# Exercises Solutions Paper

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The population is employed adult women, the sample is the 48 club members who returned the survey. . 2 WHAT IS THE POPULATION? For each of the following sampling situations identify the population as exactly as possible. That is, say what kind of individuals the population consists of and say exactly which individuals fall in the population. Fifth information given is not complete, complete the description of the population in a reasonable way. (a) Each week, the Gallup Poll questions a sample of about ISO adult U. S, residents to determine national opinion on a wide variety of issues.
An individual is a person; the population is all adult LLC_S_ (b) The 2000 census tried to gather basic information from every should in the United States. But a “long form” requesting much additional information was sent to a sample of about of households. An individual is a household; the population is all U. S. Households. (c) A machinery manufacturer purchases voltage regulators from a supplier. There are reports that variation in the output voltage of the regulators is affecting the performance of the finished products.
TO assess the quality Of the supplier’s production, the manufacturer sends a sample of 5 regulators from the last shipment to a laboratory for study. An individual is a voltage regulator; the population is all the regulators in the last hinted. 5. 3 TEACHING READING An educator wants to compare the effectiveness of computer software that teaches reading with that of a standard reading curriculum, He tests the reading ability of each student in a class of fourth graders, then divides them into vivo groups.
One group uses the computer regularly while the other studies a standard curriculum. At the end of the year, he retests all the students and compares the increase in reading ability in the two groups. 15 this an experiment? Why or why not? What are the explanatory and response variables? This is an experiment: A treatment is imposed. The explanatory variable is the teaching method (computer assisted or standard), and the response variable is the increase in reading ability based on the pre- and opposites. 5. ALCOHOL AND HEART ATTACKS Many studies have found that people who drink alcohol in moderation have lower risk of heart attacks that either nondrinkers or heavy drinkers. Does alcohol consumption also improve survival after a heart attack? One study followed 1913 people who were hospitalized after severe heart attacks. In the year before their heart attack, 47% of these people did not drink, 36% drank moderately, and drank heavily. After four years, ewer of the moderate drinkers had died. Is this an observational study or an experiment? What are the explanatory and response variables?
Observational. The researcher did not attempt to change the amount that people drank. The explanatory variable is alcohol consumption. The response variable is survival after 4 years. 5. 6 ARE ANESTHETICS SAFE? The National Halftone study was a major investigation of the safety of anesthetics used in surgery, Records of over 850,000 operations performed in 34 major hospitals showed the following death rates for four common anesthetics Anesthetic: Death Rate: A I B I C D I There is a clear association between the anesthetic used and the death rate of patients.
Anesthetic C appears to be dangerous. (a) Explain why we call the National Halftone Study an Observational study rather than an experiment, even though it compared the results of using different anesthetics in actual surgery _ The data was collected after the anesthesia was administered. (b) When the study looked at other variables that are confounded with a doctors choice Of anesthetic, it found that Anesthetic C was not causing extra deaths. Suggest several variables that are mixed up with what anesthetic a patient receives.
Type of surgery, length of surgery, (maybe longer operations require anesthetic C), age of patient, (maybe older patients respond better to anesthetic C) patient allergy to certain anesthetics, how healthy the patient was before the surgery.. 5. 7 CALL THE SHOTS A newspaper advertisement for USA Today: The Television Show once said: Should handgun control be tougher? You call the shots in a special call-in poll tonight. If yes, call If no, call 1-900-720-6182. Charge is SO cents for the first minute. Explain why this opinion poll is almost certainly biased.
Only persons with a strong opinion on the subject-?strong enough that they are willing to spend the time, and SC cents-?will respond to this advertisement. 3 HOW 9, 10, 13 – 15 5. 9 CHOOSE YOUR SAMPLE You must choose an SIRS of 10 of the 440 retail outlets in New York, that sell your company’s product’* How would you label this population? Use Table 8, starting at line 105, to choose your sample. Labeling from OIC to 440, we select 400, 077, 172, 417, 350, 131, 211, 273, 208, and 074. 5. 10 WHO SHOULD BE INTERVIEW OWED A firm wants to understand the attitudes of its minority managers toward its System for assessing management performance.
