Stat 1350 - Elementary Statistics Graded Homework Assignment 1 Unit 1 - Lessons 1 and 2 1. Athletes' salaries. Here is a small part of a data set that describes Major League Baseball players as of opening day of the 2011 season: (a) What individuals does this data set describe? (b) In addition to the player's name, how many variables does the data set contain? Which of these variables take numerical values? Which of the variables are not numerical variables? (c) What do you think are the units in which each of the numerical variable salary is expressed? For example, what does it mean to give Josh Beckett's annual salary as 17,000? (Hint: The average annual salary of a Major League Baseball player on opening day, 2011, was $3,305,393.) 2. Sampling moms. Pregnant and breast-feeding women should eat at least 12 ounces of fish and seafood per week to ensure their babies' optimal brain development, according to a coalition of top scientists from private groups and federal agencies. A nutritionist wants to know whether pregnant women are eating at least 12 ounces of fish per week. To do so, she obtains a list of the 340 members of a local chain of prenatal fitness clubs and mails a questionnaire to 60 of these women selected at random. Only 21 questionnaires are returned. (a) What is the variable measured in this study? (b) What is the population in this study? (c) What is the sample from which information is actually obtained? (d) What percentage of the women whom the nutritionist tried to contact responded? (e) Is this an observational study or an experiment? 3. Oatmeal and cholesterol. Does eating oatmeal reduce the level of bad cholesterol (LDL)? Here are two ways to study this question. 1. A researcher finds 500 adults over 40 who regularly eat oatmeal or products made from oatmeal. She matches each with a similar adult who does not regularly eat oatmeal or products made from oatmeal. She measures the bad cholesterol (LDL) for each adult and compares both groups. 2. Another researcher finds 1000 adults over 40 who do not regularly eat oatmeal or products made from oatmeal and are willing to participate in a study. She randomly assigns 500 of these to a diet that includes a daily breakfast of oatmeal. The other 500 continue their usual habits. After 6 months, she compares changes in LDL levels. (a) One of these studies is an observational study and the other is an experiment. Identify with study it the experiment and which study is the observational study and explain why for each. (b) Why does the experiment give more useful information about whether oatmeal reduces LDL? 4. Choose your study type. What is the best way to answer each of the questions below: an experiment, a sample survey, or an observational study that is not a sample survey? Explain your choices. (a) Is your school's basketball team called for fewer fouls in home games than in away games? (b) Are college students satisfied with the quality of recreational facilities available to them? (c) Do college students who have access to audio recordings of course lectures perform better in the course than those who don't? 5. Choose your study purpose. Give an example of a question about college students, their behavior, or their opinions that would best be answered by (a) a sample survey. (b) an observational study that is not a sample survey. (c) an experiment. 6. Definitions. What is the difference between a census and a sample survey? 7. Instant opinion. On March 29, 2007, BusinessWeek ran an online poll on their Web site and asked readers the questio think Google is too powerful?\" Readers clicked on one of three buttons (\"Yes,\" \"No,\" or \"Not sure\") to vote. In all, 1336 said \"Yes,\" 2051 (55.1%) said \"No,\" and 335 (9.0%) said \"Not sure.\" (a) What is the sample size for this poll? (b) At the Web site, BusinessWeek includes the following statement about its online poll. \"Note: These are surveys, not s polls.\" Explain why the poll may give unreliable information. (c) Just above the poll question was the following statement: \"Google's accelerating lead in search and its moves into so traditional advertising are sparking a backlash among rivals.\" How might this statement affect the poll results? 