class (the class that contains the median). We then assume that the values in that class are evenly distributed and we can interpolate.This process can be described by where n is
35. The quadratic mean (or root mean square, or R.M.S.) is usually used in physical applications. In power distribution systems, for example, voltages and currents are usually referred to in terms of their R.M.S. values. The quadratic mean of a set of values is obtained by squaring each value,
34. The geometric mean is often used in business and economics for finding average rates of change, average rates of growth, or average ratios. Given n values (all of which are positive), the geometric mean is the nth root of their product. The average growth factor for money compounded at annual
33. The harmonic mean is often used as a measure of central tendency for data sets consisting of rates of change, such as speeds. It is found by dividing the number of values n by the sum of the reciprocals of all values, expressed as(No value can be zero.) Four students drive from New York to
32. Transformed Data In each of the following, describe how the mean, median, mode, and midrange of a data set are affected.a. The same constant k is added to each value of the data set.b. Each value of the data set is multiplied by the same constant k.
31. Censored Data An experiment is conducted to study longevity of trees treated with fertilizer. The experiment is run for a fixed time of five years. (The test is said to be censored at five years.) The sample results (in years) are 2.5, 3.4, 1.2, (where indicates that the tree was still alive at
30. Degrees of Freedom Ten values have a mean of 75.0. Nine of the values are 62, 78, 90, 87, 56, 92, 70, 70, and 93.a. Find the 10th value.b. We need to create a list of n values that have a specific known mean. We are free to select any values we desire for some of the n values. How many of the n
29. Trimmed Mean Because the mean is very sensitive to extreme values, we say that it is not a resistant measure of center. The trimmed mean is more resistant. To find the 10% trimmed mean for a data set, first arrange the data in order, then delete the bottom 10% of the values and the top 10% of
28. Body Temperatures The accompanying frequency distribution summarizes a sample of human body temperatures. (See the temperatures for midnight on the second day, as listed in Data Set 2 in Appendix B.) How does the mean compare to the value of 98.6°F, which is the value assumed to be the mean by
27. Speeding Tickets The given frequency distribution describes the speeds of drivers ticketed by the Town of Poughkeepsie police. These drivers were traveling through a 30 mi h speed zone on Creek Road, which passes the author’s college. How does the mean compare to the posted speed limit of 30
24. BMI and Gender Exercise 20 includes BMI values from 12 men and 12 women. Repeat Exercise 20 with the complete list of BMI values found in Data Set 1 in Appendix B. Do your conclusions change when the larger data sets are used?In Exercises 25–28, find the mean of the data summarized in the
23. Pennies Revisited Exercise 19 includes weights of pennies made before 1983 and after 1983. Repeat Exercise 19 with the complete list of weights of pennies made before 1983 and the complete list of pennies made after 1983 as listed in Data Set 14 of Appendix B. Do your conclusions change when
22. Regular Diet Coke Exercise 18 includes weights of regular Coke and Diet Coke listed in Data Set 12 in Appendix B. (The data in Exercise 18 are from the first six cans>>90 Chapter 3 Statistics for Describing, Exploring, and Comparing Data of regular Coke and the first six cans of Diet Coke.)
