7.1 Draw Scatter Plots and

Transcription

1 7.1 Draw Scatter Plots and Best-Fitting Lines Georgia Performance Standard(s) MM2D2a, MM2D2b, MM2D2d Your Notes Goal p Fit lines to data in scatter plots. VOCABULARY Scatter plot Positive correlation Negative correlation Correlation coefficient Best-fitting line Linear regression Median-median line Algebraic model Inference Copyright McDougal Littell/Houghton Mifflin Company. Georgia Notetaking Guide, Mathematics 2 255

2 Your Notes Eample 1 Describe and estimate correlation coefficients Describe the data as having a positive correlation, a negative correlation, or approimately no correlation. Tell whether the correlation coefficient for the data is closest to 21, 20.5, 0, 0.5, or 1. a. y y b Solution a. The scatter plot shows a strong correlation. So, the best estimate given is r 5. b. The scatter plot shows a weak correlation. So, r is between and, but not too close to either one. The best estimate given is r 5. Checkpoint For the scatter plot, (a) tell whether the data has a positive correlation, a negative correlation, or approimately no correlation, and (b) tell whether the correlation coefficient for the data is closest to 21, 20.5, 0, 0.5, or y y Georgia Notetaking Guide, Mathematics 2 Copyright McDougal Littell/Houghton Mifflin Company.

3 Your Notes Eample 2 Approimate the best-fitting line The table below gives the number of people y who attended each of the first seven football games of the season. Approimate the best-fitting line for the data y Draw a. 2. Sketch the best-fitting line. 3. Choose two points on the line. For the scatter plot shown, you might choose (1, ) and (2, ). Number of people y Football game 4. Write an equation of the line. The line that passes through the two points has a slope of: m 5 5 Use the point-slope form to write the equation. y 2 y 1 5 m( 2 1 ) Point-slope form y 2 5 Substitute for m, 1, and y 1. y 5 Simplify. An approimation of the best-fitting line is y 5. Checkpoint Complete the following eercise. 3. The table gives the average class score y on each chapter test for the first si chapters of the tetbook y a. Approimate the best-fitting line for the data. b. Use your equation from part (a) to Average class score y Test predict the average class score on the chapter 9 test. Copyright McDougal Littell/Houghton Mifflin Company. Georgia Notetaking Guide, Mathematics 2 257

4 Your Notes Eample 3 Find a median-median line Find the equation of the median-median line for the data. (1, 34), (2, 25), (3, 40), (5, 60), (6, 35), (7, 65), (9, 50), (10, 45), (11, 60) Solution Step 1 Organize the data so that the -values are in order from least to greatest. Then separate the coordinates into three equal sized groups. Step 2 Find the median -values and the median y-values for each group. y Median Median Group -values y-values -values y-values 1 1,, 3, 34, , 6, 35, 60, 3, 10, 11 45,, 60 Step 3 Create a summary point for each group by combining the median -value and the median y-value into an ordered pair. Group 1: ( ) Group 2: ( ) Group 3: ( ) Step 4 Determine the equation of the line between the two outer points by finding m and then using point-slope form. m y 2 5 ( 2 ) y Georgia Notetaking Guide, Mathematics 2 Copyright McDougal Littell/Houghton Mifflin Company.

5 Your Notes Eample 4 Find a median-median line (continued) Step 5 Move the equation one-third of the way toward the middle summary point. Middle summary point: ( ) Predicted value at 5 : y 5 2( ) One-third of the difference between y 5 and y y 5 : 1 } 3 ( 2 ) 5 New equation: y The equation of the median-median line is. Checkpoint Complete the following eercise. 4. Find the equation of the median-median line for the data: (1, 25), (2, 20), (4, 35), (5, 43), (7, 53), (8, 40). Homework Copyright McDougal Littell/Houghton Mifflin Company. Georgia Notetaking Guide, Mathematics 2 259

6 Name Date LESSON 7.1 Practice Tell whether and y have a positive correlation, a negative correlation, or approimately no correlation. 1. y 2. y 3. y Draw a scatter plot of the data. Tell whether the data have a positive correlation, a negative correlation, or approimately no correlation y y y y y y y y y y y y Georgia Notetaking Guide, Mathematics 2 Copyright McDougal Littell/Houghton Mifflin Company.