8. Ann Landers takes a sample. Advice columnist Ann Landers once asked her divorced readers whether they regretted decision to divorce. She received approximately 30,000 responses, about 23,000 of which came from women. Nearly 75 were glad they divorced, and most of them said they wished they had done it sooner. Explain why this sample is certainl What is the likely direction of the bias? That is, is 75% probably higher or lower than the truth about the population of a who have been divorced? 9. A call-in opinion poll. In 2005 the San Francisco Bay Times reported on a poll in New Zealand that found that New Z opposed the nation's new gay-inclusive civil-unions law by a 3-1 ratio. This poll was a call-in poll that cost $1 to particip San Francisco Bay Times article also reported that a scientific polling organization found that New Zealanders favor the margin of 56.4% to 39.3%. Explain to someone who knows no statistics why the two polls can give such widely differin which poll is likely to be more reliable. 10. Choose an SRS. A firm wants to understand the attitudes of its minority managers toward its system for assessing m performance. Below is a list of all the firm's managers who are members of minority groups. Use Table A at line 134 to be interviewed in detail about the performance appraisal system. 01 Berliner 09 Hans 17 Liu 25 Rumsey 02 Browne 10 Herbei 18 MacEachern 26 Shantner 03 Calder 11 Holloma n 19 Niller 27 Shi 04 Craigmile 12 Hsu 20 Nagaraja 28 Stasny 05 Cressie Kaizar 21 Notz 29 Turkmen 06 Critchlow 14 Kubatko 22 Ozturk 30 Verducci 07 Dean 15 Lee 23 Pearl 31 Wolfe 08 Goel 16 Lin 24 Peruggia 32 Xu 13 11. An election day sample. You want to choose an SRS of 20 of a city's 480 voting precincts for special voting-fraud s on election day. (a) Explain clearly how you would label the 480 precincts. How many digits make up each of your labels? What is the g number of precincts you could label using this number of digits? (b) Use Table A to choose the SRS, and list the labels of the precincts you selected. Enter Table A at line 107. 12. Apartment living. You are planning a report on apartment living in a college town. You decide to select three apartm complexes at random for in-depth interviews with residents. Use Table A, starting at line 121, to select a simple random three of the following apartment complexes. 01 Albany Commons 13 Gaslight Village 25 Oak Run 02 Apple Run 14 Georgetowne 26 Old Nantucket 03 Bexley Court 15 Golf Pointe 27 Parliament Ridge 04 Brooks Edge 16 Hickory Mill 28 Pheasant Run 05 Canterbury Way 17 Highview Place 29 Ravine Bluff 06 Chablis Villas 18 Indian Creek 30 Rocky Creek 07 Cherryblossom Way 19 Jefferson Commons 31 Scioto Commons 08 Dublin Plaza 20 Kenbrook Village 32 Stratford East 09 English Village 21 Lawn Manor 33 Timbercreek 10 Fairway Lakes 22 Little Brook Place 34 Walnut Knolls 11 Forest Creek 23 Marble Cliff 35 Woodland Trace 12 Forest Park 24 Morse Glen 36 York Terrace TABLE A Random digits Line 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 19223 73676 45467 52711 95592 68417 82739 60940 36009 38448 81486 59636 62568 45149 61041 14459 38167 73190 95857 35476 71487 13873 54580 71035 96746 96927 43909 15689 36759 69051 05007 68732 45740 27816 66925 08421 53645 66831 55588 12975 96767 72829 88565 62964 19687 37609 54973 00694 71546 07511 95034 47150 71709 38889 94007 35013 57890 72024 19365 48789 69487 88804 70206 32992 77684 26056 98532 32533 07118 55972 09984 81598 81507 09001 12149 19931 99477 14227 58984 64817 16632 55259 41807 78416 55658 44753 66812 68908 99404 13258 35964 50232 42628 88145 12633 59057 86278 05977 05233 88915 05756 99400 77558 93074 69971 15529 20807 17868 15412 18338 60513 04634 40325 75730 94322 31424 62183 04470 87664 39421 29077 95052 27102 43367 37823 36089 25330 06565 68288 87174 81194 84292 65561 18329 39100 77377 61421 40772 70708 13048 23822 97892 17797 83083 57857 66967 88737 19664 53946 41267 28713 01927 00095 60227 91481 72765 47511 24943 39638 24697 09297 71197 03699 66280 24709 80371 70632 29669 92099 65850 14863 90908 56027 49497 71868 74192 64359 14374 22913 09517 14873 08796 33302 21337 78458 28744 47836 21558 41098 45144 96012 63408 49376 69453 95806 83401 74351 65441 68743 16853 96409 27754 32863 40011 60779 85089 81676 61790 85453 39364 00412 19352 71080 03819 73698 65103 23417 84407 58806 04266 61683 73592 55892 72719 18442 77567 40085 13352 18638 84534 04197 43165 07051 35213 11206 