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elementary statistics
Elementary Statistics Picturing The World 5th Edition Ron Larson, Betsy Farber - Solutions
Explain. 8.a. Estimate the mean age of cars driven by students at your college.b. Use the range rule of thumb to make a rough estimate of the standard deviation of the ages of cars driven by students at your college.
Comparing Scores An industrial psychologist for the Citation Corporation develops two different tests to measure job satisfaction. Which score is better: A score of 72 on the management test, which has a mean of 80 and a standard deviation of 12, or a score of 19 on the test for production
Empirical Rule Assume the ages of past, present, and future presidents have a bellshaped distribution with a mean of 54.8 years and a standard deviation of 6.2 years.a. What does the empirical rule say about the percentage of ages between 48.6 years and 61.0 years (or within 1 standard deviation of
Boxplot Using the same ages listed in Problem 1, construct a boxplot and identify the values constituting the 5-number summary.
Histogram Using the frequency distribution from Exercise 3, construct a histogram and identify the general nature of the distribution (such as uniform, bell-shaped, skewed).
Frequency Distribution Using the same ages listed in Exercise 1, construct a frequency distribution. Use six classes with 40 as the lower limit of the first class, and use a class width of 5.
a. John F. Kennedy was 43 years of age when he was inaugurated. Using the results from Exercise 1, convert his age to a z score.b. Is Kennedy’s age of 43 years “unusual”? Why or why not?c. Using the range rule of thumb, identify any other listed ages that are unusual.d. Although the list of
Ages of Presidents Senator Hayes is considering a run for the U.S. presidency, but she is only 35 years of age, which is the minimum required age. While investigating this issue, she finds the ages of past presidents when they were inaugurated, and those ages are listed below. Using the ages
Clancy, Rowling, Tolstoy Refer to Data Set 14 in Appendix B and use the Flesch reading ease scores for the sample pages from Tom Clancy’s The Bear and the Dragon, J. K. Rowling’s Harry Potter and the Sorcerer’s Stone, and Leo Tolstoy’s War and Peace. (Higher scores indicate easier reading.)
Find the 5-number summaries for the other two groups, then construct the three boxplots using the same scale. Are there any apparent differences?
Cotinine Levels Refer to Table 2-1 located in the Chapter Problem. We have already found that the 5-number summary for the cotinine levels of smokers is 0, 86.5, 170, 251.5, and
Alcohol in Children’s Movies Refer to Data Set 7 for the 50 times (in seconds) of scenes showing alcohol use in animated children’s movies. Find the 5-number summary and construct a boxplot. Based on the boxplot, does the distribution appear to be symmetric or is it skewed?
Bear Lengths Refer to Data Set 9 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?
Red M&Ms Refer to Data Set 19 for the 21 weights (in grams) of the red M&M candies. Find the 5-number summary and construct a boxplot. Are the red sample values likely to be representative of M&M candies of all colors?
Nicotine in Cigarettes Refer to Data Set 5 for the 29 amounts of nicotine (in mg per cigarette). Find the 5-number summary and construct a boxplot. Are the sample values likely to be representative of cigarettes smoked by an individual consumer?
Lottery Refer to Data Set 26 and use only the 40 digits in the first column of the Win 4 results from the New York State Lottery (9, 7, 0, and so on). Find the 5-number summary and construct a boxplot. What characteristic of the boxplot suggests that the digits are selected with a random and fair
Deciles and Quintiles For a given data set, there are nine deciles, denoted by D1, D2, . . . , D9 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 five groups, with about 20% of the values in
Interpolation When finding percentiles using Figure 2-15, 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 so that a locator of 23.75 leads to a value that is 0.75 (or 3 4) of the way between the 23rd and 24th
Cotinine Levels of Smokers Use the sorted cotinine levels of smokers listed in Table 2-13.a. Find the interquartile range.b. Find the midquartile.c. Find the 10–90 percentile range.d. Does P50 5 Q2? If so, does P50 always equal Q2?e. Does Q2 5 (Q1 1 Q3) 2? If so, does Q2 always equal (Q1 1 Q3) 2?