7 Name Date LESSON 7.1 Practice continued Approimate the best-fitting line for the data. 8. y 9. y Household Size The table shows the average household size y in the United States from 1930 to Draw a scatter plot of the data and describe the correlation shown. Let t represent the number of years since Year, t Household size, y Household size Years since Household Size Model Use the linear regression feature of a graphing calculator to approimate the best-fitting line for the data in Eercise Household Size Prediction Using the model from Eercise 11, predict the average household size in Find the equation of the median-median line for the data y Copyright McDougal Littell/Houghton Mifflin Company. Georgia Notetaking Guide, Mathematics 2 261

8 7.2 Write Quadratic Functions and Models Georgia Performance Standard(s) Goal p Write quadratic functions and models. MM2D2a, MM2D2c Your Notes VOCABULARY Quadratic regression Best-fitting quadratic model Curve fitting Eample 1 Write a quadratic function in verte form Write a quadratic function whose graph has verte (22, 23) and passes through the point (0, 5). Solution y 5 a( 2 h) 2 1 k Verte form y 5 a( ) 2 Substitute for h and k. Use the point (, ) to find a. 5 a( ) 2 Substitute for and y. 5 a Solve for a. A quadratic function for the parabola is. 262 Georgia Notetaking Guide, Mathematics 2 Copyright McDougal Littell/Houghton Mifflin Company.

9 Your Notes Checkpoint Complete the following eercise. 1. Write a quadratic function whose graph has verte (2, 1) and passes through the point (0, 4). Eample 2 Write a quadratic function in intercept form Write a quadratic function whose graph has -intercepts 23 and 2, and passes through the point (22, 24). Solution y 5 a( 2 p)( 2 q) Intercept form y 5 a( )( ) Substitute for p and q. Use the point (22, 24) to find a. 5 a( )( ) Substitute for and y. 5 a Solve for a. A quadratic function for the parabola is. Checkpoint Complete the following eercise. 2. Write a quadratic function whose graph has -intercepts 24 and 2, and passes through the point (3, 21). Copyright McDougal Littell/Houghton Mifflin Company. Georgia Notetaking Guide, Mathematics 2 263

10 Your Notes Substitute 6 for c in Equation 1. Substitute 6 for c in Equation 3. Eample 3 Write a quadratic function in standard form Write a quadratic function in standard form for the parabola that passes through the points (22, 26), (0, 6), and (2, 2). Substitute the coordinates of each point into y 5 a 2 1 b 1 c to obtain a system of three equations. 5 a( ) 2 1 b( ) 1 c Substitute for and y. 5 Equation 1 5 a( ) 2 1 b( ) 1 c Substitute for and y. 5 Equation 2 5 a( ) 2 1 b( ) 1 c Substitute for and y. 5 Equation 3 Rewrite the system as a system of two equations. 5 Substitute for c. 5 Revised Equation 1 5 Substitute for c. 5 Revised Equation 3 Solve the system consisting of revised Equations 1 and 3. Revised Equation 1 Revised Equation 3 Add equations. a 5 Solve for a. So, 5, which means b 5. A quadratic function for the parabola is. Checkpoint Complete the following eercise. 3. Write a quadratic function in standard form for the parabola that passes through the points (21, 25), (2, 1), and (3, 21). 264 Georgia Notetaking Guide, Mathematics 2 Copyright McDougal Littell/Houghton Mifflin Company.

11 Your Notes Eample 4 Best-fitting quadratic model for data Baseball The table shows the height of a baseball that is hit, with representing the time (in seconds) and y representing the baseball s height (in feet). Use a graphing calculator to find the best-fitting quadratic model for the data. Time, Height, y Enter the data into two lists of a graphing calculator. Make a scatter plot of the data. L1 L2 L L1(1)=0 Use the quadratic regression Check how well the model feature to find the model fits the data by best-fitting quadratic model graphing the model and for the data. the data in the same QuadReg viewing window. y 5 a 2 1 b 1 c a 5 b 5 c 5 The best-fitting quadratic model is. Checkpoint Complete the following eercise. Homework 4. Use a graphing calculator to find the best-fitting model for the data in the table. Time, Height, y Copyright McDougal Littell/Houghton Mifflin Company. Georgia Notetaking Guide, Mathematics 2 265