75592 12609 47781 43563 72321 94591 77919 61762 46109 09931 60705 47500 20903 72460 84569 12531 42648 29485 85848 53791 57067 55300 90656 46816 42006 71238 73089 22553 56202 14526 62253 26185 90785 66979 35435 47052 75186 33063 96758 35119 88741 16925 49367 54303 06489 85576 93739 93623 37741 19876 08563 15373 33586 56934 81940 65194 44575 16953 59505 02150 02384 84552 62371 27601 79367 42544 82425 82226 48767 17297 50211 94383 87964 83485 76688 27649 84898 11486 02938 31893 50490 41448 65956 98624 43742 62224 87136 41842 27611 62103 48409 85117 81982 00795 87201 45195 31685 18132 04312 87151 79140 98481 79177 48394 00360 50842 24870 88604 69680 43163 90597 19909 22725 45403 32337 82853 36290 90056 52573 59335 47487 14893 18883 41979 08708 39950 45785 11776 70915 32592 61181 75532 86382 84826 11937 51025 95761 81868 91596 39244 41903 36071 87209 08727 97245 96565 97150 09547 68508 31260 92454 14592 06928 51719 02428 53372 04178 12724 00900 58636 93600 67181 53340 88692 03316 Stat 1350 - Elementary Statistics Graded Homework Assignment 2 Chapters 3 and 4 3.4 Each boldface number in the next paragraph is the value of either a parameter or a statistic. In each case, state which it is. A carload lot of ball bearings has an average diameter of 2.503 centimeters (cm). This is within the specifications for acceptance of the lot by the purchaser. The inspector happens to inspect 100 bearings from the lot with an average diameter of 2.515 cm. This is outside the specified limits, so the lot is mistakenly rejected. 3.6 Each boldface number in the next paragraph is the value of either a parameter or a statistic. In each case, state which it is. A national polling organization uses a random digit dialing device to dial residential landline phone numbers in the United States. Of the first 100 numbers dialed, 32 are unlisted numbers. This is not surprising, because 34% of all residential phones in the United States, including cell-phone-only and many unlisted landline phone households, are not covered by current landline telephone number sampling methods. 3.8 A sampling experiment. Let us illustrate sampling variability in a small sample from a small population. Ten of the 25 club members listed below are female. Their names are marked with asterisks in the list. The club chooses 5 members at random to receive free trips to the national convention. (a) Label the sampling frame starting with '01'. Draw one SRS of 5 starting at line 117 of Table A. Then draw 19 SRSs of size 5, using a different part of Table A each time. Record the number of females in each of your samples. Make a histogram like that in Figure 3.1 to display your results. What is the average number of females in your 20 samples? (b) Do you think the club members should suspect discrimination if none of the 5 tickets go to women? 3.10 Bigger samples, please. Explain in your own words the advantages of bigger random samples in a sample survey. 3.12 Health care satisfaction. A November 2011 Gallup Poll of 1012 adults found that 607 are satisfied with the total cost they pay for their health care. The announced margin of error is 4 percentage points. The announced confidence level is 95%. (a) What is the value of the sample proportion who say they are satisfied with the total cost they pay for their health care? Explain in words what the population parameter p is in this setting. (b) Make a confidence statement about the parameter p. 3.13 Bias and variability. Figure 3.5 shows the behavior of a sample statistic in many samples in four situations. These graphs are like those in Figure 3.1 and Figure 3.2. That is, the heights of the bars show how often the sample statistic took various values in many samples from the same population. The true value of the population parameter is marked on each graph. Label each of the graphs in Figure 3.5 as showing high or low bias and as showing high or low variability. Figure 3.5 Take many samples from the same population and make a histogram of the values taken by a sample statistic. Here are the results for four different sampling methods, for Exercise 3.13. 3.14 Is a larger sample size always better? In February 2004, USA Today conducted an online poll. Visitors to their Web site were asked the following question: \"Should the U.S. pass a constitutional amendment banning gay marriage?