Fibonacci Sequence Here are the first several terms of the famous Fibonacci sequence: 1, 1, 2, 3, 5, 8, 13.a. Find the mean and standard deviation s, then convert each value to a z score.Don’t round the z scores; carry as many places as your calculator can handle.b. Find the mean and standard
Distribution of z Scoresa. A data set has a distribution that is uniform. If all of the values are converted to z scores, what is the shape of the distribution of the z scores?b. A data set has a distribution that is bell-shaped. If all of the values are converted to z scores, what is the shape of
Converting a z Score Heights of women have a mean of 63.6 in. and a standard deviation of 2.5 in.a. Julia Roberts, who is one of the most successful actresses in recent years, has a height that converts to a z score of 2.16. How tall (in inches) is Julia Roberts?b. Female rapper Lil’ Kim has a
Units of Measurement When finding a z score for the height of a basketball player in the NBA, how is the result affected if, instead of using inches, all heights are expressed in centimeters? In general, how are z scores affected by the particular unit of measurement that is used?
Green M&Ms Refer to Data Set 19 in Appendix B for the sample of weights of green M&M candies. Convert the weight of the heaviest green M&M candy to a z score. Is the weight of that heaviest green M&M an unusual weight for green M&Ms?
Weights of Coke Refer to Data Set 17 in Appendix B for the sample of 36 weights of regular Coke. Convert the weight of 0.7901 to a z score. Is 0.7901 an unusual weight for regular Coke?
Comparing Scores Three students take equivalent tests of a sense of humor and, after the laughter dies down, their scores are calculated. 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
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.
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 of
Body Temperature Human body temperatures have a mean of 98.20° and a standard deviation of 0.62°. An emergency room patient is found to have a temperature of 101°. Convert 101° to a z score. Is that temperature unusually high? What does it suggest?
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
Pulse Rates of Adults Assume that adults have pulse rates (beats per minute) with a mean of 72.9 and a standard deviation of 12.3 (based on data from the National Health Examination). When this exercise question was written, the author’s pulse rate was 48.a. What is the difference between the
IQ Scores 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 Einstein’s IQ
Why Not Go MAD? Exercise 41 shows that the sample variance s2 is an unbiased estimator of s2. Do the following with the same population of {3, 6, 9} to show that the mean absolute deviation of a sample is a biased estimator of the mean absolute deviation of a population.a. Find the mean absolute
Why Divide by n21? Let a population consist of the values 3, 6, 9. Assume that samples of two values are randomly selected with replacement.a. Find the variance s2 of the population {3, 6, 9}.b. List the nine different possible samples of two values selected with replacement, then find the sample
Phony Data? For any data set of n values with standard deviation s, every value must be within of the mean. A statistics teacher reports that the test scores in her class of 17 students had a mean of 75.0 and a standard deviation of 5.0. Kelly, the class’s self-proclaimed best student, claims
Understanding Standard Deviation A sample consists of 10 test scores that fall between 70 and 100 inclusive. What is the largest possible standard deviation?
Skewness In Section 2-4 we introduced the general concept of skewness. Skewness can be measured by Pearson’s index of skewness:If I 1.00 or I # 21.00, the data can be considered to be significantly skewed. Find Pearson’s index of skewness for the cotinine levels of smokers listed in Table 2-1,
Genichi Taguchi developed a method of improving quality and reducing manufacturing costs through a combination of engineering and statistics. A key tool in the Taguchi method is the signal-to-noise ratio. The simplest way to calculate this ratio is to divide the mean by the standard deviation. Find
Transforming Data In each of the following, describe how the range and standard deviation 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.c. For the body temperature data listed in Data Set 4
Comparing Data Sets Two different sections of a statistics class take the same quiz and the scores are recorded below. Find the range and standard deviation for each section. What do the range values lead you to conclude about the variation in the two sections? Why is the range misleading in this
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?2-5 Beyond the
Comparing Car Batteries The Everlast and Endurance brands of car battery are both labeled as lasting 48 months. In reality, they both have a mean life of 50 months, but the Everlast batteries have a standard deviation of 2 months, while the Endurance batteries have a standard deviation of 6 months.