Below is a list of all the firm’s managers who are members of minority groups. Use Table B at line 139 to choose 6 to be interviewed in detail about the performance appraisal system. Augural Gates Peters Anderson Geol. Pledge Baxter Gomez Purr Bonds Hernandez Richards Bowman Hang Rodriguez Castillo Kim Santiago Cross Lila Sheen Deal Mourning Vega Fernando Enable Wang Fleming Starting with 01 and numbering down the columns, one chooses 04-Bonds, ID-Fleming, 17 -Lila, 13-Enable, 12-Geol., and 13-Gomez. 5. 3 SAMPLE ENG FRAME The list of individuals from which a sample is actually selected is called the sampling frame. Ideally, the frame should list every individual in the population, but in practice this is often difficult, A frame that leaves out part of the population is a common source to undercover. (a) Suppose that a sample of households in a community is selected at random trot the telephone directory. What households are omitted trot this frame? What types of people do you think are likely to live in these households? These people will probably be underrepresented in the sample.
Households without telephones, or with unlisted numbers. Such households would likely be made up of poor individuals (who cannot afford a phone), those who choose not to have hones, and those who do not voguish to hue their phone number published (b) It is more common in telephone surveys to use random digit dialing equipment that selects the last four digits of a telephone number at random after being given the exchange (the first three digits). Which Of the households you mentioned in your answer to (a) will be included in the sampling frame by random digit dialing?
Those With unlisted numbers would be included in the sampling frame when a random digit dialer is used. 4 5. 14 RING-NO-ANSWER A common form of moroseness in telephone surveys is “ring. Answer. That is, a call is made to an active number but no one answers. The Italian National Statistical Institute looked at moroseness to a government survey of households in Italy during the periods January 1 to Easter and July 1 to August 31. All calls were made between 7 and 10 p. M. , but 214% gave “ring- no-answer in one period versus 41. 5% “ring-no-answer in the other period.
Which period do you think had the higher rate of no answers? Why? Explain why a high rate of moroseness makes sample results less reliable. The higher no- answer was probably the second period-?more families are likely to be gone for vacations, etc. Moroseness of this type might underrepresented those who are more affluent (and are able to travel), 5. 1 S QUESTION WORDING During the 2000 presidential campaign, the candidates debated what to do with the large government surplus. The Pew Research Center asked two questions of random samples of adults. Both questions stated that social security would be “fixed. Here are the uses suggested for the remaining surplus: Should the money be used for a tax cut, or should it be used to fund new government programs? Should the money be used for a tax cut, or should it be spent on programs for education, the environment, lath care, crime-fighting and military defense? One of the questions drew 60% favoring a tax cut; the Other, only 22%. Which wording pulls respondents toward a tax cut? Why? The first wording would pull respondents toward a tax cut because the second wording mentions several popular alternative uses for tax money.
HOW 17, 18, 21, 24, 26, 27, 30 5. 17 EQUAL PAY FOR MALE AND FEMALE ATHLETES? The Excite Poll can be found online at http://elite. Excite. Com. The question appears on the screen, and you simply click buttons to vote “Yes,” “No,” or “Not Sure. ” On January 25, 2000, the question was “Should female athletes e paid the same as men for the work they do? ” In all, 13,147 (44%) said “Yes,” another 15,182 (50%) said “No,” and the remaining 1448 said “Not Sure. ” (a) What is the sample size for this poll? 13,147 4 15,182 4′ 1448 = 29,777, (b) That’s a much larger sample than standard sample surveys.
In spite of this, we can’t trust the result to give good information about any clearly defined population. Why? There’s nothing to prevent a person from answering several times. Also, the respondents were only those who went to that Web site and took the time to respond. We cannot define “moroseness” in this situation. C) More men than women use the Web. How might this affect the poll results? The results are slanted toward the Opinions Of men, who might be less likely to feel that female athletes should earn as much as men. 5 5. 18 WORDING BIAS Comment on each of the following as a potential sample survey question.
Is the question clear? Is it slanted toward a desired response? (a) “Some cell phone users have developed brain cancer. Should all cell phones come with a warning label explaining the danger of using cell phones? ‘ The wording is clear. The question is somewhat slanted in favor of warning labels. B) ’00 you agree that a national system of health insurance should be favored because it would provide health insurance for everyone and would reduce administrative costs? ” The question is clear, but it is clearly slanted in favor of national health insurance by asserting it would reduce administrative costs. C) “In view of escalating environmental degradation and incipient resource depletion, would you favor economic incentives for recycling to resource-intensive consumer goods? ” The question could be clearer by using simpler language. It is slanted in favor of incentives by starting out discussing environmental degradation. 5. 21 TESTING CHEMICALS A manufacturer of chemicals chooses 3 from each lot of 25 containers of a reagent to test for purity and potent}L Below are control numbers stamped on the bottles in the current lot. Use Table 8 at line 111 to choose an SIRS of 3 of these bottles.
