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Statistics The Exploration And Analysis Of Data 6th Edition John M Scheb, Jay Devore, Roxy Peck - Solutions
=+temperatures were recorded, and the treatment was considered successful if there had been a reduction in a patient’s temperature. Denoting success by S and failure by F, the 10 observations are S S F S S S F F S S
=+4.12 Suppose that 10 patients with meningitis received treatment with large doses of penicillin. Three days later, x
=+. Find a value of x5 such that 5 sample median.
=+4.11 ▼ A sample consisting of four pieces of luggage was selected from among those checked at an airline counter, yielding the following data on x 5 weight (in pounds):x1 5 33.5, x2 5 27.3, x3 5 36.7, x4 5 30.5 Suppose that one more piece is selected; denote its weight by x5
=+4.10 Consider the following statement: More than 65%of the residents of Los Angeles earn less than the average wage for that city. Could this statement be correct? If so, how? If not, why not?
=+of these statements correct? For each statement that is incorrect, explain why it is incorrect and propose a new wording that would correct any errors in the statement.
=+saying “There have been some fairly expensive houses selling, which pulls the median up.” Robert Kleinhenz, deputy chief economist for the California Association of Realtors explained the volatility of house prices by stating: “Fewer sales means a relatively small number of very high or
=+4.9 Houses in California are expensive, especially on the Central Coast where the air is clear, the ocean is blue, and the scenery is stunning. The median home price in San Luis Obispo County reached a new high in July 2004 soaring to$452,272 from $387,120 in March 2004. (San Luis Obispo Tribune,
=+e. Compute the mean and median for the highest cost premium data.
=+4.13 An experiment to study the lifetime (in hours) for a certain type of component involved putting 10 components into operation and observing them for 100 hr. Eight of the components failed during that period, and those lifetimes were recorded. The lifetimes of the two components still
=+Which of the measures of center discussed in this section can be calculated, and what are the values of those measures?
=+c. Memorial Day and Labor Day are holidays that always occur on Monday and Thanksgiving always occurs on a
=+b. Without computing the standard deviation of the Memorial Day data, explain whether the standard deviation for the Memorial Day data would be larger or smaller than the standard deviation of the New Year’s Day data.
=+a. Compute the standard deviation for the New Year’s Day data.
=+4.19 ● The U.S. Department of Transportation reported the accompanying data on the number of speedingrelated crash fatalities during holiday periods for the years from 1994 to 2003 (Traffic Safety Facts, July 20, 2005).
=+Explain why the standard deviation is a reasonable measure of volatility and why it is reasonable to interpret a smaller standard deviation as meaning less risk.
=+In short, the more diversified portfolio had a slightly better return and much less risk.
=+ as 9.26 percent. When me assets in the portfolio real estate, commodities, and options, the 10-year return rose to 10.55 percent while the standard deviation fell to 7.97 percent.
=+data from 1994 to 2004 to see what returns they would achieve. The first portfolio invested in Treasury b d d ti t k i t national stocks, and ual return was 9.85 per-ured as the standard de-
=+4.18 The article “Rethink Diversification to Raise Returns, Cut Risk” (San Luis Obispo Tribune, January 21, 2006) included the following paragraph:In their research, Mulvey and Reilly compared the results of two hypothetical portfolios and used actual
=+spends the same amount of money and there is some variation. Do you think a data set consisting of the amount spent at the beginning of the school year for each student at a particular elementary school would have a large or a small standard deviation? Explain.
=+4.17 Going back to school can be an expensive time for parents—second only to the Christmas holiday season in terms of spending (San Luis Obispo Tribune, August 18, 2005). Parents spend an average of $444 on their children at the beginning of the school year stocking up on clothes, notebooks,
=+4.15 A sample of n 5 5 college students yielded the following observations on number of traffic citations for a moving violation during the previous year:x1 5 1 x2 5 0 x3 5 0 x4 5 3 x5 5 2 Calcul 4.16 G mean of five differe
=+d. Construct an appropriate graphical display for the highest cost premium data.
=+c. Compute the mean and median for the lowest cost premium data.
=+i. the mean will be less than the median ii. the mean will be approximately equal to the median iii. the mean will be greater than the median
=+c. Will an 8% trimmed mean be larger or smaller than the mean for this data set? Explain your reasoning.
