Draw Scatter Plots and Best-Fitting Lines

Copyright © McDougal Littell/Houghton Mifflin Company. Georgia Notetaking Guide, Mathematics 2 255

7.1 Draw Scatter Plots and Best-Fitting LinesGoal p Fit lines to data in scatter plots.Georgia

PerformanceStandard(s)

MM2D2a, MM2D2b, MM2D2d

Your Notes

VOCABULARY

Scatter plot

Positive correlation

Negative correlation

Correlation coefficient

Best-fitting line

Linear regression

Median-median line

Algebraic model

Inference

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256 Georgia Notetaking Guide, Mathematics 2 Copyright © McDougal Littell/Houghton Mifflin Company.

Your Notes

Describe the data as having a positive correlation, a negative correlation, or approximately no correlation. Tell whether the correlation coefficient for the data is closest to 21, 20.5, 0, 0.5, or 1.

a.

x

y

1

1

b.

x

y

1

1

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 .

Example 1 Describe and estimate correlation coefficients

1.

x

y

1

1

2.

x

y

1

1

Checkpoint For the scatter plot, (a) tell whether the data has a positive correlation, a negative correlation,or approximately no correlation, and (b) tell whether the correlation coefficient for the data is closest to 21, 20.5, 0, 0.5, or 1.

ga2nt-07.indd 153 4/16/07 9:04:04 AM



Your Notes

The table below gives the number of people y who attended each of the first seven football games x of the season. Approximate the best-fitting line for the data.

x 1 2 3 4 5 6 7

y 722 763 772 826 815 857 897

1. Draw a .

4 65 7

6500

700

750

800

850

900

x

y

Nu

mb

er

of

pe

op

le

Football game

2 310

2. Sketch the best-fitting line.

3. Choose two points on the line. For the scatter plot shown, you might choose (1, ) and (2, ).

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 y1 5 m(x 2 x1) Point-slope form

y 2 5 Substitute for m, x1, and y1.

y 5 Simplify.

An approximation of the best-fitting line is y 5 .

Example 2 Approximate the best-fitting line

3. The table gives the average class score y on each chapter test for the first six chapters x of the textbook.

x 1 2 3 4 5 6

y 84 83 86 88 87 90

a. Approximate the best-fitting line for the data.

b. Use your equation from part (a) to4 65

820

84

86

88

90

x

y

Ave

rag

e c

lass s

co

re

Test

2 310

predict the average class score on the chapter 9 test.

Checkpoint Complete the following exercise.

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Your Notes

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

8 1210 14

200

25

30

35

40

45

50

55

60

65

x

y

4 620

the -values are in order from least to greatest. Then separate the coordinates into three equal sized groups.

Step 2 Find the median x-valuesand the median y-values for each group.

Median MedianGroup x-values y-values x-values y-values

1 1, , 3 , 34, 40

2 5, 6, 35, 60,

3 , 10, 11 45, , 60

Step 3 Create a summary point for each group by combining the median x-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 5 5 5

y 2 5 (x 2 )

y 5

Example 3 Find a median-median line

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Your Notes

Step 5 Move the equation one-third

8 1210 14

200

25

30

35

40

45

50

55

60

65

x

y

4 62

of the way toward the middle summary point.

Middle summary point: ( )

Predicted value at x 5 :y 5 2( ) 1 30 5

One-third of the difference between y 5 and

y 5 : 1}3 ( 2 ) 5

New equation: y 5 2x 1 30 1 5 2x 1

The equation of the median-median line is .

Example 4 Find a median-median line (continued)

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

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Tell whether x and y have a positive correlation, a negative correlation, or approximately no correlation.

1.

x

y

1

1

2.

x

y

1

1

3.

x

y

1

1

Draw a scatter plot of the data. Tell whether the data have a positive correlation, a negative correlation, or approximately no correlation.

4. x 1 2 3 4 5

y 4 5 4 3 3

x 6 7 8 9 10

y 2 3 2 1 1

x

y

1

2

5. x 1 2 3 4 5

y 7 4 23 2 1

x 6 7 8 9 10

y 24 8 0 21 5

x

y

2

2

6. x 1 2 3 4 5

y 3 2 3 4 6

x 6 7 8 9 10

y 8 7 10 13 13

x

y

2

2

7. x 1 2 3 4 5

y 7 22 1 5 0

x 6 7 8 9 10

y 8 2 21 0 6

x

y

2

2

LESSON

7.1 Practice

Name ——————————————————————— Date ————————————



Name ——————————————————————— Date ————————————

LESSON

7.1 Practice continued

Approximate the best-fi tting line for the data.