12 Name Date LESSON 7.2 Practice Write a quadratic function in verte form whose graph has the given verte and passes through the given point. 1. verte: (2, 0) 2. verte: (1, 23) 3. verte: (22, 2) point: (3, 1) point: (0, 21) point: (0, 0) Write a quadratic function in intercept form whose graph has the given intercepts and passes through the given point. 4. -intercepts: 1, intercepts: 23, intercepts: 25, 0 point: (2, 26) point: (22, 24) point: (21, 8) 266 Georgia Notetaking Guide, Mathematics 2 Copyright McDougal Littell/Houghton Mifflin Company.

13 Name Date LESSON 7.2 Practice continued Write a quadratic function in standard form whose graph passes through the given points. 7. (22, 3), (0, 1), (2, 7) 8. (21, 2), (0, 22), (3, 22) 9. (0, 3), (1, 5), (2, 3) In Eercises 10 and 11, use the following information. Youth Football The table shows the number of participants y in a local youth football program from 2003 to Assume that t represents the number of years since Year, t Participants, y Use a graphing calculator to find the best-fitting quadratic model for the data. 11. Using the model, how many participants are projected for 2011? Copyright McDougal Littell/Houghton Mifflin Company. Georgia Notetaking Guide, Mathematics 2 267

14 7.3 Find Measures of Central Tendency and Dispersion Georgia Performance Standard(s) MM2D1b, MM2D1c Your Notes Goal p Describe data using statistical measures. VOCABULARY Statistics Measure of central tendency Mean Median Mode Measure of dispersion Range Standard deviation 268 Georgia Notetaking Guide, Mathematics 2 Copyright McDougal Littell/Houghton Mifflin Company.

15 Your Notes Eample 1 Find measures of central tendency Find the mean, median, and mode of the data set. Solution To find the mean, divide the sum of the scores by the number of scores. Quiz Scores 19, 15, 22, 17, 21, 17, 25, 18, 17 } To find the median, first order the quiz scores from least to greatest. Because there is an odd number of scores, the median is the middle number,. There is one mode, most frequently., because this number occurs STANDARD DEVIATION OF A DATA SET The standard deviation s (read as sigma ) of 1, 2,..., n is: }}}} s 5 Î}}}} n Eample 2 Find measures of dispersion Find the range and standard deviation for the quiz scores in Eample 1. Solution To find the range, subtract the least data value from the greatest data value. Range To find the standard deviation, substitute the scores and the mean into the formula. s 5 ø Î}}}}} }}}}} Copyright McDougal Littell/Houghton Mifflin Company. Georgia Notetaking Guide, Mathematics 2 269

16 Your Notes Eample 3 Compare data sets The lists show the number of memberships sold each month for one year by two competing athletic clubs. Compare the mean and standard deviation for the numbers of memberships sold by the two athletic clubs. Club A: 12, 9, 14, 6, 10, 11, 19, 6, 17, 11, 4, 13 Club B: 17, 10, 22, 15, 14, 19, 4, 8, 12, 22, 20, 5 Solution Club A: Mean: } Std. Dev.: }}}} s 5 Î }}}} ø Club B: Mean: } Std. Dev.: s 5 Î}}}} ø Athletic Club has a greater mean and a greater standard deviation than Athletic Club. Checkpoint Complete the following eercise. 1. The data set below gives the recorded speeds (in mi/h) of 10 different cars on a local highway during a week day. 69, 62, 64, 67, 62, 64, 63, 65, 60, 64 Find the mean, median, and mode of the data set. 270 Georgia Notetaking Guide, Mathematics 2 Copyright McDougal Littell/Houghton Mifflin Company.

