Statistical Reasoning For Everyday Life 4th Edition Jeffrey Bennett - Solutions

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Assuming that a decision rule for a pattern recognition problem is as follows:decide 1 (with cost $10 for a wrong answer) when 0 ≤ x ≤ 1, and decide 0(with cost $5 for a wrong answer) when 1 < x ≤ 2 and the feature space is[0,2], with no cost for a right answer. What is the expression (in
In formulating the pattern recognition problem, we consider only the probability of error as our criterion for success. In some cases, this is not such an appropriate criterion since certain errors may be more costly than others. Describe one such situation, and suggest how one might modify the
If 0 and 1 are the subsets for which a decision rule c decides 0 and 1, respectively, write the expression for the average error rate of c?
Define what is meant by the probability of error of a decision rule. For any particular learning problem, what is the smallest probability of error of a decision rule? Is the best decision rule the one with the smallest probability of error?
(a) As discussed in Chapter 1, a very common choice for object representation is a vector of real numbers. In some cases, the entries of the vector take on a discrete set (i.e., finite number) of values. Describe a situation in which having a discrete set of values is natural. (b) In implementing
If the problem is to classify an email as spam or not spam, what features might you consider?
What are the advantages of choosing/using more features and what are the disadvantages?
What is a decision rule? If there are 10 possible feature vectors, how many possible decision rules are there?
If the probability that Alice hits any given point on the target is the same as the probability that she hits any other given point, does that imply that she is as likely to hit a point within 1 inch of the center as she is to hit a point within a 1-inch circle further away from the center? Explain.
Consider the function defined by p(x) =2 − 2x 0 ≤ x < 1 0 otherwise.(a) Sketch p(x).(b) Is p(x) a valid probability density function? Why or why not?(c) What is the probability that x ≥ 1/2?(d) What is the probability that x = 1/2?(e) For very small , what is the probability that x is within
If p1(x) and p2(x) are two probability density functions, consider the function pλ(x) = λp1(x) + (1 − λ)p2(x).(a) Is it true that pλ(x) is a valid density function for any λ ∈ [0, 1]? Why or why not?(b) What about for λ /∈ [0, 1]? Why or why not?
Given the probability density function f (x), what is the expression for P(a ≤x ≤b) (that is, the probability that x takes a value in the range [a,b])?
True or false: A probability density can take on values less than 0.
True or false: A probability density can take on values greater than 1.
True or False: Depending on the circumstances, the subjective probability of an event can be less than, equal to, or greater than its statistical probability.
True or False: if a fair coin is tossed infinitely many times, each time with a probability of 0.5 for getting heads and 0.5 for getting tails, the probability that heads will come up every time HHHH... is less than the probability that heads and tails will alternate for ever HTHTHT....
True or False: If we toss an unbiased coin (50% heads and 50% tails) 100 times, then by the Law of Large Numbers we will have exactly 50 heads and 50 tails.
Using the suppositions in question 3, suppose also that a ball is randomly drawn and then replaced, then again a ball is randomly drawn and replaced.What is the probability that the same ball is drawn both times? What is the probability that the two balls have the same features (color and shape)?
What is the difference between drawing with replacement and drawing without replacement? Does this difference affect the probabilities in any way? Explain.
Given the same suppositions as in the previous question, suppose also that the balls come in two shapes, round and egg-shaped, where the number of round balls is r and the number of egg-shaped balls is e (where w + b = r + e).What is the probability that a randomly drawn ball will be either white
Suppose that the probability of drawing a white ball from a bowl containing only black and white balls is w/(w + b), where w is the number of white balls and b is the number of black balls. What is the probability of drawing a black ball? What is the probability of drawing either a white ball or a
Why is it true that the number of ways of selecting r items from a set of n items is nCr = n!r!(n−r)!?
True or False: For any events A and B, P(A and B) < P(A)
True or False: For any events A and B, we have P(A or B) = P(A) + P(B).
If the events A and B are independent, what is P(A&B)?
True or False: For any event A, we have P(not A) = 1 − P(A)?
Given an opaque bowl containing six all blue balls, seven all red balls, and nothing else, if a ball is withdrawn at random, what is the probability that the ball is blue?
About the problem of induction (a) What is the problem of induction? (b) How does the reliability of induction compare with the reliability of deduction? (c) How might statistical learning theory say something about the reliability of induction?
Is classification a special case of estimation? What differences are there between typical cases of classification and typical cases of estimation?
For a 12 × 12 grayscale image (256 grayscale levels), how many dimensions are there for the feature vector? How many different possible feature vectors are there?
If we want to use the values of F different features, in order to classify objects, where each feature can have any of G different values, what is the dimension of the feature space?
