Statistics For Experimenters Design Innovation And Discovery 2nd Edition George E. P. Box, J. Stuart Hunter, William G. Hunter - Solutions

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Do the same for figure 9. P-698
Do the same for figure 8. P-698
Figure 7 below shows a shaded region. Which of the following two points is in the region: (1, 2) or (2, 1)? P-698
The table below shows four points. In each case, the y-coordinate is computed from the x-coordinate by the rule $$y = 2x + 1$$. Fill in the blanks, then plot the four points. What can you say about them? P-698 x | y------- | --------1 | 3 2 | 5 3 |4 |
Three out of the following four points lie on a line. Which is the maverick? Is it above or below the line? P-698(0,0)(0.5, 0.5)(1,2) (2.5, 2.5)
Draw a pair of axes and plot each of the following points: P-698(1,1)(2, 2) (3, 3)(4,4)What can you say about them?
One point in figure 3 has a y-coordinate 1 bigger than the y-coordinate of point E. Which point is that? P-698
As you move from point A to point B in figure 3, your x-coordinate goes up by ; your y-coordinate goes up by P-698
Figure 3 shows five points. Write down the x-coordinate and y-coordinate for each point. P-698
This part of the book introduced two basic descriptive statistics, the av-erage and the standard deviation; histograms were used to summarize data. For many data sets, the histogram follows the normal curve. Chapter 6 illustrates these ideas on measurement data. Later in the book, histograms will
The average and SD can be strongly influenced by outliers. Then the his-togram will not follow the normal curve at all well. P-698
Even in careful measurement work, a small percentage of outliers can be expected. P-698
Bias, or systematic error, causes measurements to be systematically too high or systematically too low. The equation is individual measurement = exact value + bias + chance error.The chance error changes from measurement to measurement, but the bias stays the same. Bias cannot be estimated just by
The likely size of the chance error in a single measurement can be esti-mated by the SD of a sequence of repeated measurements made under the same conditions. P-698
No matter how carefully it was made, a measurement could have turned out a bit differently. This reflects chance error. Before investigators rely on a measurement, they should estimate the likely size of the chance error. The best way to do that: replicate the measurement. P-698
In some jurisdictions, there are "pretrial conferences," where the judge con-fers with the opposing lawyers to settle the case or at least to define the issues before trial. Observational data suggest that pretrial conferences promote set-tlements and speed up trials, but there were doubts.In New
Breast cancer is one of the most common malignancies among women in Canada and the U.S. If it is detected early enough-before the cancer spreads-chances of successful treatment are much better. Do screening programs speed up detection by enough to matter? Many studies have examined this
To measure the effect of exercise on the risk of heart disease, investigators compared the incidence of this disease for two large groups of London Transport Authority busmen-drivers and conductors. The conductors got a lot more exercise as they walked around all day collecting fares.The age
In March, the Current Population Survey asks a large, representative sample of Americans to say what their incomes were during the previous year. A histogram for family income in 2004 is shown at the top of the next page.(Class intervals include the left endpoint but not the right.) From $15,000
For a certain group of women, the 25th percentile of height is 62.2 inches and the 75th percentile is 65.8 inches. The histogram follows the normal curve.Find the 90th percentile of the height distribution. P-698
A large, representative sample of Americans was studied by the Public Health Service, in the Health and Nutrition Examination Survey (HANES2). The percentage of respondents who were left-handed decreased steadily with age, from 10% at 20 years to 4% at 70. "The data show that many people change
A teaching assistant gives a quiz to his section. There are 10 questions on the quiz and no part credit is given. After grading the papers, the TA writes down for each student the number of questions the student got right and the number wrong. The average number of right answers is 6.4 with an SD
Table 1 on p. 99 reported 100 measurements on the weight of NB 10; the top panel in figure 2 on p. 102 shows the histogram. The average was 405 micro-grams, and the SD was 6 micrograms. If you used the normal approximation to estimate how many of these measurements were in the range 400 to 406
Repeat exercise 6, when there are 600 men in the class, and 400 women. (The separate averages and SDs for the men and women stay the same.) P-698
Among entering students at a certain college, the men averaged 650 on the Math SAT, and their SD was 125. The women averaged 600, but had the same SD of 125. There were 500 men in the class, and 500 women.(a) For the men and the women together, the average Math SAT score was(b) For the men and the
In Cycle III of the Health Examination Survey (like HANES, but done in 1966-70), there were 6,672 subjects. The sex of each subject was recorded at two different stages of the survey. In 17 cases, there was a discrepancy:the subject was recorded as male at one interview, female at the other. How
Among first-year students at a certain university, scores on the Verbal SAT follow the normal curve; the average is around 550 and the SD is about 100.(a) What percentage of these students have scores in the range 400 to 700? P-698
A personality test is administered to a large group of subjects. Five scores are shown below, in original units and in standard units. Fill in the blanks.79 64 52 72 1.8 0.8 ______ ______-1.4 P-698
