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logic functions and equations
A Concise Introduction To Logic 11th Edition Patrick J. Hurley - Solutions
17. Th e visual impression made by graphs can be exaggerated by changing one of the scales while leaving the other unchanged. True or False.
★16. Data refl ecting the size of full-grown horses would exhibit greater dispersion than would data refl ecting the size of full-grown dogs. True or False.
15. Statements about averages oft en present an incomplete picture, lacking information about the dispersion. True or False.
14. Range, variance, and standard deviation are measurements of dispersion. True or False.
★13. If a set of data conform to the normal probability distribution, then the mean, median, and mode have the same value. True or False.
12. Data refl ecting the results of a random sample conform fairly closely to the normal probability distribution. True or False.
11. If one needed to know whether a sizable portion of a group were above or below a certain level, the most useful sense of average would be mode. True or False.
★10. Th e modal value of a set of data is the arithmetical average. True or False.
9. Th e median value of a set of data is the middle point when the data are arranged in ascending order. True or False.
8. The mean value of a set of data is the value that occurs with the greatest frequency. True or False.
★7. Th e personal interaction between a surveyor and a respondent can aff ect the outcome of a survey. True or False.
6. When a sample consists of human beings, the purpose for which the sample is taken can aff ect the outcome. True or False.
5. In general, if sample A is twice as large as sample B, then the sampling error for A is one-half that for B. True or False.
★4. To ensure the same precision, a population of 1 million would require a much larger random sample than would a population of 100,000. True or False.
3. If a sample is randomly selected, the larger the sample is, the more closely it replicates the population. True or False.
2. If a population is randomly arranged, a sample obtained by selecting every tenth member would be a random sample. True or False.
1. If a sample is very large, it need not be randomly selected. True or False.
6. An instructor gave a ten-question multiple-choice quiz to twelve students.Th e scores were 10, 10, 9, 9, 8, 8, 8, 7, 7, 7, 7, 6. What is the mean score? What is the variance and standard deviation of these scores?
5. A small company has fi ve employees who missed work during a certain month.Th e number of days missed were 1, 1, 2, 4, 7. What is the mean number of days missed? What is the variance and standard deviation of this set of data?
★4. A day-care center cares for ten children. Th eir ages are 1, 1, 2, 2, 2, 3, 3, 4, 6, 6.Construct a histogram that represents the distribution of ages. What is the mean age? What is the variance and standard deviation of these ages?
3. Given the following group of people together with their salaries, what is the average salary in the sense of mean, median, and mode?Number of people Salary 1 $95,000 2 85,000 1 70,000 3 40,000 1 30,000 2 20,000 5 15,000
2. Given the following group of people together with their weights, what is the average weight in the sense of mean, median, and mode?Number of people Weight 2 150 4 160 3 170 1 180 1 190 1 200 1 220 2 230
What fi gures should be written in the left -hand column of Table 12.1 to produce a similar table based on a confi dence level of 99 percent? For a confi dence level of 99 percent, the margin of error is approximately equal to 1.29/√n.
20. Criticize the following arguments in light of the material presented in this section: An effi ciency expert was hired to increase the productivity of a manufacturing fi rm and was given three months to accomplish the task. At the end of the period the productivity had increased from 1,500 units
★19. Criticize the following arguments in light of the material presented in this section: Th ere were 20 percent more traffi c accidents in 2005 than there were in 1980.Th erefore, it was 20 percent more dangerous to drive a car in 2005 than it was in 1980.
18. Criticize the following arguments in light of the material presented in this section: During a certain year, a grocery store chain had total sales of $100 million and profi ts of $10 million. Th e profi ts thus amounted to a modest 10 percent for that year.
17. Criticize the following arguments in light of the material presented in this section: Forced to make cutbacks, the president of a manufacturing fi rm reduced certain costs as follows: advertising by 4 percent, transportation by 5 percent, materials by 2 percent, and employee benefi ts by 3
★16. Criticize the following arguments in light of the material presented in this section: A corporation’s sales for two consecutive years are represented in a bar graph.Since the bar for the later year is twice as high as the one for the previous year, it follows that sales for the later year
15. Criticize the following arguments in light of the material presented in this section: An insecticide manufacturer prints the following graph on the side of its spray cans:Obviously, the insecticide is highly eff ective at killing bugs, and it keeps working for a long time. Number of bugs killed
14. Criticize the following arguments in light of the material presented in this section: Th e average IQ (in the sense of mean, median, and mode) of the students in Dr. Jacob’s symbolic logic class is 120. Th us, none of the students should have any trouble mastering the subject matter.
