Skills Practice Skills Practice for Lesson.1 Name Date To New Heights! Variance in Subjective and Random Samples Vocabulary Define each term. 1. sample 2. subjective sample 3. random sample 4. random number generator Problem Set Select a subjective sample of four for each data set. Explain the criteria on which you selected your sample. 1. The test scores for a math test are shown. 0 5 89 60 95 8 54 82 91 6 Sample answer: 54, 5, 6, 95 54 and 95 were chosen because they were the maximum and minimum values 5 and 6 were chosen because were about in the middle of the highest and lowest test scores. Chapter l Skills Practice 463
2. The weights in kilograms of wildebeest in a zoo are shown. 130 242 22 186 250 192 215 203 232 15 3. The number of crimes committed each month over a ten-month period are shown. 2 1 0 3 3 4 5 2 0 6 4. The prices of DVDs in an electronics store, in dollars, are shown. 5.99.95 10.00 14.5 8.35 13.95 21.99 13.2 8.5 11.95 5. The batting averages of ten baseball players in a season are shown. 0.120 0.215 0.240 0.283 0.15 0.160 0.220 0.302 0.254 0.193 6. The heights of ten buildings in a city, in feet, are shown. 102 54 6 95 250 3 65 48 2 85 Use your calculator to generate four random whole numbers that are within the given interval.. [1, 10] 8. [50, 200] Sample answer: 1, 3, 4, 10 9. [10, 1000] 10. [2, 1] 464 Chapter l Skills Practice
Name Date For each data set, use your calculator to generate four random numbers between 1 and 10. Then use the numbers you generated to create a random sample of four from the data set. 11. Each doctor in a town is given a phone number that ends in the digits 0001 through 0010. Phone Number Doctor s Name 0001 0002 0003 0004 0005 0006 000 0008 0009 0010 Thomas Easton Wu Rodriguez Pasles Farris Shea Wong Price Siegelman Sample answer: 0002, 0003, 0008, 0010 Easton, Wu, Wong, Siegelman 12. Each contestant participating in a contest is assigned a number. Contestant Number 1 2 3 4 5 6 8 9 10 Contestant s Name Lia Joe Ariel Jess Victor Roberto Wen Anita Mia Ana 13. Ten students record the number of times a coin is flipped until it lands on heads. Trial Number 1 2 3 4 5 6 8 9 10 Number of Flips 1 1 1 2 3 4 1 5 2 1 14. A factory worker records the weights, in ounces, of the first ten bolts that he manufactured. Bolt Number 1 2 3 4 5 6 8 9 10 Weight 2.1 2.2 2.3 2.4 2.2 2.1 2.3 2.1 2.2 2.1 Calculate the variance of each data set. Round decimals to the nearest hundredth. 15. Prices of cars at a dealership: 12,000 14,500 22,000 1,50 13,450 16,85 56,000 12,50 13,650 14,35 14,292,160.00 Chapter l Skills Practice 465
16. Heights of players on a softball team, in meters: 2.1 1.8 1.5 1.6 1.6 2.2 1.3 1. 1.8 2.0 1. Shoe sizes of professional bowlers in a tournament: 9.5 10.5 11.0 9.0 10.0 10.0 12.5.0 10.5 9.5 18. Weights, in ounces, of ten apples from the same apple tree: 4 3 2 4 6 5 6 3 3 Calculate the standard deviation of each data set. Round decimals to the nearest hundredth. 19. Scores on an English test: 54 68 53 5 42 48 0 58 64 63 10.3 20. Scores on a biology test: 9 83 86 92 8 96 84 88 91 84 21. Prices of the same computer at ten different stores: 450 315 425 30 385 345 430 440 390 410 22. Changes in a stock price over ten days: 1.25 0.50 0.5 2.15 0.35 3.15 0.35 0.25 0.10 1.25 466 Chapter l Skills Practice
Skills Practice Skills Practice for Lesson.2 Name Date Size How Sample Size Affects Results Vocabulary Complete each sentence by using one of the following words: median, subjective sample, random sample, sample size, or mean. 1. On an English test, half of the students scored above you and half of the students scored below you. Your test score is the. 2. The of the numbers 1, 4, 6,, 8 is 5.2. 3. You could select a of your class by putting everyone s name in a hat and drawing four names. 4. The of a sample is always smaller than the number of objects in the population. 5. You could select a of the residents of Albany by choosing those people whose last name begins with the letter M. Problem Set Calculate the variance of each data set. Round decimals to the nearest hundredth. 1. Number of pairs of pants sold each month in a department store in the last ten months: 3 4 4 0 2 6 4 5 4.84 2. Number of pairs of shoes sold each month in a boutique in a ten-month period: 0 0 2 3 2 1 4 5 2 0 3. Scores on a math test: 63 5 2 1 63 82 6 86 92 6 Chapter l Skills Practice 46