What is a feature space? What do the dimensions of such a space represent?What is a vector? What is a feature vector?
Investigate recent developments in the debate over GM foods. Does the new information alter any of the major arguments in the debate? Explain.
Some people advocate giving the choice about GM foods to consumers by requiring labeling on all products that contain genetically modified ingredients. Do you think this is a good idea? Why or why not?
Ignoring any safety issues of GM foods, make a list of as many ways as you can think of in which GM foods might be beneficial to humanity. Then, ignoring any benefits of GM foods, make a list of as many ways as you can think of in which GM foods might be dangerous. Overall, do you think that
Propose an experiment that could be used to test the safety of a GM food product, such as corn. Describe your experiment in detail, and discuss any practical difficulties that might be involved in carrying it out or interpreting its results.
Can the GM crops cause any unforeseen environmental damage, such as transferring their genes into weeds (thereby making “superweeds”) or killing animals besides the insect pests?
Do the new proteins contained in GM foods cause allergic reactions in some people?
Do GM foods have any toxic effects in humans?
Education correlates with healthier lives as well as longer lives, which means that more educated people tend to have lower health care costs. Can you think of any ways in which this fact could be used to help get health care costs under control? Discuss with friends or classmates.
Smoking is well known to be one of the biggest risk factors in disease and early death. As a result, the government and health care groups have often undertaken expensive advertising campaigns in hopes of convincing people to stop smoking (or never start). But the smoking rate drops dramatically
Why do you think education contributes to longer life?For example, do you think the mere fact of staying in school makes people live longer, or is it the extra learning associated with more years of schooling that makes the difference? How would you test your hypothesis?
Figure 10 presents a wealth of data. Interpret it carefully.How does it support the hypothesis that more education leads to longer life? Explain.
If you incorrectly conclude that professional comedians have a mean IQ score greater than 110 when their actual mean IQ score is 100, have you made a type I error or a type II error?assume that we want to use a 0.05 significance level to test the claim that the mean IQ score of professional
What are the two possible conclusions that can be reached about the claim being tested?assume that we want to use a 0.05 significance level to test the claim that the mean IQ score of professional comedians is greater than 110.
What are the two possible conclusions that can be reached about the null hypothesis?assume that we want to use a 0.05 significance level to test the claim that the mean IQ score of professional comedians is greater than 110.
If the test results in a P-value of 0.007, what do you conclude about the given claim?assume that we want to use a 0.05 significance level to test the claim that the mean IQ score of professional comedians is greater than 110.
What is the alternative hypothesis?assume that we want to use a 0.05 significance level to test the claim that the mean IQ score of professional comedians is greater than 110.
What is the null hypothesis?assume that we want to use a 0.05 significance level to test the claim that the mean IQ score of professional comedians is greater than 110.
What is the alternative hypothesis that results from the claim that the proportion of convicted felons who serve time in prison is equal to 0.6?
What is the null hypothesis that is used for testing the claim that the proportion of college graduates who voted in the last election is greater than 0.5?
What is the alternative hypothesis that results from the claim that the mean brain volume of adults is larger than 1,126 cm3?
Finding a job Through networking. In a survey of 703 randomly selected workers, 429 got their jobs through networking (based on data from Taylor Nelson Sofres Research).a. Use the sample data with a 0.05 significance level to test the claim that most (more than 50% of) workers get their jobs
In a study of smokers who tried to quit smoking with nicotine patch therapy, 39 were smoking one year after the treatment, and 32 were not smoking one year after the treatment (based on data from “High Dose Nicotine Patch Therapy,” by Dale et al., Journal of the American Medical Association,
Randomly selected cans of Coke are measured for the amount of cola, in ounces. The sample values listed below have a mean of 12.19 ounces and a standard deviation of 0.11 ounce. Assume that we want to use a 0.05 significance level to test the claim that cans of Coke have a mean amount of cola
Hypothesis Testing in the news. Find a news article or research report that describes (perhaps not explicitly) a hypothesis test for a population proportion.Attach the article and summarize the method used.
county data. The Statistical Abstract of the United States and the Current Population Survey provide an extensive supply of social, economic, and vital statistics at the county, state, and local levels. Use their Web sites to compare state data to national data in the following way.a. Choose a
Women college students. Use the Internet or library references to find the proportion of college students in the United States who are women. Test the claim that the proportion of women students at your college is different from the proportion of all U.S. college students. Collect sample data from
smoking. Use the Internet or library references to determine the proportion of Americans who smoke. Test the claim that the proportion of students at your college who smoke is different from the proportion of all Americans.Collect sample data from at least 50 randomly selected students.