Tioga AY AY BI 102 BI 189 AY All 13 80386 81 103 81223 AY 117 81011 81110 81277 AY AY 81036 BI 81286 AY 108 AY 81101 Bal 137 81299 Number the bottles across the rows from 01 to 25, then select 12 -? 80986, 04 -? AY, and 11 – AY. (If numbering is done down columns instead, the sample ill be AY, Bal 102, and AY. ) 5. 24 RANDOM DIGITS Which of the following statements are true of a table of random digits, and which are false? Briefly explain your answers. (a) There are exactly four So in each row of 40 digits.
False-?if it were true, then after looking at 39 digits, we would know whether or not the 40th digit was a O, contrary to property 2 (b) Each pair of digits has chance 1/100 of being CO. True-?there are 100 pairs of digits 00 through 99, and all are equally likely. (c) The digits 0000 can never appear as a group, because this pattern is not random. False-?OOH is just s likely as any other string of four digits, 6 5,26 CHECKING FOR BIAS Comment on each of the following as a potential response? (a) Which of the following best represents your opinion on gun control? 1. The government should confiscate our guns. . We have the right to keep and bear arms. This question will likely elicit more responses against gun control (that is, more people will choose 2). The two options presented are too extreme; no middle position on gun control is allowed. (b) A freeze in nuclear weapons should be favored because it would begin a much needed process to stop everyone in the world from building nuclear paeans now and reduce the possibility Of nuclear war in the future. DO you agree or disagree? The phrasing of this question will tend to make people respond in favor Of a nuclear freeze. Only one side Of the issue is presented. C) In view of escalating environmental degradation and incipient resource depletion, would you favor economic incentives for recycling of resource- intensive consumer goods? The wording is too technical for many people to understand-?and for those that do understand it, it is slanted because it suggests reasons why one should support recycling. It could be rewritten to meeting like: “Do you support economic incentives to promote recycling? ‘ 5. 27 SAMPLE ENG ERROR A New York Times opinion poll on women’s issues contacted a sample to 1025 women and 472 men by randomly selecting telephone numbers.
The Times publishes complete descriptions of its polling methods. Here is part of the description for this poll: In theory, in 19 cases out of 20 the results based on the entire sample will differ by no more than three percentage points in either direction from what would have been obtained by seeking out all adult Americans. The potential sampling error for smaller Bosporus is larger. For example, for men it is plus or minus 5 percentage points. Explain why the margin of error is larger for conclusions about men alone than for conclusions about all adults.
A smaller sample gives less information about the population. “table” constituted only about nonwhite of our sample, so we know less about that group than we know about all adults. 5. 30 SYSTEMATIC RANDOM SAMPLE sample surveys often use a systematic random sample to choose a sample Of apartments in a large building or dwelling units in a block at the last stage of a multistage sample. An example will illustrate the idea of a systematic sample. Suppose that we must choose 4 addresses out of 100. Because 100/4 = 25, we can think of the list as four lists of 25 addresses.
Choose 1 of the first 25 addresses at random using Table B. The sample contains this address and the addresses 25, 50, and 75 places down the list from it. If the table gives 13, for example, then the systematic random sample consists of the addresses numbered 13, 38, 63, and 88. (a) use Table B to choose a systematic random sample to 5 addresses trot a list of 200. Enter the table at line 120. Split the 200 addresses into S groups of 40 each. Looking for 2-digit numbers trot 01 to 40, we tint 35, and so take 35, 75, 1 15, 155, and 195. B) Like an a systematic random sample gives all individuals the same chance to be chosen. Explain why this is true. Then explain carefully why a systematic sample is nonetheless not an SIRS. Every address has a I-in-40 chance of being selected, but not every subset has an equal chance of being picked-?for example, 01, 02, 03, 04, and SO cannot be selected by this method. HOW 31, 36 For each Of the experimental situations described in Exercises 5. 31 to 5. 34, identify the experimental units or subjects, the factors, the treatments, and the response variables. 5. 1 RESISTING DROUGHT The ability to grow in shade may help pines found in the dry forests of Arizona to resist drought. How well do these pines grow in shade? Investigators planted pine seedlings in a greenhouse in either full light or light reduced to 5% of normal by shade cloth. At the end of the study, they dried the young trees and weighed them. Units are the individual trees. Factor is the amount of light, Treatments are full light and reduced light, Response variable is the weight tooth trees. 5. 3 IMPROVING RESPONSE RATE How can we reduce the rate of refusals in telephone surveys?