17 Your Notes Checkpoint Complete the following eercises. 2. Find the range and standard deviation of the data set in Eercise Compare the means and standard deviations of Set A and Set B. Set A Set B Homework Copyright McDougal Littell/Houghton Mifflin Company. Georgia Notetaking Guide, Mathematics 2 271

18 Name Date LESSON 7.3 Practice Find the mean, median, and mode of the data set. 1. 1, 6, 3, 9, 6, 8, 4, 4, , 5, 6, 2, 6, 1, 7, 6, , 13, 12, 12, 13, 16, 12, 13, 14, , 14, 11, 15, 14, 18, 9, 11, 13, 10 Find the range and standard deviation of the data set , 8, 17, 15, 12, , 14, 24, 21, 30, , 24, 31, 34, 23, 27, , 46, 39, 43, 32, 35, 40 In Eercises 9 and 10, find the mean, median, mode, range, and standard deviation of the data set. 9. Quiz Scores The data set below gives the quiz scores for a student on quizzes consisting of 10 points each. 7, 9, 7, 10, 8, 7, Travel Distance The data set below gives the distances (in miles) that several people travel to and from work each day. 12, 15, 11, 8, 11, 13, 10, Georgia Notetaking Guide, Mathematics 2 Copyright McDougal Littell/Houghton Mifflin Company.

19 Name Date LESSON 7.3 Practice continued In Eercises 11 and 12, find the mean, median, mode, range, and standard deviation of the data set. 11. Oil Change The data set below gives the waiting times (in minutes) for several people having the oil changed in their cars at an auto mechanics shop. 22, 18, 25, 21, 28, 26, 20, 28, Hockey The data set below gives the numbers of goals for the 10 players who scored the most goals during the National Hockey League regular season. 41, 41, 41, 38, 38, 36, 35, 35, 34, Telephone Calls The data sets below give the lengths (in minutes) of long distance telephone calls made from a household during two months. Compare the mean and standard deviation for the calls made during the two months. Month A: 11, 15, 10, 37, 17, 14, 9, 15 Month B: 13, 9, 16, 8, 17, 20, 8, 13 Copyright McDougal Littell/Houghton Mifflin Company. Georgia Notetaking Guide, Mathematics 2 273

20 7.4 Use Normal Distributions Georgia Performance Standard(s) MM2D1d Your Notes Goal p Study normal distributions. VOCABULARY Normal distribution Normal curve Standard normal distribution z-score AREAS UNDER A NORMAL CURVE A normal distribution with mean } and standard deviation s has these properties: The total area under the related normal curve is. About % of the area lies within 1 standard deviation of the mean. About % of the area lies within 2 standard deviations of the mean. About % of the area lies within 3 standard deviations of the mean. 34% 34% 68% 95% 99.7% 13.5% 13.5% 2.35% 2.35% 0.15% 0.15% 2 3s 2 2s 2 s 1 s 1 2s 1 3s 2 3s 2 2s 2 s 1 s 1 2s 1 3s 274 Georgia Notetaking Guide, Mathematics 2 Copyright McDougal Littell/Houghton Mifflin Company.

21 Your Notes Eample 1 Find a normal probability A normal distribution has mean } and standard deviation s. For a randomly selected -value from the distribution, find P( } 2 s } 1 2s). Solution The probability that a randomly selected -value lies between and is the shaded area under the normal curve. Therefore: P( } 2 s } 1 2s) s 2 2s 2 s 1 s 1 2s 1 3s Checkpoint Complete the following eercise. 1. A normal distribution has mean } and standard deviation s. For a randomly selected -value from the distribution, find P( } 2 s). Eample 2 Interpret normally distributed data Math Scores The math scores of an eam for the state of Georgia are normally distributed with a mean of 496 and a standard deviation of 109. About what percent of the test-takers received scores between 387 and 605? Solution The scores of 387 and 605 repressent standard deviation on either side of the mean. So, the percent of test-takers with scores between 387 and 605 is % 1 % 5 %. Copyright McDougal Littell/Houghton Mifflin Company. Georgia Notetaking Guide, Mathematics 2 275

22 Your Notes Eample 3 Use a z-score and the standard normal table In Eample 2, find the probability that a randomly selected test-taker received a math score of at most 630. Solution Step 1 Find the z-score corresponding to an -value of 630. z 5 2 } } 5 ø s Step 2 Use the standard normal table to find P( 630) ø P(z ). z The table shows that P(z ) 5. So, the probability that a randomly selected test-taker received a math score of at most 630 is about. Checkpoint Complete the following eercises. 2. In Eample 2, what percent of the test-takers received scores between 496 and 714? Homework 3. In Eample 3, find the probability that a randomly selected test-taker received a math score of at most Georgia Notetaking Guide, Mathematics 2 Copyright McDougal Littell/Houghton Mifflin Company.