8.

x

y

1.0

0.5

9. y

x

0.5

0.5

10. Household Size The table shows the average household size y in the United States from 1930 to 2000. Draw a scatter plot of the data and describe the correlation shown. Let t represent the number of years since 1930.

Year, t 0 10 20 30 40 50 60 70

Household size, y 4.11 3.67 3.37 3.35 3.14 2.76 2.63 2.62

0 2010 30 40 50 60 70 800

2.00

2.50

3.00

3.50

4.00

4.50

5.00

Years since 1930

Ho

useh

old

siz

e

11. Household Size Model Use the linear regression feature of a graphing calculator to approximate the best-fi tting line for the data in Exercise 10.

12. Household Size Prediction Using the model from Exercise 11, predict the average household size in 2030.

13. Find the equation of the median-median line for the data.

x 1 2 3 5 6 7 9 10 11

y 74 30 90 61 50 80 100 80 90



7.2 Write Quadratic Functions and ModelsGoal p Write quadratic functions and models.Georgia


MM2D2a, MM2D2c

Your Notes

VOCABULARY

Quadratic regression

Best-fitting quadratic model

Curve fitting

Write a quadratic function whose graph has vertex (22, 23) and passes through the point (0, 5).

Solutiony 5 a(x 2 h)2 1 k Vertex form

y 5 a(x )2 Substitute for h and k.

Use the point ( , ) to find a.

5 a( )2 Substitute for x and y.

5 a Solve for a.

A quadratic function for the parabola is .

Example 1 Write a quadratic function in vertex form

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Your Notes

Write a quadratic function whose graph has x-intercepts23 and 2, and passes through the point (22, 24).

Solutiony 5 a(x 2 p)(x 2 q) Intercept form

y 5 a(x )(x ) Substitute for p and q.

Use the point (22, 24) to find a.

5 a( )( ) Substitute for x and y.

5 a Solve for a.


Example 2 Write a quadratic function in intercept form

1. Write a quadratic function whose graph has vertex (2, 1) and passes through the point (0, 4).


2. Write a quadratic function whose graph has x-intercepts 24 and 2, and passes through the point (3, 21).


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Your Notes

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 ax2 1 bx 1 c to obtain a system of three equations.

5 a( )2 1 b( ) 1 c Substitute for x and y.5 Equation 1



Rewrite the system as a system of two equations.

5 Substitute for c.5 Revised Equation 15 Substitute for c.5 Revised Equation 3

Solve the system consisting of revised Equations 1 and 3.

Revised Equation 1Revised Equation 3Add equations.

a 5 Solve for a.

So, 5 , which means b 5 .


Example 3 Write a quadratic function in standard form

Substitute 6 for cin Equation 1.

Substitute 6 for cin Equation 3.

3. Write a quadratic function in standard form for the parabola that passes through the points (21, 25), (2, 1), and (3, 21).


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Your Notes

Baseball The table shows the height of a baseball that is hit, with x 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, x 0 2 4 6 8

Height, y 3 28 40 37 26

Enter the data into two lists Make a scatter plot of of a graphing calculator. the data.

L1 L2 L30 32 284 406 378 26

L1(1)=0

Use the quadratic regression Check how well the model fits the data by graphing the model and the data in the same viewing window.

model feature to find the best-fitting quadratic model for the data.

QuadReg

y 5 ax2 1 bx 1 c

a 5

b 5

c 5

The best-fitting quadratic model is

.

Example 4 Best-fitting quadratic model for data

4. Use a graphing calculator to find the best-fitting model for the data in the table.

Time, x 0 2 4 6 8

Height, y 4 23 30 25 7


Homework

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Write a quadratic function in vertex form whose graph has the given vertex and passes through the given point.

1. vertex: (2, 0) 2. vertex: (1, 23) 3. vertex: (22, 2)

point: (3, 1) point: (0, 21) point: (0, 0)

Write a quadratic function in intercept form whose graph has the given x–intercepts and passes through the given point.