left-Handedness. Given the claim that 10% of Americans are left-handed, randomly select at least 50 students at your college and determine whether they are left-handed. Test the claim with a formal hypothesis test.
clinical Test. In clinical tests of the drug Lipitor, 863 patients were treated with the drug and 19 of them experienced flu symptoms (based on data from Parke-Davis).Test the claim that the percentage of treated patients with flu symptoms is greater than the 1.9% rate for patients not given
natural gas use. According to the Energy Information Administration, 53.0% of households nationwide used natural gas for heating in 1997. A recent survey of 3,600 randomly selected households showed that 54.0% used natural gas. Use a 0.05 significance level to test the claim that the 53.0% national
internet use. When 3011 adults were surveyed in a Pew Research Center poll, 2198 said that they use the Internet.Is it OK for a newspaper reporter to write that “3/4 of all adults use the Internet”? Why or why not?use a 0.05 significance level to conduct a hypothesis test using the four-step
Abortion survey. An annual survey of first-year college students, conducted by the Higher Education Research Institute at UCLA, asks approximately 276,000 students about their attitudes on a variety of subjects. According to a recent survey, 51% of first-year students believe that abortion should
Poverty. According to recent estimates, 12.1% of the 4,342 people in Custer County, Idaho, live in poverty. Assume that the people in this county represent a random sample of all people in Idaho. Based on this sample, test the claim that the poverty rate in Idaho is less than the national rate of
drug use. A Department of Health and Human Services study of illegal drug use among 12- to 17-year-olds reported a decrease in use (from 11.4% in 1997) to 9.9%now. Suppose a survey in a large high school reveals that, in a random sample of 1,050 students, 98 report using illegal drugs. Test the
Married Adults. In a recent year, 125.8 million adults, or 58.6% of the adult American population, were married. In a New England town, a simple random sample of 1,445 adults includes 56.0% who are married. Test the claim that this sample comes from a population with a married percentage of less
grade Pressure. A study commissioned by the U.S. Department of Education, based on responses from 1,015 randomly selected teenagers, concluded that 44% of teenagers cite grades as their greatest source of pressure.Test the claim that fewer than half of all teenagers in the population feel that
smoking and college Education. A survey showed that among 785 randomly selected subjects who completed four years of college, 144 smoke and the others do not smoke (based on data from the American Medical Association). Test the claim that the rate of smoking among those with four years of college
Voter Poll. In a pre-election poll, a candidate for district attorney receives 205 of 400 votes. Assuming that the people polled represent a random sample of the voting population, test the claim that a majority of voters support the candidate.use a 0.05 significance level to conduct a hypothesis
Alternative Hypothesis. The claim of p 6 0.25 can never be supported if the sample proportion pn is greater than 0.25.decide whether the statement makes sense (or is clearly true) or does not make sense (or is clearly false). Explain clearly. Not all of these statements have definitive answers, so
Alternative Hypothesis. In a two-tailed hypothesis test of a claim about a proportion, the P-value is the area to the right of the standard score, z.
null and Alternative Hypotheses. In a hypothesis test involving a claim made about a population proportion, if there is sufficient evidence to reject the null hypothesis, then there is sufficient evidence to support the alternative hypothesis.decide whether the statement makes sense (or is clearly
null Hypothesis. In a test of the claim that a majority of Americans favor registration of all handguns, the null hypothesis is p = 0.5 and the alternative hypothesis is p 7 0.5.decide whether the statement makes sense (or is clearly true) or does not make sense (or is clearly false). Explain
P-Value. A P-value of 0.00001 is obtained when sample data are used to test the claim that the majority of car crashes occur within 5 miles of home. What does this Pvalue tell us?
scream. A survey of 61,647 people included several questions about office relationships. Of the respondents, 26%reported that bosses scream at employees. The survey is an Elle/MSNBC.COM survey in which Internet users chose whether to respond. Is it valid to use the sample results for testing the
distribution. In conducting a hypothesis test as described in this section, which term best describes the particular distribution that is used: uniform, normal, probability, weighted?
notation. What do p, pn, and P-value represent?
Power of a Test. Using a search engine such as Google, search for “power” of a hypothesis test. Describe what the power of a hypothesis test is.
Hypothesis Test Applet. Using a search engine such as Google, search for “hypothesis testing” and “applet.” Find an applet and run it. Describe how the applet works and what it illustrates.
county data. The Statistical Abstract of the United States and the Current Population Survey provide an extensive supply of social, economic, and vital statistics at the county, state, and local levels. Use their Web sites to compare state data to national data in the following way.a. Choose a
comparisons with national Averages. Choose several variables that are relatively easy to measure in a class or sample of students. The variables should involve a quantity that can be averaged (for example, height, weight, family size, blood pressure, heart rate, reaction time). Use the Internet or
H0: The mean length of a bolt in the suspension system of new Audi cars is 3.456 centimeters.Ha: The mean length of a bolt in the suspension system of new Audi cars is not equal to 3.456 centimeters.a null and alternative hypothesis are given. Without using the terms “null hypothesis” and
H0: The lottery is fair.Ha: The lottery is biased.a null and alternative hypothesis are given. Without using the terms “null hypothesis” and “alternative hypothesis,” identify the type I error and identify the type II error.