23 Name Date LESSON 7.4 Practice A normal distribution has mean } and standard deviation s. Find the indicated probability for a randomly selected value from the distribution. 1. P( } 2 s) 2. P( } 1 3s) 3. P( } 2 3s) Give the percent of the area under the normal curve represented by the shaded region s 2 2s 2 s 1 s 1 2s 1 3s 2 3s 2 2s 2 s 1 s 1 2s 1 3s A normal distribution has a mean of 25 and a standard deviation of 5. Find the probability that a randomly selected value from the distribution is in the given interval. 6. Between 25 and Between 15 and Between 20 and At least At least At most 15 Copyright McDougal Littell/Houghton Mifflin Company. Georgia Notetaking Guide, Mathematics 2 277

24 Name Date LESSON 7.4 Practice continued A normal distribution has a mean of 75 and a standard deviation of 10. Use the standard normal table of your tetbook to find the indicated probability for a randomly selected value from the distribution. 12. P( 75) 13. P( 85) 14. P( 55) 15. P( 87) 16. P( 69) 17. P( 45) In Eercises 18 and 19, use the following information. Breakfast A restaurant is busiest on Sunday from 6:00 A.M. to 9:00 A.M. During these hours, the waiting time for customers in groups of 5 or less to be seated is normally distributed with a mean of 20 minutes and a standard deviation of 4 minutes. 18. What is the probability that customers in groups of 5 or less will wait 8 minutes or less to be seated during the busy Sunday morning hours? 19. What is the probability that customers in groups of 5 or less will wait 24 minutes or more to be seated during the busy Sunday morning hours? In Eercises 20 and 21, use the following information. Light Bulbs A company produces light bulbs having a life epectancy that is normally distributed with a mean of 1800 hours and a standard deviation of 65 hours. 20. Find the z-score for a life epectancy of 2000 hours. 21. What is the probability that a randomly selected light bulb will last at most 2000 hours? 278 Georgia Notetaking Guide, Mathematics 2 Copyright McDougal Littell/Houghton Mifflin Company.

25 7.5 Select and Draw Conclusions from Samples Georgia Performance Standard(s) MM2D1a Your Notes Goal p Study different sampling methods for collecting data. VOCABULARY Population Sample Unbiased sample Biased sample Population mean Margin of error MARGIN OF ERROR FORMULA When a random sample of size n is taken from a large population, the margin of error is approimated by: Margin of error 5 6 This means that if the percent of the sample responding a certain way is p (epressed as a decimal), then the percent of the population that would respond the same way is likely to be between p 2 and p 1. Copyright McDougal Littell/Houghton Mifflin Company. Georgia Notetaking Guide, Mathematics 2 279

26 Your Notes Eample 1 Classify samples Assemblies A student wants to survey everyone at his school about the quality of the school's assemblies. Identify the type of sample described as a self-selected sample, a systematic sample, a convenience sample, or a random sample. a. The student surveys every 8th student that enters the assembly. b. From a random name lottery, the student chooses 125 students and teachers to survey Solution a. The student uses a rule to select students, so the sample is a sample. b. The student chooses from a random name lottery, so the sample is a sample. Checkpoint Identify the type of sample described. 1. A local mayor wants to survey local area registered voters. She mails surveys to the individuals that are members of her political party and uses only the surveys that are returned. Eample 2 Identify biased solutions Tell whether each sample in Eample 1 is biased or unbiased. Eplain your reasoning. Solution a. The sample is because the student surveys the students, but not the teachers. b. The sample is because both students and teachers are surveyed. 280 Georgia Notetaking Guide, Mathematics 2 Copyright McDougal Littell/Houghton Mifflin Company.