=+b. Calculate the mean and median copper content.
=+a. Construct a dotplot for these data.
=+4.3 ● Bidri is a popular and traditional art form in India.Bidri articles (bowls, vessels, and so on) are made by casting from an alloy containing primarily zinc along with some copper. Consider the following observations on copper content (%) for a sample of Bidri artifacts in London’s
=+d. Explain why it would not be reasonable to generalize from this sample of 20 newspapers to the population of daily newspapers in the United States.
=+c. Of the mean and median, which does the best job of describing a typical value for this data set?
=+The Greek letter P is used to denote the population proportion of S’s.* We will see later how the value of p from a particular sample can be used to make inferences about p.p 5 915 5 .60*Note that we are using the symbol p to represent a population proportion and not as the mathematical
=+This sample contains nine S’s, so That is, 60% of the sample responses are S’s. Of those surveyed, 60% are satisfied with their cell phone service.■
=+Example 4.6 Can You Hear Me Now?It is not uncommon for a cell phone user to complain about the quality of his or her service provider. Suppose that each person in a sample of n 5 15 cell phone users is asked if he or she is satisfied with the cell phone service. Each response is classified as S
=+b. Compute the values of the mean and the median of this data set.
=+4.2 ● USA Today (May 9, 2006) published the accompanying average weekday circulation for the six month period ending March 31, 2006 for the top 20 newspapers in the country:2,272,815 2,049,786 1,142,464 851,832 724,242 708,477 673,379 579,079 513,387 438,722 427,771 398,329 398,246 397,288
=+Compute the values of the mean and the median. Why are these values so different? Which of the mean and median is more representative of the data set, and why?
=+4.4 ● The chapter introduction gave the accompanying data on the percentage of those eligible for a low-income subsidy who had signed up for a Medicare drug plan in each of 49 states (information was not available for Vermont) and the District of Columbia (USA Today, May 9, 2006).24 27 12 38
=+a. Compute the mean for this data set.
=+b. The article stated that nationwide, 24% of those eligible had signed up. Explain why the mean of this data set from Part (a) is not equal to 24. (No information was available for Vermont, but that is not the reason that the mean differs—the 24% was calculated excluding Vermont.)
=+b. Based on the display in Part (a), which of the following would you expect to be the case for the lowest cost premium data?
=+a. Construct a dotplot or a stem-and-leaf display of the lowest premium cost data.
=+4.8 Note: This exercise requires the use of a computer.Refer to the Medicare drug plan premium data of Exercise 4.7.
=+f. the mean of the minimum cost of all states beginning with the letter “M”
=+Which of the following can be determined from the data?If it can be determined, calculate the requested value. If it cannot be determined, explain why not.a. the median premium cost in Coloradob. the number of plan choices in Virginiac. the state(s) with the largest difference in cost between
=+$104.89. Here are the lowest and highest monthly premiums for stand-alone Medicare drug plans for each state:State $ Low $ High Alabama 14.08 69.98 Alaska 20.05 61.93 Arizona 6.14 64.86 Arkansas 10.31 67.98 California 5.41 66.08 Colorado 8.62 65.88 Connecticut 7.32 65.58 Delaware 6.44 68.91
=+4.7 ● ▼ Medicare’s new medical plans offer a wide range of variations and choices for seniors when picking a drug plan (San Luis Obispo Tribune, November 25, 2005). The monthly cost for a stand-alone drug plan can vary from a low of $1.87 in Montana, Wyoming, North Dakota, South Dakota,
=+b. Is it possible that another medical procedure might have a median wait time that is greater than the time reported for “90% completed within”? Explain.
=+What does this suggest about the distribution of wait times for these two procedures?
=+4.6 The ministry of Health and Long-Term Care in Ontario, Canada, publishes information on its web site(www.health.gov.on.ca) on the time that patients must wait for various medical procedures. For two cardiac procedures completed in fall of 2005 the following information was provided:Number
=+c. Explain why it is not reasonable to generalize from this sample of 20 days to the other 345 days of the year.