21. Weather Forecast Accuracy Exercise 15 includes temperature forecast data for 14 days. Repeat Exercise 15 after referring to Data Set 8 in Appendix B. Use the data for all 35 days to expand the list of differences shown in Exercise 15. (The data in Exercise 15 are based on the first 14 days in
20. BMI and Gender It is well known that men tend to weigh more than women, and men tend to be taller than women. The body mass index (BMI) is a measure based on weight and height. Listed below are BMI values from randomly selected men and women. Does there appear to be a notable difference?Men:
19. Penny Thoughts U.S. pennies made before 1983 are 97% copper and 3% zinc, whereas pennies made after 1983 are 3% copper and 97% zinc. Listed below are weights (in grams) of pennies from each of those two time periods. (Data were obtained by the author.) Does there appear to be a considerable
18. Regular Diet Coke Weights (in pounds) of samples of the contents in cans of regular Coke and Diet Coke are listed below. Does there appear to be a significant difference between the two data sets? How might such a difference be explained?Regular: 0.8192 0.8150 0.8163 0.8211 0.8181 0.8247 Diet:
17. Customer Waiting Times Waiting times (in minutes) of customers at the Jefferson Valley Bank (where all customers enter a single waiting line) and the Bank of Providence (where customers wait in individual lines at three different teller windows)are listed below. Determine whether there is a
16. Treatment Effect Researchers at Pennsylvania State University conducted experiments with poplar trees. Listed below are weights (kg) of poplar trees given no 21 22 22 21 24 2 23 26 29 22 21 2 23 22 3-2 Measures of Center 89 treatment and poplar trees treated with fertilizer and irrigation. Does
15. Weather Forecast Accuracy In an analysis of the accuracy of weather forecasts, the actual high temperatures are compared to the high temperatures predicted one day earlier and the high temperatures predicted five days earlier. Listed below are the errors between the predicted temperatures and
14. Ages of Stowaways The Queen Mary sailed between England and the United States, and stowaways were sometimes found on board. The ages (years) of stowaways from eastbound crossings and westbound crossings are given below (data from the Cunard Steamship Co., Ltd.). Compare the two data
13. It’s Raining Cats Statistics are sometimes used to compare or identify authors of different works. The lengths of the first 20 words in the foreword written by Tennessee Williams in Cat on a Hot Tin Roof are listed along with the first 20 words in The Cat in the Hat by Dr. Seuss. Does there
12. Personal Income Listed below are the amounts of personal income per capita (in dollars)for the first five states listed in alphabetical order: Alabama, Alaska, Arizona, Arkansas, and California (data from the U.S. Bureau of Economic Analysis). When the 45 amounts from the other states are
11. Fruit Flies Listed below are the thorax lengths (in millimeters) of a sample of male fruit flies. Fruit flies (Drosophila) are a favorite subject of researchers because they have a simple chromosome composition, they reproduce quickly, they have large numbers of offspring, and they are easy to
10. Body Temperatures Researchers at the University of Maryland collected body temperature readings from a sample of adults, and eight of those temperatures are listed below (in degrees Fahrenheit). Does the mean of this sample equal 98.6, which is commonly believed to be the mean body temperature
9. Blood Pressure Measurements Fourteen different second-year medical students at Bellevue Hospital measured the blood pressure of the same person. The systolic readings(in mmHg) are listed below. What is notable about this data set?138 130 135 140 120 125 120 130 130 144 143 140 130 150
8. Old Faithful Geyser Listed below are intervals (in minutes) between eruptions of the Old Faithful geyser in Yellowstone National Park. After each eruption, the National Park Service provides an estimate of the length of time to the next eruption. Based on these values, what appears to be the
7. Phenotypes of Peas An experiment was conducted to determine whether a deficiency of carbon dioxide in the soil affects the phenotypes of peas. Listed below are the phenotype codes, where smooth-yellow, smooth-green, wrinkled-yellow, and wrinkled-green. Can the measures of center be obtained for
6. Cereal A dietician obtains the amounts of sugar (in centigrams) from 100 centigrams(or 1 gram) in each of 10 different cereals, including Cheerios, Corn Flakes, Fruit Loops, and 7 others. Those values are listed below. Is the mean of those values likely to be a good estimate of the mean amount
5. Perception of Time Statistics students participated in an experiment to test their ability to determine when 1 minute (or 60 seconds) has passed. The results are given below in seconds. Identify at least one good reason why the mean from this sample might not be a good estimate of the mean for
4. Mean Commuting Time A sociologist wants to find the mean commuting time for all working U.S. residents. She knows that it is not practical to survey each of the millions of working people, so she conducts an Internet search and finds the mean commuting time for each of the 50 states. She adds
3. Nominal Data In Chapter 1 it was noted that data are at the nominal level of measurement if they consist of names or labels only. A New England Patriots football fan records the number on the jersey of each Patriots player in a Super Bowl game. Does it make sense to calculate the mean of those
2. Mean and Median A statistics class consists of 24 students, all of whom are unemployed or are employed in low-paying part-time jobs. The class also includes a professor who is paid an enormous salary. Which does a better job of describing the income of a typical person in the class of 25 people

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