4. Scores on a history test are shown: 6 2 3 84 5 81 89 92 3 62 5. Daily attendance at a zoo over a ten-day period: 52 3 64 42 3 125 134 43 65 61 6. Number of people who visit the school library each day in the last ten days: 34 56 51 3 61 42 3 62 3 28 Calculate the standard deviation of each data set. Round decimals to the nearest hundredth.. Daily rainfall amounts, in inches, in the past ten days: 1.0 2.4 0.2 0.5 0.0 0.0 0.0 0.0 0.2 0.3 0.5 8. Forecasted visibility each day over the past ten days, in kilometers: 20 16 12 18 2 28 34 28 24 16 9. GPAs at a high school: 3.25 2.46 2.30 3.1 3.34 2.84 1.6 3.83 3.29 2.54 10. GPAs at a college: 2.6 3.46 2.49 2.86 3.3 3.64 2.6 2.30 2.9 3.14 11. Weights of peanut butter jars as they leave a processing plant, in ounces: 18.1 18.3 1.8 18.0 1.9 1.8 18.1 18.2 18.0 18.0 468 Chapter l Skills Practice
Name Date 12. Weights of green cabbage heads from a farm, in pounds: 4.9 4.8 5.0 5.5 4.3 5.2 5.3 5.2 5.1 4.6 Calculate the summary statistics for each data set. 13. Distances track and field athletes run to prepare for a track meet, in miles: 14 13 16 12 1 18 20 8 13 16 Mean: 14. Range: 12 First Quartile: 13 Median: 15 Third Quartile: 1 Interquartile Range: 4 14. Distances swim team members swim to prepare for a swim meet, in miles: 3 4 3 4 6 5 3 4 2 2 Mean: Range: First Quartile: Median: Third Quartile: Interquartile Range: 15. Rates that math tutors charge, in dollars per hour: 25 20 30 15 35 15 20 25 30 20 Mean: Range: First Quartile: Median: Third Quartile: Interquartile Range: Chapter l Skills Practice 469
16. Rates that Spanish tutors charge, in dollars per hour: 15 20 20 25 30 15 20 20 25 20 Mean: Range: First Quartile: Median: Third Quartile: Interquartile Range: Use your calculator to create a random sample of each data set. Use a sample size that is one-fourth of the size of the data set. 1. Lengths of television shows in a series, in minutes: TV Show Number 1 2 3 4 5 6 8 Show Length 2 26 24 28 23 24 25 26 Sample size is 2; Random samples will vary. 18. Lengths of the last eight movies you saw, in minutes: Movie Number 1 2 3 4 5 6 8 Movie Length 115 135 9 142 105 128 134 13 19. Amount of contaminants in samples of water from the houses on Green Street with house numbers 421-424: House Number 421 422 423 424 Number of Contaminants 42 31 2 38 20. Number of pallets in shipping containers 34-3: Container Number 34 35 36 3 Number of Pallets 5 13 16 8 40 Chapter l Skills Practice
Name Date 21. Student ID numbers and student heights, in inches: ID Number 101 102 103 104 105 106 10 108 109 110 111 112 113 114 115 116 Height 50 64 6 61 62 61 68 3 64 63 68 55 58 64 65 62 22. Student ID numbers and student GPAs: ID Number 101 102 103 104 105 106 10 108 109 110 111 112 113 114 115 116 GPA 1.34 1.86 3.51 3.20 2.09 2.3 2.46 2.51 2.6 2.81 2.03 1.6 1.04 2.3 3.3 2.15 Chapter l Skills Practice 41
42 Chapter l Skills Practice
Skills Practice Skills Practice for Lesson.3 Name Date Sampling Comparing Sampling Techniques Vocabulary If you were to take a political poll in the town of Jamestown, give an example of how you would use each sampling method. 1. stratified random sample 2. clustered sample Chapter l Skills Practice 43
Problem Set In Exercises 1 through 6, use the given data set to create a stratified random sample of the specified size. Explain the criteria by which you selected your sample. 1. The data set below shows the highest temperature recorded for select cities on different continents. Highest Temperature Recorded North America Europe Asia Africa 81 95 94 101 92 81 86 96 90 102 92 103 104 98 9 94 8 8 10 98 111 103 91 10 6 92 102 9 94 9 9 98 95 100 93 112 89 96 88 96 a. Create a stratified random sample of 4 temperatures. Sample answer: {81, 103, 9, 98}; I randomly chose one temperature from each of the four continents. b. Create a stratified random sample of 8 temperatures. 44 Chapter l Skills Practice