Most people who answer at all listen to the interviewer’s introductory remarks and then decide whether to continue. One study made telephone calls to randomly selected households to ask opinions about the next election. In some calls, the interviewer gave her name, in others she identified the university she was representing, and in still others she identified both herself and the university. For each type of call, the interviewer either did or did not offer to send a copy of the final survey results to the person interviewed. Do these differences in the introduction affect whether the interview is completed?
The units are the individuals vivo were called. One factor is what information is offered. Second factor is offering to send a copy of the results. Treatments are (I) giving name, (2) identifying university, (3) both Of these. The treatments are either offering or not offering. The response is whether the interview was completed. 8 5. 34 SICKLE-CELL DISEASE Sickle-cell disease is an inherited disorder of the red blood cells that in the United States affects mostly blacks. It can cause severe pain and many complications. Can the drug hydroxide reduce the severe pain caused by sickle-cell disease?
A study by the National Institutes of Health gave the drug to 150 sickle-cell sufferers and a placebo (a dummy medication) to another 150. The researchers then counted the episodes of pain reported by each subject. Subjects: 300 sickle cell patients. Factor: drug given. Treatments: hydroxide and placebo. Response variable: number of pain episodes. COMPARING LEARNING METHODS An educator wants to compare the effectiveness of computer software that teaches reading with that of a standard reading curriculum. She tests the reading ability of each student in a class of fourth graders, then divides them into two groups.
One group uses the computer regularly, while the other studies a standard curriculum. At the end of the year, she retests all the students and compares the increase in reading ability in the tuft groups. (a) Is this an experiment? Why or why not? This is an experiment, since the teacher imposes treatments (instruction methods). (b) What are the explanatory and response variables? The explanatory variable is the method used (computer software or standard curriculum), and the response is the hang in reading ability. 536 OPTIMIZING A PRODUCTION PROCESS A chemical engineer is designing the production process for a new product.
The chemical reaction that produces the product may have higher or lower yield, depending on the temperature and the stirring rate in the vessel in which the reaction takes place. The engineer decides to investigate the effects of combinations of tuft temperatures (517′ C and ICC) and three stirring rates (60 RPM, 90 RPM, and 120 RPM) on the yield of the process. She will process vivo batches of the product at each combination of temperature and stirring rate. A) What are the experimental units and the response variable in this experiment?
The experimental units are the batches of the product; the yield of each batch is the response variable. (b) How many doctors are there? How many treatments? Create a table to lay out the treatments. There are two factors: temperature (with 2 levels) and stirring rates (with 3 levels), for a total of 6 treatments. (c) How many experimental units are required for the experiment? Since two experimental units will be used for each treatment, eve need 12. G HOW #33 39-41, 46, 49, 56 539 RECRUITING FEMALE EMPLOYEES Will providing child care for employees sake a company more attractive to women, even those who are unmarried?
You are designing an experiment to answer this question. You prepare recruiting material for two fictitious companies, both in similar businesses in the same location. Company As brochure does not mention child care. There are two versions of Company Bi’s brochure, identical except that one describes the company’s on-site childcare facility. Your subjects are 40 unmarried women who are college seniors seeking employment. Each subject will read recruiting material for both companies and choose the one she would prefer to work for. You Will give each version of Company Bi’s brochure to half the women.
You expect that a higher percentage of those who read the description that includes child care will choose Company B. (a) Outline an appropriate design tort the experiment. Randomly select 20 women for Group 1, which will see the “childcare” version of Company Bi’s brochure, and assign the other 20 women to Group 2 (the “no childcare” group). Allow all women to examine the appropriate brochures, and observe which company they choose, Compare the number from Group 1 who choose Company B with the corresponding number from Group 2. B) The names of the subjects appear below. SE Table B, beginning at line 131, to do the randomization required by your design List the subjects who will read the version that mentions child care. Abram Adamson Fife Brown Scansion Chem. Cortez Curia’s Danielson Durra Edwards r-Luray Garcia Surgeons Green Guppy Guttering Howard Hang Sessile Jangle Kaplan Kim Loiterer Lifespan Martinez McNeill Morse Eng Quinine’s Riviera Roberts Rosen Suburbia’s Thompson Traverse Turing Almsman Williams Wong Numbering from 01 to 40, Group 1 is 05-Scansion, 32-Roberts, 19-Hang, 04- Brown, 25. Lifespan, 29. Eng, 20-sensei, 16. Guppy, 37. Turing, 39.