=+4.5 ● The U.S. Department of Transportation reported the number of speeding-related crash fatalities for the 20 dates that had the highest number of these fatalities between 1994 and 2003 (Traffic Safety Facts, July 2005).Speeding- SpeedingRelated Related Date Fatalities Date Fatalities Jan 1
=+4.1 ●on rep movin data fo Model Repair Cost Audi A6 0 BMW 328i 0 Cadillac Catera 900 Jaguar X 1254 Lexus ES300 234 Lexus IS300 979 Mercedes C320 707 Saab 9-5 670 Volvo S60 769 Volvo S80 4194**Included cost to replace airbags, which deployed.
=+Real estate broker 102 Computer-related 87 Enlisted military 99 Dentist 86 Social worker 98 Pharmacist 85 Manual laborer 96 Proprietor 84 Analyst 95 Teacher, professor 84 Engineer 94 Accountant 84 Consultant 94 Law enforcement 79 Sales 93 Physical therapist 78 Military officer 91 Veterinarian 78
=+2. Construct a rectangular box with a left (or lower) edge is at the lower quartile and whose right (or upper) edge is at the upper quartile. The box width is then equal to the iqr.
=+1. Draw a horizontal (or vertical) measurement scale.
=+4. Extend horizontal (or vertical) line segments, called whiskers, from each end of the box to the smallest and largest observations in the data set.
=+3. Draw a vertical (or horizontal) line segment inside the box at the location of the median.
=+2. Construct a rectangular box with a left (or lower) edge at the lower quartile and a right (or upper) edge at the upper quartile. The box width is then equal to the iqr.
=+1. Draw a horizontal (or vertical) measurement scale.
=+b. Compute the coefficient of variation for each sample.Do the results surprise you? Why or why not?
=+a. For each of the given samples, calculate the mean and the standard deviation.
=+Consider two samples. Sample 1 gives the actual weight(in ounces) of the contents of cans of pet food labeled as having a net weight of 8 oz. Sample 2 gives the actual weight (in pounds) of the contents of bags of dry pet food labeled as having a net weight of 50 lb. The weights for the two
=+4.28 ● The standard deviation alone does not measure relative variation. For example, a standard deviation of $1 would be considered large if it is describing the variability from store to store in the price of an ice cube tray. On the other hand, a standard deviation of $1 would be
=+b. How does the interquartile range compare to the interquartile range for the inpatient cost-to-charge ratio from Example 4.9? Is there more variability in the inpatient or the outpatient ratio?
=+a. Use the given data to compute the quartiles and the interquartile range for the outpatient cost-to-charge ratio.
=+3. Draw a vertical (or horizontal) line segment inside the box at the location of the median.
=+4. Determine if there are any mild or extreme outliers in the data set.
=+5. Draw whiskers that extend from each end of the box to the most extreme observation that is not an outlier.
=+4.32 ● Shown here are the number of auto accidents per year for every 1000 people in each of 40 occupations(Knight Ridder Tribune, June 19, 2004):Accidents Accidents per per Occupation 1000 Occupation 1000 Student 152 Banking, finance 89 Physician 109 Customer service 88 Lawyer 106 Manager 88
=+b. Construct a modified boxplot for these data and comment on any interesting features of the plot.
=+a. Compute the mean and median values for extra travel hours. Based on the values of the mean and median, is the distribution of extra travel hours likely to be approximately symmetric, positively skewed, or negatively skewed?
=+4.31 ● ▼ A report from Texas Transportation Institute(Texas A&M University System 2005) on Congestion Reduction Strategies looked into the extra travel time (due to traffic congestion) for commute travel per traveler per year in hours for different urban areas. Below are the data for urban
=+Use these data to construct a boxplot that shows outliers.Write a few sentences describing the important characteristics of the boxplot.
=+4.30 ● The technical report “Ozone Season Emissions by State” (U.S. Environmental Protection Agency, 2002) gave the following nitrous oxide emissions (in thousands of tons) for the 48 states in the continental U.S. states:76 22 40 7 30 5 6 136 72 33 0 89 136 39 92 40 13 27 1 63 33 60 27 16
=+c. Were there any mild or extreme outliers in the data set?How can you tell?
=+b. Suppose that the minimum travel time was 1 min and that the maximum travel time in the sample was 205 min.Construct a skeletal boxplot for the travel time data.
=+a. Is the travel time distribution more likely to be approximately symmetric, positively skewed, or negatively skewed? Explain your reasoning based on the given summary quantities.