4. x-intercepts: 1, 4 5. x-intercepts: 23, 2 6. x-intercepts: 25, 0

point: (2, 26) point: (22, 24) point: (21, 8)

LESSON

7.2 Practice

Name ——————————————————————— Date ————————————



Name ——————————————————————— Date ————————————

LESSON


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 Exercises 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 2008. Assume that t represents the number of years since 2003.

Year, t 0 1 2 3 4 5

Participants, y 24 28 33 41 54 74

10. Use a graphing calculator to fi nd the best-fi tting quadratic model for the data.

11. Using the model, how many participants are projected for 2011?



7.3 Find Measures of Central Tendency and DispersionGoal p Describe data using statistical measures.Georgia


MM2D1b, MM2D1c

Your Notes

VOCABULARY

Statistics

Measure of central tendency

Mean

Median

Mode

Measure of dispersion

Range

Standard deviation

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Your Notes

Find the mean, median, and mode of Quiz Scores

19, 15, 22,17, 21, 17,25, 18, 17

the data set.

Solution

To find the mean, divide the sum of the scores by the number of scores.

}x 5 5 5

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, , because this number occurs most frequently.

Example 1 Find measures of central tendency

STANDARD DEVIATION OF A DATA SET

The standard deviation s (read as “sigma”) of x1, x2, . . . , xn is:

s 5 Î}}}}

}}}}n

Find the range and standard deviation for the quiz scores in Example 1.

Solution

To find the range, subtract the least data value from the greatest data value.

Range 5 2 5

To find the standard deviation, substitute the scores and the mean into the formula.

s 5 Î}}}}}

}}}}}

ø

Example 2 Find measures of dispersion

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Your Notes

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, 13Club B: 17, 10, 22, 15, 14, 19, 4, 8, 12, 22, 20, 5

Solution

Club A: Mean: }x 5 5 5

Std. Dev.:

s 5 Î}}}}

}}}}

ø

Club B: Mean: }x 5 5 5

Std. Dev.:

s 5 Î}}}}

}}}}

ø

Athletic Club has a greater mean and a greater standard deviation than Athletic Club .

Example 3 Compare data sets

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.


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Your Notes

2. Find the range and standard deviation of the data set in Exercise 1.

3. Compare the means and standard deviations of Set A and Set B.

Set A 4 7 5 9 10

Set B 2 6 5 4 3

Checkpoint Complete the following exercises.

Homework

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Find the mean, median, and mode of the data set.

1. 1, 6, 3, 9, 6, 8, 4, 4, 4 2. 1, 5, 6, 2, 6, 1, 7, 6, 2

3. 17, 13, 12, 12, 13, 16, 12, 13, 14, 10 4. 12, 14, 11, 15, 14, 18, 9, 11, 13, 10

Find the range and standard deviation of the data set.

5. 12, 8, 17, 15, 12, 14 6. 17, 14, 24, 21, 30, 20

7. 22, 24, 31, 34, 23, 27, 21 8. 31, 46, 39, 43, 32, 35, 40

In Exercises 9 and 10, fi nd 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, 9

10. 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, 16

LESSON

7.3 Practice

Name ——————————————————————— Date ————————————



Name ——————————————————————— Date ————————————

LESSON


In Exercises 11 and 12, fi nd 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, 20

12. Hockey The data set below gives the numbers of goals for the 10 players who scored the most goals during the 2003–2004 National Hockey League regular season.

41, 41, 41, 38, 38, 36, 35, 35, 34, 33

13. 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



7.4 Use Normal DistributionsGoal p Study normal distributions.Georgia


MM2D1d

Your Notes

VOCABULARY

Normal distribution

Normal curve

Standard normal distribution

z-score

AREAS UNDER A NORMAL CURVE

A normal distribution with mean }x 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.

x2

3s

x2

2s

x2

s x

x1

s

x1

2s

x1

3s

68%

95%

99.7%

x2

3s

x2

2s

x2

s x

x1

s

x1

2s

x1

3s

2.35% 2.35%

0.15% 0.15%

13.5% 13.5%

34% 34%

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Your Notes

A normal distribution has mean

x2

3s

x2

2s

x2

s x

x1

s

x1

2s

x1

3s

}x and standard deviation s. For a randomly selected x-value from the distribution, find P(}x 2 s ≤ x ≤ }x 1 2s).

