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Answers to Exercises

 

Contents

Accuracy and Scientific Notation

Comparing Modified Boxplots

Computing Formula Values

Coefficients of Determination and Correlation

Grouped Data

Histogram Analysis

Outliers and Influential Observations

Parameters and Statistics

Qualitative vs. Quantitative

 

Accuracy and Scientific Notation

1) 0 places, 3 sig. digits, 5.42 x 104

2) 0 places, 5 sig. digits, 1.7846 x 108

3) 7 places, 4 sig. digits, 2.314 x 10-4

4) 5 places, 3 sig. digits, 9.80 x 10-3

5) 3 places, 6 sig. digits, 1.32502 x 102

6) 2 places, 4 sig. digits, 3.741 x 101

7) 4 places, 4 sig. digits, 3.473 x 10-1

8) 1 place, 5 sig. digits, 1.4453 x 103

9) 4.897

10) 245.12

11) 83.1

12) 0.432

13) 110

14) 27.34

15) 539,500

16) 4,390,000

17) 0.00435

18) 0.0006288

19) 57,789

20) 312,200

21) 0.008324

22) 0.0000769

 

 

Comparing Modified Boxplots

1)

8 AM is more skewed, 9 AM has largest value, 9 AM has smallest value,

8 AM has largest median, 9 AM has largest range, 9 AM has largest IQR

2)

11 AM is more skewed, 10 AM has largest value, 11 AM has smallest value,

10 AM has largest median, the ranges are the same and 11 AM has largest IQR.

3)

1 PM is more skewed, the largest values are about the same, 2 PM has the smallest value,

1 PM has largest median, 2 PM has the largest range and largest IQR.

4)

3 PM is more skewed, 3 PM has largest value, 4 PM has smallest value,

3 PM has largest median, 4 PM has the largest range and IQR.

5)

5 PM is more skewed, 5 PM has largest value, 6 PM has smallest value,

5 PM has largest median, 5 PM has the largest range, the IQR's are about the same.

 

Computing Formula Values

1) 74.08

2) 55.73

3) 0.4733

4) 0.1475

5) 2.72

6) -0.85

7) -0.7171

8) 0.7191

9) 1,637,000

10) 265,400

11) 295.6

12) 94.88

 

Coefficients of Determination and Correlation

1) 45.2% of the variation is explained by the regression line.

2) 91.3% of the variation is explained by the regression line.

3) 72.1% of the variation is explained by the regression line.

4) 26.4% of the variation is explained by the regression line.

5) weak positive correlation

6) no correlation

7) strong positive correlation

8) perfect negative correlation

9) moderate positive correlation

10) moderate negative correlation

11) no correlation

12) strong negative correlation

 

Grouped Data

1) mean = 32.2, std. dev. = 11.1

2) mean = 10.7, std. dev. = 9.6

3) mean = 15.6, std. dev. = 10.8

4) mean = 21.1, std. dev. = 11.7

5) mean = 44.0, std. dev. = 10.6

6) mean = 80.5, std. dev. = 8.1

7) mean = 36.8, std. dev. = 7.6

8) mean = 31.6, std. dev. = 5.2

 

Histogram Analysis

1)

minimum = 18, maximum = 60, skewed left, one peak at 45,one gap between 24 and 30, no extreme values

2)

minimum = 12, maximum = 108, skewed left, two peaks at 54 and 90, one gap between 24 and 36, no extreme values

3)

minimum = 0, maximum = 500, skewed right, one peak at 25,

3 gaps: between 100 and 150, between 200 and 250, and between 300 and 400. Since the last gap is twice as large, values between 400 and 500 are extreme.

4)

minimum = 15, maximum = 40, skewed right, two peaks at 27.5 and 37.5 (but the second peak is barely a peak), no gaps or extreme values.

 

Outliers and Influential Observations

1) outlier near (12.9, 24.4), influential observation near (9.9, 16.1)

2) outlier near (112, 86), influential observation near (129, 121)

3) outlier near (53, 88), influential observations near (68, 108) and (76, 111)

 

Parameters and Statistics

1)

The parameter is the average height of all women aged 20 years or older.

The statistic is the average height of 63.9 inches from the sample of 45 women.

2)

The parameter is the mean amount of sodium consumed by children under the age of ten.

The statistic is the mean of 2993 milligrams of sodium obtained from the sample of 75 children.

3)

The parameter is the proportion of patients healed by Nexium in 8 weeks.

The statistic is 213/224 = 0.951, the proportion healed in the sample.

4)

The parameter is the average farm size in Kansas.

The statistic is the mean farm size of 731 acres from the sample of 40 farms.

5)

The parameter is the average oil output per well in the United States.

 

The statistic is the mean oil output of 10.7 barrels per day from the sample of 50 wells.

6)

The parameter is the proportion of adults 18 or older who read a book in the previous year.

 

The statistic is 835/1006 = 0.830, the proportion who read a book in the sample.

7)

The parameter is the average amount of calcium that male teenagers consume.

 

The statistic is the mean of 1081 milligrams of calcium from the sample of 50 teenagers.

8)

The parameter is the proportion of adults with kids under 18 who ate together 7 days a week.

 

The statistic is 337/1122 = 0.300, the proportion in the sample who ate together.

9)

The parameter is the mean verbal SAT score for students whose first language is not English.

 

The statistic is the mean SAT verbal score of 458 from the sample of 20 students.

 

Qualitative vs. Quantitative

1)

Name - designator, Height - quantitative, River - qualitative,

State - qualitative, Completed - quantitative

2)

No. - designator, Year - designator, Winner - qualitative,

Winning Score - quantitative, Loser - qualitative, Losing Score - quantitative, Winning Coach - qualitative, Game Site - qualitative

 

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