Understanding Units of Measurement If a data set consists of the fines for speeding(in dollars), what are the units used for standard deviation? What are the units used for variance?
Equality for All What do you know about the values in a data set having a standard deviation of s 5 0?
Coefficient of Variation for Coke and Pepsi Refer to Data Set 17 in Appendix B. Find the coefficient of variation for the weights of regular Coke, then find the coefficient of variation for the weights of regular Pepsi. Compare the results. Does either company appear to have weights that are
Coefficient of Variation for Cereal Refer to Data Set 16 in Appendix B. Find the coefficient of variation for the calories and find the coefficient of variation for the grams of sugar per gram of cereal. Compare the results.
Weights of Regular Coke Using the weights of regular Coke listed in Data Set 17 from Appendix B, we find that the mean is 0.81682 lb and the standard deviation is 0.00751 lb. What can you conclude from Chebyshev’s theorem about the percentage of cans of regular Coke with weights between 0.79429
Heights of Women If heights of women have a mean of 63.6 in. and a standard deviation of 2.5 in., what can you conclude from Chebyshev’s theorem about the percentage of women between 58.6 in. and 68.6 in.?
Weights of Regular Coke Using the weights of regular Coke listed in Data Set 17 from Appendix B, we find that the mean is 0.81682 lb, the standard deviation is 0.00751 lb, and the distribution is approximately bell-shaped. Using the empirical rule, what is the approximate percentage of cans of
Heights of Women Heights of women have a bell-shaped distribution with a mean of 63.6 in. and a standard deviation of 2.5 in. Using the empirical rule, what is the approximate percentage of women betweena. 61.1 in. and 66.1 in.?b. 56.1 in. and 71.1 in.?
Heights of Women Heights of women have a mean of 63.6 in. and a standard deviation of 2.5 in. (based on data from the National Health Survey). Use the range rule of thumb to estimate the minimum and maximum “usual” heights of women. In this context, is it unusual for a woman to be 6 ft tall?
Leg Lengths For 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 estimate the minimum and maximum “usual”upper leg lengths for women. Is a length of 47.0 cm
Test Scores Use the range rule of thumb to estimate the standard deviation of the scores on the first statistics test in your class.
Teacher Ages Use the range rule of thumb to estimate the standard deviation of ages of all teachers at your college.
Head Circumferences In order to correctly diagnose the disorder of hydrocephalus, a pediatrician investigates head circumferences of 2-year-old boys and girls. Use the sample results listed in Data Set 3. Does there appear to be a difference between the two genders?
Bufferin Tablets Listed below are the measured weights (in milligrams) of a sample of Bufferin aspirin tablets. Given that this medication should be manufactured in a consistent way so that dosage amounts can be controlled, do the measures of variation seem to indicate that the variation is at an
Reaction Times The author visited the Reuben H. Fleet Science Museum in San Diego and repeated an experiment of reaction times. The following times (in hundredths of a second) were obtained. How do the measures of variation reflect the fact that these times appear to be very consistent?19 20 17 21
Motorcycle Fatalities Listed below are ages of motorcyclists when they were fatally injured in traffic crashes (based on data from the U.S. Department of Transportation).How does the variation of these ages compare to the variation of ages of licensed drivers in the general population?17 38 27 14
Drunk Driving The blood alcohol concentrations of a sample of drivers involved in fatal crashes and then convicted with jail sentences are given below (based on data from the U.S. Department of Justice). When a state wages a campaign to “reduce drunk driving,” is the campaign intended to lower
Body Mass Index As part of the National Health Examination, the body mass index is measured for a random sample of women. Some of the values included in Data Set 1 from Appendix B are listed below. Is the standard deviation of this sample reasonably close to the standard deviation of 6.17, which is
Cereal A dietitian obtains the amounts of sugar (in grams) from 1 gram in each of 16 different cereals, including Cheerios, Corn Flakes, Fruit Loops, Trix, and 12 others.Those values, included in Data Set 16 from Appendix B, are listed below. Is the standard deviation of these values likely to be a
Harry Potter In an attempt to measure the reading level of a book, the Flesch Reading Ease ratings are obtained for 12 randomly selected pages from Harry Potter and the Sorcerer’s Stone by J. K. Rowling. Those values, included in Data Set 14 from Appendix B, are listed below. Given that these
Tobacco Use in Children’s Movies In “Tobacco and Alcohol Use in G-Rated Children’s Animated Films,” by Goldstein, Sobel, and Newman (Journal of the American Medical Association, Vol. 281, No. 12), the lengths (in seconds) of scenes showing tobacco use were recorded for animated movies from
Censored Data An experiment is conducted to test the lives of car batteries. 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, 51, 51 (where 51 indicates that the battery was still working at the
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 tenth 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
Mean of Means Using an almanac, a researcher finds the mean teacher’s salary for each state. He adds those 50 values, then divides by 50 to obtain their mean. Is the result equal to the national mean teacher’s salary? Why or why not?