Fill in the blanks, using the options below, and give examples to show that you picked the right answers.(a) The SD of a list is 0. This means __________.(b) The r.m.s. size of a list is 0. This means __________.Options:(i) there are no numbers on the list(ii) all the numbers on the list are the
In one course, a histogram for the scores on the final looked like the sketch below. True or false: because this isn't like the normal curve, there must have been something wrong with the test. Explain. P-6980 25 50 75 100
Nineteen students in a beginning statistics course were asked to measure the thickness of a table top, using a vernier gauge reading to 0.001 of an inch.Each person made two measurements, shown at the top of the next page. (The units are inches; for instance, the first person got 1.317 and 1.320
You send a yardstick to a local laboratory for calibration, asking that the pro-cedure be repeated three times. They report the following values: P-698 35.96 inches 36.01 inches 36.03 inches If you send the yardstick back for a fourth calibration, you would expect to get 36 inches give or take-.01
True or false, and explain.(a) Bias is a kind of chance error.(b) Chance error is a kind of bias.(c) Measurements are usually affected by both bias and chance error. P-698
A carpenter is using a tape measure to get the length of a board.(a) What are some possible sources of bias?(b) Which is more subject to bias, a steel tape or a cloth tape?(c) Would the bias in a cloth tape change over time? P-698
True or false, and explain: "An experienced scientist who is using the best equipment available only needs to measure things once-provided he doesn't make a mistake. After all, if he measures the same thing twice, he'll get the same results both times." P-698
In the U.S. in 2000, there were 2.4 million deaths from all causes, compared to 1.9 million in 1970-a 25% increase. 10 True or false, and explain: the data show that the public's health got worse over the period 1970-2000. plo47
Data from the Salk vaccine field trial suggest that in 1954, the school districts in the NFIP trial and in the randomized controlled experiment had similar exposures to the polio virus. (a) The data also show that children in the two vaccine groups (for the ran- domized controlled experiment and
Polio is an infectious disease; for example, it seemed to spread when children went swimming together. The NFIP study was not done blind: could that bias the results? Discuss briefly. plo47
The Salk vaccine field trials were conducted only in certain experimental areas (school districts), selected by the Public Health Service in consultation with local officials. In these areas, there were about 3 million children in grades 1, 2, or 3; and there were about 11 million children in those
Linus Pauling thought that vitamin C prevents colds, and cures them too. Thomas Chalmers and associates did a randomized controlled double-blind experiment to find out. 12 The subjects were 311 volunteers at the National Institutes of Health. These subjects were assigned at random to 1 of 4 groups:
(Hypothetical.) One of the other drugs in the Coronary Drug Project (section 2) was nicotinic acid.13 Suppose the results on nicotinic acid were as reported below. Something looks wrong. What, and why? Nicotinic acid Placebo Number Deaths Number Deaths Adherers 558 13% 1,813 15% Non-adherers 487
(Hypothetical.) In a clinical trial, data collection usually starts at "baseline," when the subjects are recruited into the trial but before they are assigned to treatment or control. Data collection continues until the end of followup. Two clinical trials on prevention of heart attacks report
Some studies find an association between liver cancer and smoking. However, alcohol consumption is a confounding variable. This means- (i) Alcohol causes liver cancer. (ii) Drinking is associated with smoking, and alcohol causes liver cancer. Choose one option, and explain briefly. plo47
Breast cancer is one of the most common malignancies among women in the U.S. If it is detected early enough-before the cancer spreads-chances of successful treatment are much better. Do screening programs speed up detection by enough to matter? The first large-scale trial was run by the Health
(This continues exercise 9.)(a) To show that screening reduces the risk from breast cancer, someone wants to compare 1.1 and 1.5. Is this a good comparison? Is it biased against screening? For screening?(b) Someone claims that encouraging women to come in for breast cancer screening increases their
Cervical cancer is more common among women who have been exposed to the herpes virus, according to many observational studies. 15 Is it fair to conclude that the virus causes cervical cancer?plo47
Physical exercise is considered to increase the risk of spontaneous abortion. Fur-thermore, women who have had a spontaneous abortion are more likely to have another. One observational study finds that women who exercise regularly have fewer spontaneous abortions than other women. 16 Can you
A hypothetical university has two departments, A and B. There are 2,000 male applicants, of whom half apply to each department. There are 1,100 female ap-plicants: 100 apply to department A and 1,000 to department B. Department A admits 60% of the men who apply and 60% of the women. Department B
Say whether each of the following is about 1%, 10%, 25%, or 50%-(a) 39 out of 398(c) 57 out of 209(b) 99 out of 407(d) 99 out of 197plo47
Among beginning statistics students in one university, 46 students out of 446 reported family incomes ranging from $40,000 to $50,000 a year.(a) About what percentage had family incomes in the range $40,000 to$50,000 a year?(b) Guess the percentage that had family incomes in the range $45,000
The Federal Bureau of Investigation reports state-level and national data on crimes. 17(a) An investigator compares the incidence of crime in Minnesota and in Michigan. In 2001, there were 3,584 crimes in Minnesota, compared to 4,082 in Michigan. He concludes that Minnesotans are more law-abiding.