\" Visitors could vote by clicking a button. The results as of 3:30 P.M. on February 25 were that 68.61% voted \"No\" and 31.39% voted \"Yes.\" A total of 63,046 votes had been recorded. Using our quick method, we find that the margin of error for 95% confidence for a sample of this size is roughly equal to fourtenths of one percentage point. Is it correct to say that, based on this USA Today online poll, we are 95% confident that 68.61% 0.4% of American adults are opposed to having the United States pass a constitutional amendment banning gay marriage? Explain your answer. Be careful not to confuse your personal opinion with the statistical issues. 3.16 Take a bigger sample. A management student is planning a project on student attitudes toward part-time work while attending college. She develops a questionnaire and plans to ask 25 randomly selected students to fill it out. Her faculty adviser approves the questionnaire but suggests that the sample size be increased to at least 100 students. Why is the larger sample helpful? Back up your statement by using the quick method to estimate the margin of error for samples of size 25 and for samples of size 100. 3.22 The death penalty. In October 2011, the Gallup Poll asked a sample of 1005 adults, \"Are you in favor of the death penalty for a person convicted of murder?\" The proportion who said they were in favor was 61%. (a) How many of the 1005 people interviewed said they were in favor of the death penalty for a person convicted of murder? (b) Gallup says that the margin of error for this poll is 4 percentage points. Explain to someone who knows no statistics what \"margin of error 4 percentage points\" means. (c) Use the quick method to estimate the margin of error for statements about the population of all adults. Is your result close to the 4% margin of error announced by Gallup? 3.34 Simulation. Random digits can be used to simulate the results of random sampling. Suppose that you are drawing simple random samples of size 25 from a large number of college students and that 20% of the students are unemployed during the summer. To simulate this SRS, let 25 consecutive digits in Table A stand for the 25 students in your sample. The digits 0 and 1 stand for unemployed students, and other digits stand for employed students. This is an accurate imitation of the SRS because 0 and 1 make up 20% of the 10 equally likely digits. Simulate the results of 50 samples by counting the number of 0s and 1s in the first 25 entries in each of the 50 rows of Table A. Make a histogram like that in Figure 3.1 to display the results of your 50 samples. Is the truth about the population (20% unemployed, or 5 in a sample of 25) near the center of your graph? What are the smallest and largest counts of unemployed students that you obtained in your 50 samples? What percentage of your samples had either 4, 5, or 6 unemployed? 4.4 What kind of error? Each of the following is a source of error in a sample survey. Label each as sampling error or nonsampling error, and explain your answers. (a) The telephone directory is used as a sampling frame. (b) The subject cannot be contacted in five calls. (c) Interviewers choose people on the street to interview. 4.6 College parents. An online survey of college parents was conducted during February and March 2007. Email was sent to 41,000 parents who were listed in either the College Parents of America database or the Student Advantage database. Parents were invited to participate in the online survey. Out of those invited, 1727 completed the online survey. The survey protected the anonymity of those participating in the survey but did not allow more than one response from an individual IP address. One of the survey results was that 33% of mothers communicate at least once a day with their child while at school. (a) What was the response rate for this survey? (The response rate is the percentage of the planned sample that is, those invited to participatewho responded.) (b) Use the quick method (page 46) to estimate the margin of error for a random sample of size 1727. (c) Do you think that the margin of error is a good measure of the accuracy of the survey's results? Explain your answer. 