91影视

The National Health and Nutrition Examination Survey (NHANES) collects demographic, socioeconomic, dietary, and health related information on an annual basis. Here is a sample of \({\rm{20}}\) observations on HDL cholesterol level \({\rm{(mg/dl)}}\) obtained from the \({\rm{2009 - 2010}}\) survey (HDL is 鈥済ood鈥� cholesterol; the higher its value, the lower the risk for heart disease):

\(\begin{array}{l}{\rm{35 49 52 54 65 51 51}}\\{\rm{47 86 36 46 33 39 45}}\\{\rm{39 63 95 35 30 48}}\end{array}\)

a. Calculate a point estimate of the population mean HDL cholesterol level.

b. Making no assumptions about the shape of the population distribution, calculate a point estimate of the value that separates the largest \({\rm{50\% }}\) of HDL levels from the smallest \({\rm{50\% }}\).

c. Calculate a point estimate of the population standard deviation.

d. An HDL level of at least \({\rm{60}}\) is considered desirable as it corresponds to a significantly lower risk of heart disease. Making no assumptions about the shape of the population distribution, estimate the proportion \({\rm{p}}\) of the population having an HDL level of at least \({\rm{60}}\).

A Pareto diagram is a variation of a histogram forcategorical data resulting from a quality control study.Each category represents a different type of product non-conformity or production problem. The categories areordered so that the one with the largest frequencyappears on the far left, then the category with the secondlargest frequency, and so on. Suppose the following information on nonconformities in circuit packs isobtained: failed component, 126; incorrect component,210; insufficient solder, 67; excess solder, 54; missingcomponent, 131. Construct a Pareto diagram.

The cumulative frequency and cumulative relativefrequency for a particular class interval are the sum offrequencies and relativefrequencies, respectively, forthat interval and all intervals lying below it. If, forexample, there are four intervals with frequencies 9,16, 13, and 12, then the cumulative frequencies are 9,25, 38, and 50, and the cumulative relative frequenciesare .18, .50, .76, and 1.00. Compute the cumulativefrequencies and cumulative relative frequencies for thedata of Exercise 24.

Fire load (MJ/m2) is the heat energy that could bereleased per square meter of floor area by combustionof contents and the structure itself. The article 鈥淔ireLoads in Office Buildings鈥� (J. of Structural Engr.,

1997: 365鈥�368) gave the following cumulative percentages(read from a graph) for fire loads in a sample of388 rooms:

Value0 150 300 450 600

Cumulative %0 19.3 37.6 62.7 77.5

Value750 900 1050 1200 1350

Cumulative %87.2 93.8 95.7 98.6 99.1

Value1500 1650 1800 1950

Cumulative %99.5 99.6 99.8 100.0

a. Construct a relative frequency histogram and commenton interesting features.

b. What proportion of fire loads are less than 600? At least 1200?

c. What proportion of the loads are between 600 and1200?

The May 1, 2009, issue of the Mont clarian reported the following home sale amounts for a sample of homes in Alameda, CA that were sold the previous month (1000s of $):

590 815 575 608 350 1285 408 540 555 679

1. Calculate and interpret the sample mean and median.
2. Suppose the 6th observation had been 985 rather than 1285. How would the mean and median change?
3. Calculate a 20% trimmed mean by first trimming the two smallest and two largest observations.
4. Calculate a 15% trimmed mean.

Exposure to microbial products, especially endotoxin, may have an impact on vulnerability to allergic diseases. The article 鈥淒ust Sampling Methods for Endotoxin鈥擜n Essential, But Underestimated Issue鈥� (Indoor Air,2006: 20鈥�27) considered various issues associated with determining endotoxin concentration. The following data on concentration (EU/mg) in settled dust for one sample of urban homes and another of farm homes was kindly supplied by the authors of the cited article.

U: 6.0 5.0 11.0 33.0 4.0 5.0 80.0 18.0 35.0 17.0 23.0

F: 4.0 14.0 11.0 9.0 9.0 8.0 4.0 20.0 5.0 8.9 21.0

9.2 3.0 2.0 0.3

1. Determine the sample mean for each sample. How do they compare?
2. Determine the sample median for each sample. How do they compare? Why is the median for the urban sample so different from the mean for that sample?
3. Calculate the trimmed mean for each sample by deleting the smallest and largest observation. What are the corresponding trimming percentages? How do the values of these trimmed means compare to the corresponding means and medians?

Mercury is a persistent and dispersive environmental contaminantfound in many ecosystems around the world.When released as an industrial by-product, it often finds itsway into aquatic systems where it can have deleteriouseffects on various avian and aquatic species. The accompanyingdata on blood mercury concentration (mg/g) for adult

females near contaminated rivers in Virginia was read from a graph in the article 鈥淢ercury Exposure Effects the Reproductive Success of a Free-Living Terrestrial Songbird, the Carolina Wren鈥� (The Auk, 2011: 759鈥�769;this is a publication of the American Ornithologists鈥� Union).

.20 .22 .25 .30 .34 .41 .55 .56

1.42 1.70 1.83 2.20 2.25 3.07 3.25

a. Determine the values of the sample mean and sample median and explain why they are different. (Hint:\(\sum {{{\bf{x}}_{\bf{1}}}{\bf{ = 18}}{\bf{.55}}} \))

b. Determine the value of the 10% trimmed mean and compare to the mean and median.

c. By how much could the observation .20 be increased without impacting the value of the sample median?

A sample of 26 offshore oil workers took part in a simulated escape exercise, resulting in the accompanying data on time (sec) to complete the escape (鈥淥xygen Consumption and Ventilation During Escape from an Offshore Platform,鈥� Ergonomics, 1997: 281鈥�292):

389 356 359 363 375 424 325 394 402

373 373 370 364 366 364 325 339 393

392 369 374 359 356 403 334 397

a. Construct a stem-and-leaf display of the data. How does it suggest that the sample mean and median will compare?

b. Calculate the values of the sample mean and median.(Hint:\(\sum {{x_i} = } \)9638.)

c. By how much could the largest time, currently 424, be increased without affecting the value of the sample median? By how much could this value be decreased without affecting the value of the sample median?

d. What are the values of \(\bar x\)and \(\tilde x\), when the observations are re expressed in minutes?

The article 鈥淪now Cover and Temperature Relationships in North America and Eurasia鈥� (J. Climate and Applied Meteorology, 1983: 460鈥�469) used statistical techniques to relate the amount of snow cover on each continent to average continental temperature. Data presented there included the following ten observations on October snow cover for Eurasia during the years 1970鈥�1979 (in million\({\bf{k}}{{\bf{m}}^{\bf{2}}}\)):

6.5 12.0 14.9 10.0 10.7 7.9 21.9 12.5 14.5 9.2

What would you report as a representative, or typical, value of October snow cover for this period, and what prompted your choice?

Blood pressure values are often reported to the nearest5 mmHg (100, 105, 110, etc.). Suppose the actual bloodpressure values for nine randomly selected individuals are

118.6 127.4 138.4 130.0 113.7 122.0 108.3131.5 133.2

1. What is the median of the reportedblood pressure values?
2. Suppose the blood pressure of the second individual is 127.6 rather than 127.4 (a small change in a single value). How does this affect the median of the reported values? What does this say about the sensitivity of the median to rounding or grouping in the data?