The National Highway and Traffic Safety Administration analyzed thefts of new cars in 2002, as well as sales figures for that year. 18(a) There were 99 Corvettes stolen, and 26 Infiniti Q45 sedans. Should you conclude that American thieves prefer American cars? Or is something missing from the
From table 1 in chapter 1 (p. 6), those children whose parents refused to participate in the randomized controlled Salk trial got polio at the rate of 46 per 100,000. On the other hand, those children whose parents consented to participation got polio at the slightly higher rate of 49 per 100,000
The Public Health Service studied the effects of smoking on health, in a large sample of representative households. 19 For men and for women in each age group, those who had never smoked were on average somewhat healthier than the current smokers, but the current smokers were on average much
There is a rare neurological disease (idiopathic hypoguesia) that makes food taste bad. It is sometimes treated with zinc sulfate. One group of investigators did two randomized controlled experiments to test this treatment. In the first trial, the subjects did not know whether they were being given
(Continues the previous exercise.) The second trial used what is called a"crossover" design. The subjects were assigned at random to one of four groups: plo47
According to a study done at Kaiser Permanente in Walnut Creek, California, users of oral contraceptives have a higher rate of cervical cancer than non-users, even after adjusting for age, education, and marital status. Investigators concluded that the pill causes cervical cancer. 21(a) Is this a
Ads for ADT Security Systems claim 22 When you go on vacation, burglars go to work.... According to FBI statistics, over 25% of home burglaries occur between Memorial Day and Labor Day.Do the statistics prove that burglars go to work when other people go on vacation? Answer yes or no, and explain
People who get lots of vitamins by eating five or more servings of fresh fruit and vegetables each day (especially "cruciferous" vegetables like broccoli)have much lower death rates from colon cancer and lung cancer, according to many observational studies. These studies were so encouraging that
A study of young children found that those with more body fat tended to have more "controlling" mothers; the San Francisco Chronicle concluded that "Parents of Fat Kids Should Lighten Up."24(a) Was this an observational study or a randomized controlled experi-ment?(b) Did the study find an
California is evaluating a new program to rehabilitate prisoners before their release; the object is to reduce the recidivism rate—the percentage who will be back in prison within two years of release. The program involves sev-eral months of "boot camp"—military-style basic training with very
(Hypothetical.) A study is carried out to determine the effect of party affili-ation on voting behavior in a certain city. The city is divided up into wards.In each ward, the percentage of registered Democrats who vote is higher than the percentage of registered Republicans who vote. True or false:
9. What are statistical dependence, randomness, correlation, covariance, auto- correlation, random sampling, and a sampling distribution?
6. Which techniques in this book do you expect to be most useful to you?
5. Can you give examples (if possible from your own field) of real confusion (perhaps controversy) that has arisen because of one or more of these diffi- culties?
4. What are three common difficulties encountered in experimental investiga- tions?
3. What is achieved by good statistical analysis? By good statistical design? Which do you believe is more important?
2. In what ways can statistics be useful to experimenters?
1. What is meant by the iterative nature of learning?
7. How should you use the techniques in this book?
8. Can you think of an experimental investigation that (a) was and (b) was not iterative?
8. When must at distribution be used instead of a normal distribution?
7. What is meant by the IID assumption and the NIID assumption?
6. What two parameters characterize the normal distribution?
5. What does a normal distribution look like and why is it important?
4. What is the central limit effect and why is it important?
3. Distinguish between a standard deviation and a standard error.
2. What is meant by a population of observations, a sample of observations, a random drawing from the population, and a random sample of observations? Define population mean, population variance, sample average, and sample variance.