★13. Criticize the following arguments in light of the material presented in this section: Tim Cassidy, who works for a construction company, is told to load a pile of rocks onto a truck. Th e rocks are randomly sized, and the average piece weighs 50 pounds. Th us, Tim should have no trouble
12. Criticize the following arguments in light of the material presented in this section: Pamela intends to go shopping for a new pair of shoes. She wears size 8. Since the average size of the shoes carried by the Bon Marche is size 8, Pamela can expect to fi nd an excellent selection of shoes in
11. Criticize the following arguments in light of the material presented in this section: Anthony Valardi, who owns a fi sh market, pays $2 per pound to fi shermen for silver salmon. A certain fi sherman certifi es that the average size of the salmon in his catch of the day is 10 pounds, and that
★10. Criticize the following arguments in light of the material presented in this section: Janet Ryan can aff ord to pay no more than $15 for a birthday gift for her eightyear-old daughter. Since the average price of a toy at General Toy Company is $15, Janet can expect to fi nd an excellent
9. Criticize the following arguments in light of the material presented in this section: To determine the percentage of patients who follow the advice of their personal physician, researchers asked 200 randomly chosen physicians to put the question to their patients. Of the 4,000 patients surveyed,
8. Criticize the following arguments in light of the material presented in this section: To determine the percentage of adult Americans who have never read the U.S.Constitution, surveyors put this question to a random sample of 1,500 adults.Only 13 percent gave negative answers. Th erefore, since
★7. Criticize the following arguments in light of the material presented in this section: In a survey conducted by the manufacturers of Ultrasheen toothpaste, 65 percent of the dentists randomly sampled preferred that brand over all others.Clearly Ultrasheen is the brand preferred by most
6. Criticize the following arguments in light of the material presented in this section: To predict the results of a U.S. Senate race in New York State, two polls were taken. One was based on a random sample of 750 voters, the other on a random sample of 1,500 voters. Since the second sample was
5. Criticize the following arguments in light of the material presented in this section: To determine the public’s attitude toward TV soap operas, 1,000 people were contacted by telephone between 8:00 a.m. and 5:00 p.m. on weekdays. Th e numbers were selected randomly from the phone directories
★4. Criticize the following arguments in light of the material presented in this section: When a random sample of 600 voters was taken on the eve of the presidential election, it was found that 51 percent of those sampled intended to vote for the Democrat and 49 percent for the Republican. Th
3. Criticize the following arguments in light of the material presented in this section: A quality-control inspector for a food-processing fi rm needed assurance that the cans of fruit in a production run were fi lled to capacity. He opened every tenth box in the warehouse and removed the can in
2. Criticize the following arguments in light of the material presented in this section: To estimate public support for a new municipality-funded convention center, researchers surveyed 100 homeowners in one of the city’s fashionable neighborhoods.They found that 89 percent of those sampled were
1. Criticize the following arguments in light of the material presented in this section: To test the algae content in a lake, a biologist took a sample of the water at one end. Th e algae in the sample registered 5 micrograms per liter. Th erefore, the algae in the lake at that time registered 5
20. Mr. Andrews, a grape merchant, inquires about a certain wine that he tastes at a party. Th e host tells him that from a total of ten bottles of that wine, six came from the north vineyard and four came from the south vineyard. From this information, the merchant concludes that he should visit
★19. Ms. Jones, a bookstore owner, wishes to send out an advertisement to potential customers. She estimates that 20 percent of the town’s residents are recreational readers, and she knows that all of the residents are either recreational readers or TV addicts (but not both). Also, a TV repair
18. A physician has diagnosed a patient as having either hepatitis or liver cancer(but not both). Statistics reveal that hepatitis occurs in the general population twice as frequently as liver cancer. Th us, the physician tentatively concludes that the patient probably has hepatitis. Later the
17. Knowing that your friend Angella studies for her tests only 40 percent of the time, you place an even bet with a third party that Angella will not study for her upcoming test. Later, you just happen to hear that Angella passed the test.Should you retract your bet? Assume that Angella passes
★16. We are given three new urns each containing seven red, fi ve green, and three white balls, and two old urns each containing fi ve red, three green, and seven white balls. The urns are identical except for an old or new date stamped beneath the base. If a single red ball is randomly drawn
15. Assign a numerical value to the strength of the following argument: The Wilson family has four children. Th erefore, at least two of the children were born on the same day of the week.
14. Assign a numerical value to the strength of the following argument: Th e odds are 5 to 3 that the Indians will win the American League pennant and 7 to 5 that the Cardinals will win the National League pennant. Therefore, the Indians and the Cardinals will meet in the World Series.