Williams, 31. Riviera, 18-Howard, 07- Cortez, 13-Garcia, 33-Rosen, 02-Adamson, 36-Traverse, 23-Kim, 27- McNeill, and 35. Thompson. 5. 40 ENCOURAGING ENERGY CONSERVATION Example 5. 13 (text page 297) describes an experiment to learn whether providing households with electronic indicators or charts will reduce their electricity consumption. An executive of the electric company objects to including a control group, He says, “It would be simpler to just compare electricity use last year (before the indicator or chart was provided) with consumption in the same period this year.
If households use less electricity this year, the indicator or chart must be working. ” Explain clearly why this design is inferior to that in Example 13_ If this year is considerably different in some way from last year, we cannot compare electricity consumption over the two years Poor example, if this summer is warmer, the customers may run their air conditioners more often. The possible differences between the two years would confound the effects of the treatments. 541 EXERCISE AND HEART ATTACKS Does regular exercise reduce the risk of a heart attack?
Here are two ways to study this question. Explain clearly why the second design Will produce more trustworthy data. A researcher finds 2000 men over 40 who exercise regularly and have not had heart attacks. She matches each With a similar man Who does not exercise regularly, and she follows both groups for 5 years. 2. Another researcher finds 4000 men over 40 who have not had heart attacks and are willing to participate in a study. She assigns 2000 of the men to a regular program of supervised exercise, The other 2000 continue their usual habits. The researcher follows both groups for 5 years.
The second design is an experiment-?a treatment is imposed on the subjects. The first is a duty: it may be confounded by the types of men in each group. In spite of the researchers attempt to match “similar men from each group, those in the first group (who exercise) could be somehow different trot men in the non-exercising group. L. 5. 46 CARBON DIOXIDE AND TREE GROWTH The concentration of carbon dioxide (CO) in the atmosphere is increasing rapidly due to our use of fossil fuels. Because plants use CO to fuel photosynthesis, more CO may cause trees and other plants to grow faster.
An elaborate apparatus allows researchers to pipe extra CO to a 30-meter circle of forest. We want to compare the growth n base area of trees in treated and untreated areas to see if extra CO does in fact increase growth. We can afford to treat three circular areas. (a) Describe the design of a completely randomized experiment using 6 well-separated 30-meter circular areas in a pine forest. Sketch the circles and carry out the randomization your design calls for. Assume that the 6 circular areas are given in advance. Number them in any order. Use Table B to select 3 for the treatment.
We used line 104. The first 4 digits are: 52 71. We cannot use the 7 because it is more than 6. Therefore, we would treat areas 5, 2 and 1. B) Areas within the forest may differ in soil fertility. Describe a matched pairs design using three pairs of circles that will reduce the extra variation due to different fertility. Sketch the circles and carry out the randomization your design calls for. If the pairs are not given in advance, divide the 6 areas into 3 pairs 50 that the elements of each pair are close to each other and therefore to similar fertility.
For each pair, we randomly pick one of the two to receive the treatment. Label the two areas in each pair A and B. Fifth random number from Table B is even, then apply the treatment to area A. Otherwise, apply the treatment to Area 8. Alternatively, we could go along the table looking for either a 0 or a 1, ignoring the other digits. If eve find a O before a I, then treat area A. Otherwise, treat B. DOES SAINT-JOHN’S WORTH RELIEVE MAJOR DEPRESSION? Here are some excerpts from the report of a study of this issue.
The study concluded that the herb is no more effective than a placebo. (a) “Design: Randomized, double-blind, placebo-controlled clinical trial. ” Explain the meaning of each of the terms in this description. “Randomized” means that patients were randomly assigned either SST. John’s Worth or the placebo. “Double-blind” means that both the subjects and those Who work With the subjects do not know Who is getting What treatment. “Placebo controlled” means that we will compare the results for the group using SSL John’s Worth to the group that received the placebo. B) “Participants . . Were randomly assigned to receive either Saint-John’s. Worth extract (n = 98) or placebo (n = 102)… The primary outcome measure was the rate of change in the Hamilton Rating Scale for Depression over the treatment period. ” Based on this information, use a diagram to outline the design of this clinical trial. . 53 DOES CALCIUM REDUCE BLOOD PRESSURE? You are participating in the design of a medical experiment to investigate whether a calcium supplement in the diet will reduce the blood pressure of middle-aged men.
You have available 40 men with high blood pressure who are willing to serum as subjects. (a) Outline an appropriate design for the experiment. Randomly assign 20 men to each of tuft groups. Record each subject’s blood pressure, then apply the treatments: a calcium supplement for Group 1, and a placebo for Group 2. After sufficient time has passed, measure blood pressure again and observe any change. B) The names Of the subjects appear below. Use Table B, beginning at line 119, to do the randomization required by your design, and list the subjects to whom you Will give the drug.

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