27 Your Notes Eample 3 Find a margin of error Newspaper Survey In a survey of 325 students and teachers, 30% said they read the school's newspaper every weekday. (a) What is the margin of error for the survey? (b) Give an interval that is likely to contain the eact percent of all students and teachers who read the school's newspaper every weekday. Solution a. Margin of error } Ï } n 56 1 ø The margin of error for the survey is about %. b. To find the interval, add and subtract %. 30% 2 % 5 % 30% 1 % 5 % It is likely that the eact percent of all students and teachers who read the school's newspaper every weekday is between % and %. Checkpoint Complete the following eercises. 2. Tell whether the sample in Eercise 1 is biased or unbiased. Eplain your reasoning. Homework 3. In Eample 3, suppose the sample size is 400 students and teachers. What is the margin of error for the survey? Copyright McDougal Littell/Houghton Mifflin Company. Georgia Notetaking Guide, Mathematics 2 281

28 Name Date LESSON 7.5 Practice Identify the type of sample described. Then tell if the sample is biased. Eplain your reasoning. 1. A gym is conducting a survey to find out how often members attend the gym each week. A gym employee asks every other person attending the gym on a particular weekend. 2. A clothing store wants to know the favorite seasons of its customers. Surveys are placed on a table for customers to fill out as they enter the store. 3. A company wants to know how often its employees use the company s cafeteria for lunch. The company asks employees that have just finished eating lunch in the cafeteria on Friday. Find the margin of error for a survey that has the given sample size. Round your answer to the nearest tenth of a percent Georgia Notetaking Guide, Mathematics 2 Copyright McDougal Littell/Houghton Mifflin Company.

29 Name Date LESSON 7.5 Practice continued Find the sample size required to achieve the given margin of error. Round your answer to the nearest whole number % % % % % % In Eercises 19 and 20, use the following information. Television In a survey of 705 people, 14% said that they watch television more than 12 hours per week. 19. What is the margin of error for the survey? Round your answer to the nearest tenth of a percent. 20. Give an interval that is likely to contain the eact percent of all people who watch television more than 12 hours per week. Copyright McDougal Littell/Houghton Mifflin Company. Georgia Notetaking Guide, Mathematics 2 283

30 7.6 Sample Data and Populations Georgia Performance Standard(s) MM2D1a, MM2D1d Your Notes Goal Eample 1 p Collect sample data from populations. Collect data by randomly sampling A gym has 467 female members and 732 male members. The marketing director of the gym wants to form a random sample of 30 female members and a separate random sample of 60 male members to answer some survey questions. Each female member has a membership number from 1 to 467 and each male member has a membership number from 1001 to Use a graphing calculator to select the members who will participate in each random sample. Random sample of female members: Using the random integer feature of a graphing calculator to generate random integers between and produces the following sample answer. The random sample of female members have membership numbers. Random sample of male members: Using the random integer feature of a graphing calculator to generate random integers between and produces the following sample answer. The random sample of male members have membership numbers. Checkpoint Complete the following eercise. 1. In Eample 1, suppose there are 245 female members and 532 male members. The marketing director wants to form a random sample of 12 female members and a separate random sample of 15 male members. Use a graphing calculator to select the members who will participate in each random sample. 284 Georgia Notetaking Guide, Mathematics 2 Copyright McDougal Littell/Houghton Mifflin Company.

31 Your Notes Eample 2 Compare statistics and parameters A company wants to know how many minutes it takes their employees to drive to work each day. Gillian and Ted, two employees, collect separate random samples. Their results are displayed below. The population mean is 18.4 and the population standard deviation is about Compare the means and standard deviations of the random samples to the population parameters. Gillian 10, 8, 20, 42, 5, 32, 8, 9, 17, 27 Ted 23, 18, 6, 47, 23, 31, 10, 13, 7, 3, 14, 55, 25, 19, 23 Solution Gillian: } Ted: } }}}}} Gillian: s 5 Î ø }}}}} Ted: s 5 Î ø The mean of Gillian's sample is the population mean, while the mean of Ted's sample is the population mean. The standard deviations of both samples are the population standard deviation. Checkpoint Complete the following eercise. Homework 2. In Eample 2, suppose the population mean is 14.5 and the population standard deviation is Compare the means and standard deviations of the random samples to the population parameters. Copyright McDougal Littell/Houghton Mifflin Company. Georgia Notetaking Guide, Mathematics 2 285

