# Statistics Problems - 4 problems, statistics homework help

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ynooengg

Mathematics

## Description

Complete the problems below .

1. Chapter 13 – Problem 63
2. Chapter 13 – Problem 64
3. Chapter 14 – Problem 35
4. Chapter 14 Case A – Century National Bank

For problems requiring computations, please ensure that your Excel file includes the associated cell computations and/or statistics output.

Submit output in one Excel file.

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Team League X1 X2 Opened Seating Capacity X3 X4 Salary 2012 X5 Arizona Diamondbacks 0 1998 48633 74.3 Atlanta Braves 0 1996 49586 83.3 Baltimore Orioles 1 1992 45971 81.4 Boston Red Sox 1 1912 37495 173.2 Chicago Cubs 0 1914 41009 88.2 Chicago White Sox 1 1991 40615 96.9 Cincinnati Reds 0 2003 42319 82.2 Cleveland Indians 1 1994 43429 78.4 Colorado Rockies 0 1995 50398 78.1 Detroit Tigers 1 2000 41255 132.3 Houston Astros 0 2000 40981 60.7 Kansas City Royals 1 1973 37903 60.9 Los Angeles Angels 1 1966 45957 154.5 Los Angeles Dodgers 0 1962 56000 95.1 Miami Marlins 0 2012 36742 118.1 Milwaukee Brewers 0 2001 41900 97.7 Minnesota Twins 1 2010 39504 94.1 New York Mets 0 2009 41922 93.4 New York Yankees 1 2009 50287 198 Oakland Athletics 1 1966 35067 55.4 Philadelphia Phillies 0 2004 43651 174.5 Pittsburgh Pirates 0 2001 38362 63.4 San Diego Padres 0 2004 42691 55.2 San Francisco Giants 0 2000 41915 117.6 Seattle Mariners 1 1999 47860 82 St. Louis Cardinals 0 2006 43975 110.3 Tampa Bay Rays 1 1990 34078 64.2 Texas Rangers 1 1994 48194 120.5 Toronto Blue Jays 1 1989 49260 75.5 Washington Nationals 0 2008 41487 81.3 Wins Attendance BA ERA HR Errors SB X6 X7 X8 X9 X 10 X 11 X 12 81 2.18 0.259 3.93 165 90 93 94 2.42 0.247 3.42 149 86 101 93 2.1 0.247 3.9 214 106 58 69 3.04 0.26 4.7 165 101 97 61 2.88 0.24 4.51 137 105 94 85 1.97 0.255 4.02 211 70 109 97 2.35 0.251 3.34 172 89 87 68 1.6 0.251 4.78 136 96 110 64 2.63 0.274 5.22 166 122 100 88 3.03 0.268 3.75 163 99 59 55 1.61 0.236 4.56 146 118 105 72 1.74 0.265 4.3 131 113 132 89 3.06 0.274 4.02 187 98 134 86 3.32 0.252 3.34 116 98 104 69 2.22 0.244 4.09 137 103 149 83 2.83 0.259 4.22 202 99 158 66 2.78 0.26 4.77 131 107 135 95 2.24 0.249 4.09 139 101 79 74 3.54 0.265 3.85 245 74 93 94 1.68 0.238 3.48 195 111 122 81 3.57 0.255 3.83 158 101 116 79 2.09 0.243 3.86 170 112 73 76 2.12 0.247 4.01 121 121 155 94 3.38 0.269 3.68 103 115 118 75 1.72 0.234 3.76 149 72 104 88 3.26 0.271 3.71 159 107 91 90 1.56 0.24 3.19 175 114 134 93 3.46 0.273 3.99 200 85 91 73 2.1 0.245 4.64 198 101 123 98 2.37 0.261 3.33 194 94 105 Average Salary 1989 \$512,930 1990 \$578,930 1991 \$891,188 1992 \$1,084,408 1993 \$1,120,254 1994 \$1,188,679 1995 \$1,071,029 1996 \$1,176,967 1997 \$1,383,578 1998 \$1,441,406 1999 \$1,720,050 2000 \$1,988,034 2001 \$2,264,403 2002 \$2,383,235 2003 \$2,555,476 2004 \$2,486,609 2005 \$2,632,655 2006 \$2,866,544 2007 \$2,944,556 2008 \$3,154,845 2009 \$3,240,206 2010 \$3,297,828 2011 \$3,305,393 2012 \$3,440,000 Frequency Distribution - Quantitative Maintenance lower 320 340 360 380 400 420 440 460 480 500 520 