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 the
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 4 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
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 authors’ college. How does the mean compare to the posted speed limit of 30 mi h?
Loaded Die The author drilled a hole in a die and filled it with a lead weight, then proceeded to roll it 200 times. The results are given in the frequency distribution in the margin. Does the result appear to be very different from the result that would be expected with an unmodified die?
Old Faithful Visitors to Yellowstone National Park consider an eruption of the Old Faithful geyser to be a major attraction that should not be missed. The given frequency distribution summarizes a sample of times (in minutes) between eruptions.
Tobacco Alcohol Use in Children’s Movies In “Tobacco and Alcohol Use in GRated Children’s Animated Films,” by Goldstein, Sobel, and Newman (Journal of the American Medical Association, Vol. 281, No. 12), the lengths (in seconds) of scenes showing tobacco use and alcohol use were recorded
Weekend Rainfall Using Data Set 11 in Appendix B, find the mean and median of the rainfall amounts in Boston on Thursday and find the mean and median of the rainfall amounts in Boston on Sunday. Media reports claimed that it rains more on weekends than during the week. Do these results appear to
Clancy, Rowling, Tolstoy A child psychologist investigates differences in reading difficulty and obtains data from The Bear and the Dragon by Tom Clancy, Harry Potter and the Sorcerer’s Stone by J. K. Rowling, and War and Peace by Leo Tolstoy. Refer to Data Set 14 in Appendix B and use the
Head Circumferences In order to correctly diagnose the disorder of hydrocephalus, a pediatrician investigates head circumferences of 2-year-old males and females. Use the sample results listed in Data Set 3. Does there appear to be a difference between the two genders?
Skull Breadths Maximum breadth of samples of male Egyptian skulls from 4000 B.C.and 150 A.D. (based on data from Ancient Races of the Thebaid by Thomson and Randall-Maciver):4000 B.C.: 131 119 138 125 129 126 131 132 126 128 128 131 150 A.D.: 136 130 126 126 139 141 137 138 133 131 134 129 Changes
Mickey D vs. Jack When investigating times required for drive-through service, the following results (in seconds) are obtained (based on data from QSR Drive-Thru Time Study).McDonald’s: 287 128 92 267 176 240 192 118 153 254 193 136 Jack in the Box: 190 229 74 377 300 481 428 255 328 270 109 109
Regular Coke Diet Coke Weights (pounds) of samples of the contents in cans of regular Coke and diet Coke: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 Does there appear to be a significant difference between the two data sets? How might such a
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):Jefferson Valley: 6.5 6.6 6.7 6.8 7.1 7.3 7.4 7.7 7.7
Bufferin Tablets Listed below are the measured weights (in milligrams) of a sample of Bufferin aspirin tablets. What is a serious consequence of having weights that vary too much?672.2 679.2 669.8 672.6 672.2 662.2 662.7 661.3 654.2 667.4 667.0 670.7 In Exercises 9–12, find the mean, median,
Reaction Times The author visited the Reuben H. Fleet Science Museum in San Diego and repeated an experiment of reaction times. The following times (in hundredths of a second) were obtained. How consistent are these results, and how does the consistency affect the usefulness of the sample mean as
Motorcycle Fatalities Listed below are ages of motorcyclists when they were fatally injured in traffic crashes (based on data from the U.S. Department of Transportation).Do the results support the common belief that such fatalities are incurred by a greater proportion of younger drivers?17 38 27 14
Drunk Driving The blood alcohol concentrations of a sample of drivers involved in fatal crashes and then convicted with jail sentences are given below (based on data from the U.S. Department of Justice). Given that current state laws prohibit driving with levels above 0.08 or 0.10, does it appear