★13. The probability of a twenty-year-old man living to age seventy is .74, and the probability of a twenty-year-old woman living to the same age is .82. If a recently married couple, both age twenty, give 8 to 1 odds on their staying married for fi ft y years, what is the probability thata. At
12. What is the probability of drawing an ace and a king on three draws (without replacement) from a poker deck? (Hint: Use the negation rule.)
11. What is the probability of drawing either an ace or a king (or both) on three draws (without replacement) from a poker deck? (Hint: Use the negation rule.)
★10. Given an urn containing three red, four green, and fi ve yellow balls, if two balls are drawn from the urn (without replacement), what is the probability thata. Both are red?b. One is green, the other yellow?c. One is either red or green?d. At least one is green?e. Both have the same color?
9. Given two urns, one containing two red, three green, and four yellow balls, the other containing four red, two green, and three yellow balls, if a single ball is drawn from each urn, what is the probability thata. Both are red?b. At least one is green?c. One is red, the other yellow?d. At least
8. If a pair of dice are rolled, what is the probability that the points add up toa. 5?b. 6?c. 7?
★7. What is the probability of getting at least one six on three rolls of a die?
6. What is the probability of getting at least one head on three tosses of a coin?
5. What is the probability of drawing at least one ace from a poker deck on two draws if the fi rst card is replaced before the second is drawn?
★4. What is the probability of drawing two aces from a poker deck in two drawsa. If the fi rst card is replaced before the second is drawn?b. If the fi rst card is not replaced before the second is drawn?
3. What is the probability of drawing either a king or a queen from a poker deck(no jokers) on a single draw?
2. What is the probability of getting heads on three successive tosses of a coin?
1. What is the probability of getting either a six or a one from a single roll of a die?
★10. Suppose you give 1:6 odds that you can roll a “1” with a single fair die. If someone accepts your bet, how much could you expect to win aft er 100 rolls if you bet $1 on each roll?
9. Given an urn containing four red balls, three green balls, and fi ve yellow balls, what are the odds of drawing a red ball on a single draw?
8. If the odds of the Broncos beating the Dolphins is 5 to 4, and you bet $10 on the Broncos, how much do you stand to win?
★7. Given an urn containing three red balls, four green balls, and fi ve yellow balls, what is the probability of drawing a red ball on a single draw?
6. If the probability of the Red Sox beating the Tigers is 6/17, what are the odds for this event?
5. What is the probability of picking a black jack from a poker deck (without jokers) on a single draw?
★4. From a sample of 7,335 seventy-fi ve-year-old women, 6,260 lived an additional fi ve years. What is the probability that a seventy-fi ve-year-old woman will live to age eighty?
3. If the standard odds are 8 to 5 that the Chargers will beat the Lions, what is the probability that this event will happen?
2. From a sample of 9,750 Ajax trucks, 273 developed transmission problems within the fi rst two years of operation. What is the probability that an Ajax truck will develop transmission problems within the fi rst two years?
1. What is the probability of rolling a fi ve on a single roll of a die? What are the odds for this event?
Identify the cause suggested by the information presented in the following tables.Is the cause a sufficient condition, necessary condition, or both sufficient and necessary condition? Can you identify the method? Possible conditions Occurrence A B C D E Phenomenon * 1 2 3 4 5 6
Identify the cause suggested by the information presented in the following tables.Is the cause a sufficient condition, necessary condition, or both sufficient and necessary condition? Can you identify the method? Possible conditions Occurrence A B 1 234 5 6 D E Phenomenon
Identify the cause suggested by the information presented in the following tables.Is the cause a sufficient condition, necessary condition, or both sufficient and necessary condition? Can you identify the method? Possible conditions Occurrence A B C D E F Phenomenon 1 2 3 " 4 5 10 6
Identify the cause suggested by the information presented in the following tables.Is the cause a sufficient condition, necessary condition, or both sufficient and necessary condition? Can you identify the method? Occurrence 1 2 A B Possible conditions C D E Phenomenon
Identify the cause suggested by the information presented in the following tables.Is the cause a sufficient condition, necessary condition, or both sufficient and necessary condition? Can you identify the method? N Possible conditions Occurrence A B C D E Phenomenon 1 * " " " 3 4 5.