1. What are a dot diagram, a histogram, and a probability distribution?
9. Read accounts of the development of a particular field of science over a period of time (e.g., read the books The Double Helix by J. D. Watson and The Bishops Boys (the Wright brothers) by T. D. Crouch, 1989). How do these developments relate to the discussion in this chapter of a scientific
10. What are the properties of the sampling distribution for the average y from a nonnormal distribution? Discuss and state your assumptions?
5. If a random variable has a normal distribution with mean 80 and standard deviation 20, what is the probability that it assumes the following values? (a) Less than 77.4(b) Between 61.4 and 72.9 (c) Greater than 90.0 (d) Less than 67.6 or greater than 88.8 (e) Between 92.1 and 95.4 (f) Between
4. (a) The following are results of fuel economy tests (miles per gallon) obtained from a sample of 50 automobiles in 1975:Plot the histogram of these data and calculate the sample average and sample standard deviation. (b) The following 50 results were obtained in 1985:Plot the histogram of these
3. Four ball bearings were taken randomly from a production line and their diameters measured. The results (in centimeters) were as follows: 1.0250, 1.0252, 1.0249, 1.0249. Calculate the average, sample variance, and sample standard deviation.
2. The following are recorded shear strengths of spot welds (in pounds): 12,560, 12,900, 12,850, 12,710. Calculate the average, sample variance, and sample standard deviation.
1. Given the following observations: 5, 4, 8, 6, 7, 8. Calculate (a) the sample average, (b) the sample variance, and (c) the sample standard deviation.
15. What is meant by the natural variance and natural standard deviation of a sample of observations?
14. Two instruments used to measure a certain phenomenon give separate res- ponses y and y2 with variances 21 and o22. What are two ways to determine whether these instrumental responses are correlated? Answer: (a) Estimate p from repeated pairs of y and y2 and (b) use the sums and difference of
13. Consider the second difference Y = y; - 2y;-1 + yi-2. What is the variance of Y if successive observations y;, i = 1, 2,..., n, all have the same variance and are (a) independent and (b) autocorrelated with p = 0.2?
12. What are the formulas for the expectation and variance for the sum and for the differences of two random variables? How might these formulas be used to check for lag1 autocorrelation.
6. Suppose the daily mill yields at a certain plant are normally distributed with a mean of 10 tons and a standard deviation of 1 ton. What is the prob- ability that tomorrow the value will be greater than 9.5? To obtain your answer, assume that the observations behave as statistically independent
7. Four samples are taken and averaged every hour from a production line and the hourly measurement of a particular impurity is recorded. Approximately one out of six of these averages exceeds 1.5% when the mean value is approximately 1.4%. State assumptions that would enable you to determine the
15. Check the approximate answer given for problem 14 by actually evaluating the Poisson frequencies.
14. The level of radiation in the control room of a nuclear reactor is to be automatically monitored by a Geiger counter. The monitoring device works as follows: Every tenth minute the number (frequency) of "clicks" occurring in seconds is counted automatically. A scheme is required such that if
13. On each die in a set of six dice the pips on each face are diamonds. It is suggested that the weight of the stones will cause the "five" or "six" faces to fall downward, and hence the "one" and "two" faces to fall upward, more frequently than they would with fair dice. To test this conjecture,
12. After examination of some thousands of observations a Six Sigma Black Belt quality engineer determined that the observed thrusts for a certain aircraft engine were approximately normally distributed with mean 1000 pounds and standard deviation 10 pounds. What percentage of such measured thrusts
11. The mean weight of items coming from a production line is 83 pounds. On the average, 19 out of 20 of these individual weights are between 81 and 85 pounds. The average weights of six randomly selected items are plotted. What proportion of these points will fall between the limits 82 and 84
10. The lengths of bolts produced in a factory may be taken to be normally distributed. The bolts are checked on two "go-no go" gauges and those shorter than 2.9 or longer than 3.1 inches are rejected. (a) A random sample of 397 bolts are checked on the gauges. If the (true but unknown) mean length
9. For each sample of 16 boxes of cereal an average box weight is recorded. Past records indicate that 1 out of 40 of these averages is less than 8.1 ounces. What is the probability that an individual box of cereal selected at random will weigh less than 8.0 ounces? State any assumptions you make.
8. Suppose that 95% of the bags of a certain fertilizer mix weigh between 49 and 53 pounds. Averages of three successive bags were plotted, and 47.5% of these were observed to lie between 51 and X pounds. Estimate the value of X. State the assumptions you make and say whether these assumptions are

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Statistics For Experimenters Design Innovation And Discovery 2nd Edition George E. P. Box, J. Stuart Hunter, William G. Hunter - Solutions

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