32 Name Date LESSON 7.6 Practice In Eercises 1 6, use a graphing calculator to generate five random integers in the given range to to to to to to 1765 For a large population, the mean is 11.2 and the standard deviation is about 8.4. Compare the mean and standard deviation of the random sample to the population parameters. 7. Random Sample A 14, 28, 19, 11, 14, 25, 27, 8, 22, Random Sample B 15, 7, 3, 11, 20, 5, 20, 1, 18, 9 9. Random Sample C 1, 28, 26, 8, 22, 8, 4, 22, 7, 18, 25, Movies Two students want to know the number of DVDs owned by each student in their school. Jake and Juan collect separate random samples. The population mean is 14.3 and the population standard deviation is about 6.7. Compare the means and standard deviations of the random samples to the population parameters. Jake 15, 3, 13, 20, 11, 25, 22, 1, 12, 12, 7, 6, 8, 24, 14, 10, 22, 29, 22, 4, 12, 18, 18, 11, 7 Juan 9, 27, 6, 16, 10, 22, 29, 28, 20, 21, 1, 4, 24, 12, 16, 15, 28, 12, 6, 13, 30, Georgia Notetaking Guide, Mathematics 2 Copyright McDougal Littell/Houghton Mifflin Company.

33 7.7 Choose the Best Model for Two-Variable Data Georgia Performance Standard(s) MM2D2a, MM2D2c Your Notes Goal Eample 1 p Choose the best model to represent a set of data. Use a linear model Teachers' Salaries The table shows the teacher's salary y (in dollars) for a certain school district, where is the number of years of teaching eperience. Use a graphing calculator to find a model for the data y 30,624 32,436 34,167 35, y 37,684 39,311 41, Make a scatter plot. The points lie approimately on a. This suggests a model. 2. Use the regression feature to find an equation of the model. 3. Graph the model along with the data to verify that the model fits the data well. A model for the data is y 5. Checkpoint Complete the following eercise. 1. Use a graphing calculator to find a model for the data. Then graph the model and the data in the same coordinate plane. y y y Copyright McDougal Littell/Houghton Mifflin Company. Georgia Notetaking Guide, Mathematics 2 287

34 Your Notes Eample 2 Use a quadratic model Roller Coaster Riders A manager at a local amusement park kept a record of the number of people who ride the most popular roller coaster at the park. The table shows the number of people y who rode the roller coaster hours after the park had opened. Use a graphing calculator to find a model for the data y Solution 1. Make a scatter plot. The points form an. This suggests a model. 2. Use the regression feature to find an equation of the model. 3. Graph the model along with the data to verify that the model fits the data well. A model for the data is y 5. Checkpoint Complete the following eercise. 2. Use a graphing calculator to find a model for the data. Then graph the model and the data in the same coordinate plane y y Homework Georgia Notetaking Guide, Mathematics 2 Copyright McDougal Littell/Houghton Mifflin Company.

35 Name Date LESSON 7.7 Practice Use a graphing calculator to find the equation that best models the data y y y y y Drive-Thru Banking A bank records the length of time y (in minutes) that a customer has to wait each hour before getting service at the drive-thru window. The bank provides drive-thru service from 9:00 A.M. to 4:30 P.M. ( 5 1 represents 9:00 A.M.) Use the regression feature of a graphing calculator to find a model for the data. If the bank etended its drive-thru hours, how long would a customer have to wait at 5:00 P.M.? Round your answer to the nearest whole minute y Copyright McDougal Littell/Houghton Mifflin Company. Georgia Notetaking Guide, Mathematics 2 289

36 Words to Review Give an eample of the vocabulary word. Scatter plot Positive correlation Negative correlation Correlation coefficient Best-fitting line Linear regression 290 Georgia Notetaking Guide, Mathematics 2 Copyright McDougal Littell/Houghton Mifflin Company.

37 Median-median line Algebraic model Inference Quadratic regression Best-fitting quadratic model Curve fitting Statistics Measure of central tendency Mean: Median: Mode: Measure of dispersion Normal distribution Range: Standard deviation: Copyright McDougal Littell/Houghton Mifflin Company. Georgia Notetaking Guide, Mathematics 2 291

38 Normal curve Standard normal distribution z-score Population Sample Unbiased sample Biased sample Population mean Margin of error 292 Georgia Notetaking Guide, Mathematics 2 Copyright McDougal Littell/Houghton Mifflin Company.