15. A cosmetics manufacturer tested a new cleansing cream on forty rabbits. Th e rabbits were virtually the same genetically and were the same age. Twenty of the rabbits were randomly placed in the experimental group and the other twenty were placed in the control group. A patch containing the
14. A sociologist conducted a study to determine if a correlation exists between grade point average at the time of graduation and income ten years after graduation. Th e sociologist visited the alumni offi ce of a local university and obtained the names and addresses of those who had graduated ten
★13. Two of Mr. Andrews’s rose bushes became infected with aphids. Mr. Andrews proceeded to spray one of the bushes with malathion insecticide but left the other bush untouched. Th e two bushes are both American Beauty, are fi ve years old, have virtually identical locations, receive the same
12. A doctor has fi ve patients who suff er from an unusual form of cancer. Th e patients are distinguished by the following living conditions. Davis, Jones, and Ellis live in a smoggy area near high-tension power lines, and Smith and Frank smoke cigarettes and live downwind from a company that
11. A metallurgist added eight substances in various combinations to seven samples of molten aluminum for the purpose of producing aluminum alloys. Th e metallurgist was interested in producing an alloy that had a special resistance to corrosion. Th e samples were distinguished by the following
★10. A psychiatrist had six adult women patients who suffered blurred ego boundaries. Th ese patients were distinguished by the following characteristics.Meg and Sue had been subjected to corporal punishment as children and both had siblings. Dot and Jane were adopted, had a male parent fi gure,
9. A man developed an allergic reaction to an unknown food. His doctor asked him about foods that oft en cause allergic reactions, and the man replied that he had eaten coconut, chocolate, nuts, milk products, shellfi sh, peppers, eggs, and wheat products prior to suff ering the reaction. Th e
8. From a comparison of statistics a criminologist detected what he thought was a correlation between fl uctuations in the employment rate and in crimes of theft . For every 2 percent increase in the employment rate, the rate of theft decreased by 1 percent, and for every 2 percent decrease in the
★7. Mrs. Wilkins sometimes has trouble sleeping. In order to determine the cause, she decided to take note of her pre-bedtime behavior over the course of a week. On Monday she drank camomile tea, had a late dinner, took a hot bath, read from a book, took a walk, and slept well. On Tuesday she had
6. Nancy was contemplating the purchase of a new oven for her kitchen, but she could not decide between an electric or a gas unit. Th us, she decided to conduct an experiment using the ovens, one gas, one electric, of two friends who live in adjoining apartments. She mixed up two identical batches
5. A manufacturer of fi shing equipment conducted a test of its products by giving them to eight fi shermen who used them with the following results. Ed and Flo used a Hot Spot lure and caught no fi sh. Dan and Amy used a Trusty rod with a Husky reel, and Amy caught fi sh but Dan did not. Jake used
★4. Th e repair manager for a manufacturer of desktop computers noticed that a large number of units were being returned for repairs. Th e manager selected a sample of seven returned units and noticed that these units were distinguished by the following characteristics. Units 1 and 3 had type X
3. An administrator for the Internal Revenue Service noticed that tax revenues for a certain year were down by 14 percent. Of this amount, the administrator attributed 6 percent to an economic slowdown that year, 3 percent to higher interest rates that led to higher write-off s, and 2 percent to
2. An eighth-grade teacher had fi ve pupils who read very well. Th ese pupils were distinguished by the following features. Tom came from a large family, had professional parents who were not wealthy, had training in phonics, read novels, lived close to a library, and watched educational TV. Andy
★1. To determine the eff ectiveness of an oil additive, a testing fi rm purchased two cars of the same make, year, and model, and drove each a distance of 30,000 miles using the same kind of gasoline, the same kind of oil, the same driver, under the same road conditions. Th e oil in one engine
★10. Flipping the wall switch to the “up” position causes the overhead lights to go on. Identify the kind of causality intended by the following statements. Is the cause a sufficient condition, necessary condition, or both sufficient and necessary condition?
9. Stretching a spring causes it to exert an opposing force. Identify the kind of causality intended by the following statements. Is the cause a sufficient condition, necessary condition, or both sufficient and necessary condition?
8. Eating contaminated food will cause one to become ill. Identify the kind of causality intended by the following statements. Is the cause a sufficient condition, necessary condition, or both sufficient and necessary condition?
★7. Pouring water on a wood fi re will cause it to be extinguished. Identify the kind of causality intended by the following statements. Is the cause a sufficient condition, necessary condition, or both sufficient and necessary condition?
6. Wetting litmus paper with an acid causes it to turn red. Identify the kind of causality intended by the following statements. Is the cause a sufficient condition, necessary condition, or both sufficient and necessary condition?
5. Pulling the trigger of a gun causes it to fi re. Identify the kind of causality intended by the following statements. Is the cause a sufficient condition, necessary condition, or both sufficient and necessary condition?
★4. Releasing the shutter of a camera causes an image to appear on the fi lm. Identify the kind of causality intended by the following statements. Is the cause a sufficient condition, necessary condition, or both sufficient and necessary condition?
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