SolutionThe probability that a randomly selected x-value lies between and is the shaded area under the normal curve. Therefore:

P(}x 2 s ≤ x ≤ }x 1 2s) 5 1 1

5

Example 1 Find a normal probability

1. A normal distribution has mean }x and standard deviation s. For a randomly selected x-value from the distribution, find P(x ≤ }x 2 s).


Math Scores The math scores of an

169 278 387 496 605 714 823

exam 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 %.

Example 2 Interpret normally distributed data

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Your Notes

2. In Example 2, what percent of the test-takers received scores between 496 and 714?

3. In Example 3, find the probability that a randomly selected test-taker received a math score of at most 620.


Homework

In Example 2, find the probability that a randomly selected test-taker received a math score of at most 630.

SolutionStep 1 Find the z-score corresponding to an x-value

of 630.

z 5x 2 }x}

s5 ø

Step 2 Use the standard normal table to findP(x ≤ 630) ø P(z ≤ ).

z .0 .1 .2

23 .0013 .0010 .0007

22 .0228 .0179 .0139

21 .1587 .1357 .1151

20 .5000 .4602 .4207

0 .5000 .5398 .5793

1 .8413 .8643 .8849

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 .

Example 3 Use a z-score and the standard normal table

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Name ——————————————————————— Date ————————————

LESSON

7.4 PracticeA normal distribution has mean } x and standard deviation s. Find the indicated probability for a randomly selected x–value from the distribution.

1. P(x ≥ } x 2 s) 2. P(x ≤ } x 1 3s) 3. P(x ≤ } x 2 3s)

Give the percent of the area under the normal curve represented by the shaded region.

4.

s

x 2

3

s

x 2

2

s

x 2

x s

x 1

s

x 1

2

s

x 1

3

5.

s

x 2

3

s

x 2

2s

x 2

x s

x 1

s

x 1

2

s

x 1

3A normal distribution has a mean of 25 and a standard deviation of 5. Find the probability that a randomly selected x–value from the distribution is in the given interval.

6. Between 25 and 30 7. Between 15 and 25 8. Between 20 and 35

9. At least 20 10. At least 40 11. At most 15



A normal distribution has a mean of 75 and a standard deviation of 10. Use the standard normal table of your textbook to fi nd the indicated probability for a randomly selected x–value from the distribution.

12. P(x ≤ 75) 13. P(x ≤ 85) 14. P(x ≤ 55)

15. P(x ≤ 87) 16. P(x ≤ 69) 17. P(x ≤ 45)


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?


Light Bulbs A company produces light bulbs having a life expectancy 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 expectancy of 2000 hours.

21. What is the probability that a randomly selected light bulb will last at most 2000 hours?

LESSON


Name ——————————————————————— Date ————————————



7.5 Select and Draw Conclusions from SamplesGoal p Study different sampling methods for

collecting data.

GeorgiaPerformanceStandard(s)

MM2D1a

Your NotesVOCABULARY

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 approximated by:

Margin of error 5 6

This means that if the percent of the sample responding a certain way is p (expressed 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 .

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Your Notes

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-selectedsample, 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

Solutiona. 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.

Example 1 Classify samples

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.

Checkpoint Identify the type of sample described.

Tell whether each sample in Example 1 is biased or unbiased. Explain 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.

Example 2 Identify biased solutions

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Your Notes

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 exact percent of all students and teachers who read the school's newspaper every weekday.

Solution

a. Margin of error 5 61

}Ï

}

n5 6

1ø

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 exact percent of all students and teachers who read the school's newspaper every weekday is between % and %.

Example 3 Find a margin of error

2. Tell whether the sample in Exercise 1 is biased or unbiased. Explain your reasoning.

3. In Example 3, suppose the sample size is 400 students and teachers. What is the margin of error for the survey?


Homework

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Identify the type of sample described. Then tell if the sample is biased. Explain your reasoning.

1. A gym is conducting a survey to fi nd 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 fi ll 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 fi nished 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.

4. 375 5. 7000 6. 120

7. 3200 8. 385 9. 4500

10. 705 11. 85 12. 5005

LESSON

7.5 Practice

Name ——————————————————————— Date ————————————



Name ——————————————————————— Date ————————————

LESSON


Find the sample size required to achieve the given margin of error. Round your answer to the nearest whole number.