4.12 Wording survey questions. Comment on each of the following as a potential sample survey question. Is the question clear? Is it slanted toward a desired response? (Survey questions on issues that one might regard as inflammatory are often prone to slanted wording.) (a) Which of the following best represents your opinion on gun control? The government should take away our guns.We have the right to keep and bear arms. (b) In light of skyrocketing gasoline prices, we should consider opening up a very small amount of Alaskan wilderness for oil exploration as a way of reducing our dependence on foreign oil. Do you agree or disagree? (c) Do you think that the excessive restrictions placed on U.S. law enforcement agencies hampered their ability to detect the 9/11 terrorist plot before it occurred? 4.20 A stratified sample. A club has 20 student members and 10 faculty members. The students are The faculty members are The club can send 3 students and 2 faculty members to a convention. It decides to choose those who will go by random selection. Label each sampling frame in alphabetical order beginning with '01'. Use Table A, starting at line 135, to choose a stratified random sample of 3 students and 2 faculty members. 4.22 Sampling by accountants. Accountants use stratified samples during audits to verify a company's records of such things as accounts receivable. The stratification is based on the dollar amount of the item and often includes 100% sampling of the largest items. One company reports 5000 accounts receivable. Of these, 100 are in amounts over $50,000; 500 are in amounts between $1000 and $50,000; and the remaining 4400 are in amounts under $1000. Using these groups as strata, you decide to verify all of the largest accounts and to sample 5% of the midsize accounts and 1% of the small accounts. How would you label the two strata from which you will sample? Use Table A, starting at line 115, to select only the first 5 accounts from each of these strata. TABLE A Random digits Line 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 19223 73676 45467 52711 95592 68417 82739 60940 36009 38448 81486 59636 62568 45149 61041 14459 38167 73190 95857 35476 71487 13873 54580 71035 96746 96927 43909 15689 36759 69051 05007 68732 45740 27816 66925 08421 53645 66831 55588 12975 96767 72829 88565 62964 19687 37609 54973 00694 71546 07511 95034 47150 71709 38889 94007 35013 57890 72024 19365 48789 69487 88804 70206 32992 77684 26056 98532 32533 07118 55972 09984 81598 81507 09001 12149 19931 99477 14227 58984 64817 16632 55259 41807 78416 55658 44753 66812 68908 99404 13258 35964 50232 42628 88145 12633 59057 86278 05977 05233 88915 05756 99400 77558 93074 69971 15529 20807 17868 15412 18338 60513 04634 40325 75730 94322 31424 62183 04470 87664 39421 29077 95052 27102 43367 37823 36089 25330 06565 68288 87174 81194 84292 65561 18329 39100 77377 61421 40772 70708 13048 23822 97892 17797 83083 57857 66967 88737 19664 53946 41267 28713 01927 00095 60227 91481 72765 47511 24943 39638 24697 09297 71197 03699 66280 24709 80371 70632 29669 92099 65850 14863 90908 56027 49497 71868 74192 64359 14374 22913 09517 14873 08796 33302 21337 78458 28744 47836 21558 41098 45144 96012 63408 49376 69453 95806 83401 74351 65441 68743 16853 96409 27754 32863 40011 60779 85089 81676 61790 85453 39364 00412 19352 71080 03819 73698 65103 23417 84407 58806 04266 61683 73592 55892 72719 18442 77567 40085 13352 18638 84534 04197 43165 07051 35213 11206 75592 12609 47781 43563 72321 94591 77919 61762 46109 09931 60705 47500 20903 72460 84569 12531 42648 29485 85848 53791 57067 55300 90656 46816 42006 71238 73089 22553 56202 14526 62253 26185 90785 66979 35435 47052 75186 33063 96758 35119 88741 16925 49367 54303 06489 85576 93739 93623 37741 19876 08563 15373 33586 56934 81940 65194 44575 16953 59505 02150 02384 84552 62371 27601 79367 42544 82425 82226 48767 17297 50211 94383 87964 83485 76688 27649 84898 11486 02938 31893 50490 41448 65956 98624 43742 62224 87136 41842 27611 62103 48409 85117 81982 00795 87201 45195 31685 18132 04312 87151 79140 98481 79177 48394 00360 50842 24870 88604 69680 43163 90597 19909 22725 45403 32337 82853 36290 90056 52573 59335 47487 14893 18883 41979 08708 39950 45785 11776 70915 32592 61181 75532 86382 84826 11937 51025 95761 81868 91596 39244 41903 36071 87209 08727 97245 96565 97150 09547 68508 31260 92454 14592 06928 51719 02428 53372 04178 12724 00900 58636 93600 67181 53340 88692 03316