H0: The defendant is not guilty.Ha: The defendant is guilty.a null and alternative hypothesis are given. Without using the terms “null hypothesis” and “alternative hypothesis,” identify the type I error and identify the type II error.
H0: The patient is free of a particular disease.Ha: The patient has the disease.a null and alternative hypothesis are given. Without using the terms “null hypothesis” and “alternative hypothesis,” identify the type I error and identify the type II error.
ncAA Football coach salaries. A simple random sample of 40 salaries of NCAA football coaches in the NCAA has a mean of $415,953. The standard deviation of all salaries of NCAA football coaches is $463,364. Test the claim that the mean salary of a football coach in the NCAA is less than $500,000.
convicted Embezzlers. When 70 convicted embezzlers were randomly selected, the mean length of prison terms was found to be 22.1 months and the standard deviation was 8.6 months (based on data from the U.S. Department of Justice). Jane Fleming is running for political office on a platform of tougher
Weights of Bears. The health of the bear population in Yellowstone National Park is monitored by periodic measurements taken from anesthetized bears. A sample of 54 bears has a mean weight of 182.9 lb. Assuming that s is known to be 121.8 lb, test the claim that the population mean of all such bear
Birth Weight. The mean birth weight of male babies born to 121 mothers taking a vitamin supplement is 3.67 kilograms with a standard deviation of 0.66 kilogram (based on data from the New York State Department of Health). Test the claim that the mean birth weight of all babies born to mothers
coin Weight. According to the U.S. Department of the Treasury, the mean weight of a quarter is 5.670 grams.A random sample of 50 quarters has a mean weight of 5.622 grams with a standard deviation of 0.068 gram. Test the claim that the mean weight of quarters in circulation is 5.670 grams.
compulsive Buyers. Researchers developed a questionnaire to identify compulsive buyers. A random sample of 32 subjects who identified themselves as compulsive buyers was obtained, and they had a mean questionnaire score of 0.83 with a standard deviation of 0.24 (based on data from “A Clinical
Baseballs. A random sample of 40 new baseballs is obtained. Each ball is dropped onto a concrete surface, and the bounce heights have a mean of 92.67 inches and a standard deviation of 1.79 inches (based on data from USA Today). Test the claim that the new baseballs have a mean bounce height that
Fuel consumption. According to the Energy Information Administration (Federal Highway Administration data), the average gas mileage of all automobiles is 21.4 miles per gallon. For a random sample of 40 sport utility vehicles(SUVs), the mean gas mileage is 19.8 miles per gallon with a standard
red Blood cell count. A simple random sample of 50 adults is obtained, and each person’s red blood cell count (in cells per microliter) is measured. The sample mean is 5.23. The population standard deviation for red blood cell counts is 0.54. Test the claim that the sample is from a population
drug Amounts. The cold medicine Dozenol lists 600 milligrams of acetominophen per fluid ounce as an active ingredient. The Food and Drug Administration tests 65 oneounce samples of the medicine and finds that the mean amount of acetominophen for the sample is 589 milligrams with a standard
Motorcycle Manufacturing. The manufacturers of motorcycles must produce axles that meet specified dimensions.In particular, the diameters of the axles must be 8.50 centimeters. The axles in a sample of n = 64 axles have a mean diameter of 8.56 centimeters with a standard deviation of 0.24
cola. A random sample of 36 cans of regular Coke is obtained and the contents are measured. The sample mean is 12.19 oz and the standard deviation is 0.11 oz. Test the claim that the contents of all such cans have a mean different from 12.00 oz, as indicated by the label.
Hospital Time. According to a study by the Centers for Disease Control, the national mean hospital stay after childbirth is 2.0 days. Reviewing records at her own hospital, a hospital administrator calculates that the mean hospital stay for a sample of 81 women after childbirth is 2.2 days with a
roper Poll. A Roper poll used a sample of 100 randomly selected car owners. Within the sample, the mean time of ownership for a single car was 7.01 years with a standard deviation of 3.74 years. Test the claim by the owner of a large dealership that the mean time of ownership for all cars is less

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Statistical Reasoning For Everyday Life 4th Edition Jeffrey Bennett - Solutions

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