Body Mass Index As part of the National Health Examination, the body mass index is measured for a random sample of women. Some of the values included in Data Set 1 from Appendix B are listed below. Is the mean of this sample reasonably close to the mean of 25.74, which is the mean for all 40 women
Cereal A dietitian obtains the amounts of sugar (in grams) from 1 gram in each of 16 different cereals, including Cheerios, Corn Flakes, Fruit Loops, Trix, and 12 others.Those values, included in Data Set 16 from Appendix B, are listed below. Is the mean of those values likely to be a good estimate
Harry Potter In an attempt to measure the reading level of a book, the Flesch Reading Ease ratings are obtained for 12 randomly selected pages from Harry Potter and the Sorcerer’s Stone by J. K. Rowling. Those values, included in Data Set 14 from Appendix B, are listed below. Given that these
Tobacco Use in Children’s Movies In “Tobacco and Alcohol Use in G-Rated Children’s Animated Films,” by Goldstein, Sobel, and Newman (Journal of the American Medical Association, Vol. 281, No. 12), the lengths (in seconds) of scenes showing tobacco use were recorded for animated movies from
a. Refer to Data Set 20 in Appendix B and construct a histogram for the axial loads of cans that are 0.0111 in. thick. That data set includes an outlier of 504 lb. (An outlier is a value that is far away from the other values.)b. Repeat part (a) after excluding the outlier of 504 lb.c. How much of
Investing in Stocks In Data Set 25, use the high values of the Dow Jones Industrial Average (DJIA) to construct a time-series graph, then determine whether there appears to be a trend. How might an investor profit from this trend?
Jobs Refer to the data given in Exercise 21, and construct a pie chart. Compare the pie chart to the Pareto chart. Can you determine which graph is more effective in showing the relative importance of job sources?
Jobs A study was conducted to determine how people get jobs. The table lists data from 400 randomly selected subjects. The data are based on results from the National Center for Career Strategies. Construct a Pareto chart that corresponds to the given data. If someone would like to get a job, what
Body Temperatures Exercise 16 in Section 2-2 referred to Data Set 4 in Appendix B.Using the frequency distribution of the body temperatures for midnight on the second day (with 8 classes beginning with a lower class limit of 96.5 and a class width of 0.4°F), construct the corresponding histogram.
Bears Exercise 15 in Section 2-2 referred to Data Set 9 in Appendix B. Using the frequency distribution of the weights of bears (with 11 classes beginning with a lower class limit of 0 and a class width of 50 lb), construct the corresponding histogram.What is the approximate weight that is at the
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. Construct a histogram corresponding to the given frequency
Student Faculty Cars Samples of student cars and faculty staff cars were obtained at the author’s college, and their ages (in years) are summarized in the accompanying frequency distribution. Construct a relative frequency histogram for student cars and another relative frequency histogram for
Interpreting Pie Chart What is the approximate percentage of people with Group B blood? Assuming that the pie chart is based on a sample of 500 people, approximately how many of those 500 people have Group B blood?
Interpreting Pie Chart What is the approximate percentage of people with Group A blood? Assuming that the pie chart is based on a sample of 500 people, approximately how many of those 500 people have Group A blood?
Consider the population of ten digits: 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9.Select three random samples of five digits from this list. Find the average of each sample. Compare your results with the average of the entire population. Comment on your results. (Hint: To find the average, sum the data
The data represent the weights (in pounds) of several professional football players. 225 250 305 285 275 265 290 310 290 250 210 225 308 325 260 165 195 245 235 298 395 255 268 190
The data represent the speeds (in miles per hour) of several vehicles. 68 88 70 72 70 69 72 62 65 70 75 52 65
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