Name Date 2. The data set below shows the number of books read by the students in four different English classes. Number of Books Read in Each Teacher s Class Mr. James Ms. Farley Mr. Nguyen Ms. Razali 2 0 3 8 4 6 12 0 3 2 8 4 11 13 8 0 2 8 4 15 6 4 8 2 3 9 0 11 12 4 14 0 3 1 6 8 2 0 6 a. Create a stratified random sample with 12 data values to describe the number of books read by the students. b. Create a stratified random sample with 16 data values to describe the number of books read by the students. Chapter l Skills Practice 45
3. The data set below shows the number of cars crossing an intersection every hour for 8 hours during 4 days. Number of Cars Crossing an Intersection Day 1 Day 2 Day 3 Day 4 124 234 184 192 213 249 253 268 26 281 29 264 302 321 314 319 354 342 349 368 312 324 313 305 29 284 28 29 251 264 255 256 a. Create a stratified random sample with 16 data values to describe the number of cars crossing the intersection hourly. b. Create a stratified random sample with 24 data values to describe the number of cars crossing the intersection. 46 Chapter l Skills Practice
Name Date 4. A group of five doctors takes turns volunteering in a hospital. Each doctor volunteers for a period of eight days, and then it is the next doctor s turn. The data set below shows the number of patients that each doctor saw during their volunteer period. Number of Patients Seen Dr. Kim Dr. Rodriguez Dr. Lao Dr. Woods Dr. Morena 16 18 13 19 1 15 16 1 18 16 21 23 24 19 21 26 2 24 29 28 24 23 19 26 23 2 28 26 24 2 13 15 1 16 14 18 16 14 1 18 a. Create a stratified random sample with 5 data values to describe the number of patients seen daily. b. Create a stratified random sample with 15 data values to describe the number of patients seen. Chapter l Skills Practice 4
5. The data set below shows the amounts of recycled material collected, in pounds, from six different neighborhoods each month for four months. Recycled Material Collected from Six Neighborhoods (in pounds) Arlington Sylvia Burns Beaverton Bayview Hillsdale 426 482 431 324 24 134 435 324 521 65 184 162 425 398 425 53 234 16 441 436 486 543 246 186 a. Create a stratified random sample with 12 data values to describe the amount of recycled material collected monthly. b. Create a stratified random sample with 18 data values to describe the amount of recycled material collected. 48 Chapter l Skills Practice
Name Date 6. The data set below shows the number of people who visit a soup kitchen on certain days. Number of People Who Visit a Soup Kitchen Monday Wednesday Friday Sunday 42 56 86 112 43 5 8 124 49 52 92 126 48 61 93 118 38 5 96 116 46 53 8 11 41 48 86 128 48 52 8 12 a. Create a stratified random sample with 16 data values to describe the number of daily visitors to the soup kitchen. b. Create a stratified random sample with 20 data values to describe the number of daily visitors to the soup kitchen. Chapter l Skills Practice 49
For each data set create two different clustered samples. Explain the criteria by which you selected each sample.. Weights of Polar Bears at Three Zoos (in pounds) Bronx Zoo San Diego Zoo Philadelphia Zoo 85 892 884 1295 1216 123 1416 135 1384 The weights from any one (or two) of the zoos is acceptable as a clustered sample. Example: {892, 1216, 135}. I choose the weights of all the polar bears in the San Diego Zoo. Example: {884, 123, 1384}. I choose the weights of all the polar bears in the Philadelphia Zoo. 8. Attendance at a Movie Theatre on Three Weekdays Monday Tuesday Wednesday 134 94 112 142 134 141 19 213 206 223 22 216 480 Chapter l Skills Practice
Name Date 9. Length of Time of Games for Four Baseball Teams (in minutes) Pirates A s Rays Bulldogs 116 123 124 108 124 126 122 123 13 136 142 129 128 126 12 128 153 148 153 149 10. Students Scores on Math Tests Hugo Miriam Anastasia Nick 85 9 82 83 8 6 2 9 69 2 1 6 82 86 8 84 3 5 2 1 Chapter l Skills Practice 481