=+4.29 Based on a large national sample of working adults, the U.S. Census Bureau reports the following information on travel time to work for those who do not work at home:lower quartile 5 7 min median 5 18 min upper quartile 5 31 min Also given was the mean travel time, which was reported as 22.4
=+7. Draw an open circle to mark the location of any extreme outliers in the data set.
=+6. Draw a solid circle to mark the location of any mild outliers in the data set.
=+4.27 ● Example 4.9 gave 2002 cost-to-charge ratios for inpatient services at 31 hospitals in Oregon. The same data source also provided the cost-to-charge ratios for outpatient services at these same 31 hospitals:75 54 50 75 58 56 56 62 66 69 100 57 45 51 53 45 84 45 48 39 51 51 65 100 63 96
=+than for holidays that can occur on different days of the week? Support your answer with appropriate measures of variability.
=+8.81 10.26 10.20 12.66 12.86 12.96 13.04 13.14 14.70 14.84
=+4.22 ● Cost-to-charge ratios (see Example 4.9 for a definition of this ratio) were reported for the 10 hospitals in California with the lowest ratios (San Luis Obispo Tribune, December 15, 2002). These ratios represent the 10 hospitals with the highest markup, because for these hospitals,
=+c. Consider houses sold in Grover Beach and Paso Robles. Based on the other information given, which is likely to have the higher median price?
=+b. Houses sold in Grover Beach and Paso Robles have very similar average prices. Based on the other information given, which is likely to have the higher standard deviation for price?
=+Grover Beach $416,405 97 $242,000 $720,000 Paso Robles $412,584 439 $170,000 $1,575,000 Oceano $390,354 59 $177,000 $1,350,000a. Explain why the average price for the combined areas of Los Osos and Morro Bay is not just the average of$511,866 and $606,456.
=+Templeton $578,249 89 $265,000 $2,350,000 San Luis $557,628 277 $258,000 $2,400,000 Obispo Nipomo $528,572 138 $263,000 $1,295,000 Los Osos $511,866 123 $140,000 $3,500,000 Santa $430,354 22 $290,000 $583,000 Margarita Atascadero $420,603 270 $140,000 $1,600,000
=+Average Number Community Price Sold Low High Cambria $728,312 85 $340,000 $2,000,000 Avila Beach $654,918 16 $475,000 $1,375,000 Morro Bay $606,456 114 $257,000 $2,650,000 Arroyo $595,577 214 $178,000 $1,526,000 Grande
=+4.21 The accompanying table shows the low price, the high price, and the average price of homes in fifteen communities in San Luis Obispo County between January 1, 2004 and August 1, 2004 (San Luis Obispo Tribune, September 5, 2004).Average Number Community Price Sold Low High Cayucos $937,366
=+c. Which of the following must be true for the 95th percentile of the data set consisting of the 539 wait times for bypass surgery?i. The 95th percentile is less than 13.ii. The 95th percentile is between 13 and 19.iii. The 95th percentile is between 13 and 42.iv. The 95th percentile is greater
=+b. Which of the following must be true for the upper quartile of the data set consisting of the 539 wait times for bypass surgery?i. The upper quartile is less than 13.ii. The upper quartile is between 13 and 19.iii. The upper quartile is between 13 and 42.iv. The upper quartile is greater than
=+a. Which of the following must be true for the lower quartile of the data set consisting of the 847 wait times for angioplasty?i. The lower quartile is less than 14.ii. The lower quartile is between 14 and 18.iii. The lower quartile is between 14 and 39.iv. The lower quartile is greater than 39.
=+4.20 The ministry of Health and Long-Term Care in Ontario, Canada publishes information on the time that patients must wait for various medical procedures on its web site (www.health.gov.on.ca). For two cardiac procedures completed in fall of 2005 the following information was provided:Number
=+a. Compute the variance and standard deviation for this data set.
=+b. If cost-to-charge data were available for all hospitals in California, would the standard deviation of this data set be larger or smaller than the standard deviation computed in Part (a) for the 10 hospitals with the lowest cost-to-charge values? Explain.
=+c. Explain why it would not be reasonable to use the data from the sample of 10 hospitals in Part (a) to draw conclusions about the population of all hospitals in California.
=+b. Based on the interquartile range, is there more or less variability in sodium content for the chocolate pudding data than for the tomato catsup data of Exercise 4.25?
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