13. 64% 14. 63% 15. 63.6%

16. 65.5% 17. 60.6% 18. 68.1%


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 exact percent of all people who watch television more than 12 hours per week.



7.6 Sample Data and PopulationsGeorgiaPerformanceStandard(s)

MM2D1a, MM2D1d

Your Notes

Goal p Collect sample data from populations.

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 1732. 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

.

Example 1 Collect data by randomly sampling

1. In Example 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.


ga2nt-07.indd 171 4/16/07 9:04:19 AM



Your Notes

2. In Example 2, suppose the population mean is 14.5 and the population standard deviation is 10.4. Compare the means and standard deviations of the random samples to the population parameters.


Homework

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 15.6. Compare the means and standard deviations of the random samples to the population parameters.

Gillian10, 8, 20, 42, 5, 32, 8, 9, 17, 27

Ted23, 18, 6, 47, 23, 31, 10, 13, 7, 3, 14, 55, 25, 19, 23

Solution

Gillian: }x 5 5 5

Ted: }x 5 5 5

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.

Example 2 Compare statistics and parameters

ga2nt-07.indd 172 4/16/07 9:04:20 AM



In Exercises 1–6, use a graphing calculator to generate fi ve random integers in the given range.

1. 1 to 100 2. 200 to 400 3. 101 to 450

4. 25 to 1000 5. 60 to 70 6. 1001 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 A14, 28, 19, 11, 14, 25, 27, 8, 22, 15

8. Random Sample B15, 7, 3, 11, 20, 5, 20, 1, 18, 9

9. Random Sample C

1, 28, 26, 8, 22, 8, 4, 22, 7, 18, 25, 29

10. 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.

Jake15, 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, 8

LESSON

7.6 Practice

Name ——————————————————————— Date ————————————



7.7 Choose the Best Model for Two-Variable DataGoal p Choose the best model to represent a set of data.Georgia


MM2D2a, MM2D2c

Your Notes

Teachers' Salaries The table shows the teacher's salary y (in dollars) for a certain school district, where x is the number of years of teaching experience. Use a graphing calculator to find a model for the data.

x 1 2 3 4

y 30,624 32,436 34,167 35,989

x 5 6 7

y 37,684 39,311 41,098

1. Make a scatter plot. The points lie approximately 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 .

Example 1 Use a linear model

1. Use a graphing calculator to find

x

y

10

1

a model for the data. Then graph the model and the data in the same coordinate plane.

x 0 1 2 3

y 2 9 19 29

x 4 5 6 7

y 40 51 61 73


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Your Notes

Homework

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 x hours after the park had opened. Use a graphing calculator to find a model for the data.

x 0 2 4 6 8 10 12

y 85 163 282 341 398 381 304

Solution1. 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 .

Example 2 Use a quadratic model

2. Use a graphing calculator to find a model for the data. Then graph the model and the data in the same coordinate plane.

x 0 2 4 6 8 10 12

y 100 178 273 314 349 324 289

x

y

40

2


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Name ——————————————————————— Date ————————————

LESSON

7.7 PracticeUse a graphing calculator to fi nd the equation that best models the data.

1. x 1 2 3 4 5 6 7

y 2 3 5 6 8 9 11

2. x 2 5 7 10 12 14 18

y 21 29 35 40 37 32 23

3. x 1 2 3 4 5 6 7

y 5 11 20 31 42 56 65

4. x 5 10 15 20 25 30 35

y 22 31 44 65 86 104 123

5. x 3 6 10 15 18 22 27

y 2 3 4 7 9 13 21

6. 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. (x 5 1 represents 9:00 A.M.) Use the regression feature of a graphing calculator to fi nd a model for the data. If the bank extended 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.

x 1 2 3 4 5 6 7 8

y 3 5 6 8 7 8 8 9



Words to ReviewGive an example of the vocabulary word.

Scatter plot

Negative correlation

Best-fitting line

Positive correlation

Correlation coefficient

Linear regression

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Median-median line

Inference

Best-fitting quadratic model

Statistics

Measure of dispersion

Range:

Standard deviation:

Algebraic model

Quadratic regression

Curve fitting

Measure of central tendency

Mean:

Median:

Mode:

Normal distribution

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Normal curve

z-score

Sample

Biased sample

Margin of error

Standard normal distribution

Population

Unbiased sample

Population mean

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Draw Scatter Plots and Best-Fitting Lines

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