11. Number of Daily Customers for a Bank Week 1 Week 2 Week 3 Week 4 Week 5 123 145 94 113 12 93 88 96 102 94 94 104 93 9 89 154 14 163 164 13 213 19 204 192 216 12. Daily Prices of a Stock on Each Weekday over 5 Weeks Week 1 Week 2 Week 3 Week 4 Week 5 2.89 2. 3.21 2.42 0.69 3.81 4.09 4.66 1. 1.35 1.48 1.82 1.0 0.96 1.10 3.86 0.98 4.56 3.52 3.33 2.2 3.0 2.59 0.91 1.1 482 Chapter l Skills Practice
Name Date Calculate the mean of each data set. Round decimals to the nearest tenth. 13. Weights of 9 players on a basketball team in pounds: 110 95 162 143 12 146 18 134 168 The mean is approximately 141.3 pounds. 14. Heights of 9 players on a baseball team in inches: 62 48 3 0 68 6 1 58 64 15. Total mileage recorded for 5 new cars in miles: 11.8 21. 10.9 2.1 8.6 16. Prices of 5 cars in a used car lot in dollars: 4400 2300 225 50 8800 1. Daily number of people in detention in a school: 2 3 4 4 4 5 6 8 1 6 9 18. Cost of a stock over five days in dollars: 1.23 2.14 2.56 2.3 4.05 Chapter l Skills Practice 483
Calculate the summary statistics for each data set. 19. Number of boxes of mandarin oranges each volunteer sold during a fundraiser: 4 8 3 6 11 12 14 8 Range: 11 First Quartile: 5 Median: 8 Third Quartile: 11.5 Interquartile Range: 6.5 20. Heights of buildings on a city block, in feet: 45 350 25 218 346 15 Range: First Quartile: Median: Third Quartile: Interquartile Range: 21. Heights of houses on a suburban block, in feet: 10 1 19 16 13 14 16 Range: First Quartile: Median: Third Quartile: Interquartile Range: 22. Cost, in dollars, of toothbrushes in a pharmacy: 1.5 1.95 2.48 3.19 3.05 2.64 2.19 2.34 0.5 Range: First Quartile: Median: Third Quartile: Interquartile Range: 484 Chapter l Skills Practice
Skills Practice Skills Practice for Lesson.4 Name Date It s the Ladies Turn! Designing an Experiment and Bias Vocabulary Define each term in your own words. 1. biased sample 2. representative sample Problem Set For each experiment, determine which of the following sampling techniques would be the most appropriate: random sampling, stratified random sampling, or clustered sampling. Then explain how you would obtain a sample and why the technique you chose is appropriate. 1. A company wants to determine who likes bagels more, men or women. Sample answer: stratified random sampling; Divide the population into two groups, men and women, and randomly select members from each group. This technique provides a random sample that includes both groups. Random sampling is typically representative of a population. 2. A newspaper wants to determine which areas of town have the least number of subscriptions. Chapter l Skills Practice 485
3. You want to estimate the number of people in your school who are vegetarians. 4. You want to determine whether 9th graders or 11th graders are more likely to be vegetarians. 5. A political campaign can only visit three neighborhoods. They want to see how well liked their candidate is. 6. Health and Human Services wants to count the number of homeless people in a town. They only have enough counters to cover one-fifth of the town.. A manufacturer wants to test the taste of their frozen vegetables as the bags of vegetables come out of a freezer. 486 Chapter l Skills Practice
Name Date 8. A manufacturer wants to compare the taste of frozen vegetables from different grocery stores as the vegetables come out of a freezer. 9. You are asked to mail questionnaires to determine who uses coupons more, men or women. 10. You are asked to mail questionnaires that ask if people use coupons or not. Determine whether the study has a source of bias. Describe the bias and why this bias makes the sample unrepresentative. 11. A survey is mailed to voters in Albany asking Will you vote for the sales tax increase in Albany? There is no bias in this study. 12. A survey is mailed to voters in Albany who make more than $100,000 a year asking Will you vote for the sales tax increase in Albany? Chapter l Skills Practice 48
13. A medical company uses healthy patients to test their drugs for side effects. 14. A medical company uses sick patients to test their competitors drugs for side effects. 15. A poll by the Department of Education is conducted online that asks Do you have a computer at home? 16. A survey that measures the popularity of a magazine is inserted into the magazine, asking Do you like this magazine? 1. A call-in program on C-SPAN is taking a national survey of their viewers in Florida. 18. To measure if students are going to college after high school, a newspaper polls 9th grade students. 488 Chapter l Skills Practice
Skills Practice Skills Practice for Lesson.5 Name Date On Your Own! Designing, Implementing, Analyzing, and Reporting a Data Experiment Vocabulary Answer the questions based on your knowledge of sampling. 1. Describe how you would design an experiment. 2. Describe some implementation techniques in sampling. 3. What types of statistics have you used to analyze data? 4. In what ways can data be displayed visually? Chapter l Skills Practice 489
Problem Set For each experiment, determine which of the following sampling techniques would be the most appropriate: random sampling, stratified random sampling, or clustered sampling. Then explain how you would obtain a sample and why the technique you choose is appropriate. 1. You want to determine the average income of public school teachers in a certain city. Sample answer: random sampling; Assign each public school teacher an ID number and use a computer to randomly generate a sample of teachers. This technique provides a random sample of the population of teachers in the city, and random sampling is typically representative of a population. 2. You want to compare the average income of male and female public school teachers in a certain city. 3. A company wants to determine whether their drugs are harmful to people in the following ages groups: 0 10, 11 21, 22 35, and 40 and above. 4. A company wants to determine whether their drugs are harmful to people in a certain vicinity. 5. A university wants to study the economy of towns that have a heavy drug presence, but they can only study three towns. 490 Chapter l Skills Practice
Name Date 6. A local hospital wants to compare the effects of drugs on people in the age groups of 14 1 and 18 23. Determine the summary statistics for each data set.. Number of fish in aquariums around the city: 8 12 14 15 2 23 11 Range: 21 First Quartile:.5 Median: 11.5 Third Quartile: 14.5 Interquartile Range: 8. Number of horses at stables in the county: 5 13 2 42 32 15 21 Range: First Quartile: Median: Third Quartile: Interquartile Range: 9. Heights of baseball players, in inches: 2 0 64 8 3 61 68 9 66 Range: First Quartile: Median: Third Quartile: Interquartile Range: Chapter l Skills Practice 491
10. Heights of soccer players, in inches: 64 68 62 63 59 0 68 6 69 Range: First Quartile: Median: Third Quartile: Interquartile Range: Draw a box and whisker plot for each data set described by the summary statistics. 11. The summary statistics are shown for the number of points a football team scored in each game. The lowest number of points the team had was 6 points. Range: 19 First Quartile: 9 Median: 13 Third Quartile: 1 Interquartile Range: 8 Points Scored per Game by a Football Team 5 10 15 20 25 30 492 Chapter l Skills Practice
Name Date 12. The summary statistics are shown for the number of minutes students use the internet during a week. The shortest time that a student used the internet was 30 minutes. Range: 80 First Quartile: 60 Median: 0 Third Quartile: 90 Interquartile Range: 30 13. The summary statistics are shown for the number of graduates from a college each year. The greatest number of graduates in a year was 625. Range: 325 First Quartile: 325 Median: 450 Third Quartile: 600 Interquartile Range: 25 Chapter l Skills Practice 493
14. The summary statistics are shown for the weights of watermelons, in pounds, at a state fair. The largest watermelon won the blue ribbon with a weight of 52 pounds. Range: 1 First Quartile: 38 Median: 42 Third Quartile: 43 Interquartile Range: 5 494 Chapter l Skills Practice