540 560 Percent Histogram 20 18 16 14 12 10 8 6 4 2 0 Maintenance Descriptive statistics count mean sample variance sample standard deviation minimum maximum range 1st quartile median 3rd quartile Maintenance 80 450.29 2,882.18 53.69 329 570 241 420.00 456.00 489.75 upper < < < < < < < < < < < < < 340 360 380 400 420 440 460 480 500 520 540 560 580 midpoint 330 350 370 390 410 430 450 470 490 510 530 550 570 width 20 20 20 20 20 20 20 20 20 20 20 20 20 frequency 3 3 1 8 5 12 12 15 7 8 1 3 2 80 interquartile range mode low extremes low outliers high outliers high extremes 69.75 329.00 0 0 0 0 Frequency Distribution - Quantitative Maintenance lower upper 300 350 400 450 500 550 < < < < < < 350 400 450 500 550 600 midpoint 325 375 425 475 525 575 width 50 50 50 50 50 50 frequency 3 12 22 29 11 3 80 midpoint 343 378 413 448 483 518 553 587 width 35 35 35 35 35 35 35 35 frequency 6 8 12 20 20 9 4 1 80 Histogram 40 35 Percent 30 25 20 15 10 5 0 Maintenance Frequency Distribution - Quantitative Maintenance lower 325 360 395 430 465 500 535 570 upper < < < < < < < < 360 395 430 465 500 535 570 605 Histogram 30 25 Percent 20 15 10 5 0 Maintenance Descriptive statistics count mean sample variance sample standard deviation minimum maximum range 1st quartile median 3rd quartile interquartile range mode Miles 80 827.53 1,188.20 34.47 741 908 167 806.00 827.00 851.50 45.50 815.00 low extremes low outliers high outliers high extremes 0 0 0 0 BoxPlot 1/28/2010 16:03.39 (1) 600 650 700 750 800 Miles 850 900 950 Descriptive statistics count mean sample variance sample standard deviation minimum maximum range 1st quartile median 3rd quartile interquartile range mode Miles 80 827.53 1,188.20 34.47 741 908 167 806.00 827.00 851.50 45.50 815.00 low extremes low outliers high outliers high extremes 0 0 0 0 BoxPlot 1/28/2010 16:06.08 (1) 600 650 700 750 800 850 900 950 850 900 950 Miles DotPlot 1/28/2010 16:06.08 (1) 600 650 700 750 800 Miles Descriptive statistics count mean sample variance sample standard deviation minimum maximum range Miles 80 830.11 1,779.85 42.19 741 1008 267 1st quartile median 3rd quartile interquartile range mode 806.00 827.00 851.50 45.50 815.00 low extremes low outliers high outliers high extremes 0 0 1 1 BoxPlot 1/28/2010 16:08.20 (1) 600 650 700 750 800 850 900 950 1000 1050 950 1000 1050 Miles DotPlot 1/28/2010 16:08.20 (1) 600 650 700 750 800 850 900 Miles Correlation Matrix Maintenance Age Miles Maintenance 1.000 .465 .450 Age Miles 1.000 .522 1.000 80 sample size ± .220 critical value .05 (two-tail) ± .286 critical value .01 (two-tail) percent 3.8 3.8 1.3 10.0 6.3 15.0 15.0 18.8 8.8 10.0 1.3 3.8 2.5 100.0 cumulative frequency percent 3 3.8 6 7.5 7 8.8 15 18.8 20 25.0 32 40.0 44 55.0 59 73.8 66 82.5 74 92.5 75 93.8 78 97.5 80 100.0 percent 3.8 15.0 27.5 36.3 13.8 3.8 100.0 percent 7.5 10.0 15.0 25.0 25.0 11.3 5.0 1.3 100.0 cumulative frequency percent 3 3.8 15 18.8 37 46.3 66 82.5 77 96.3 80 100.0 cumulative frequency percent 6 7.5 14 17.5 26 32.5 46 57.5 66 82.5 75 93.8 79 98.8 80 100.0 Data Set 3 --Buena School District Bus Data Bus Number X1 Maintenance X2 Age X3 Miles X4 Type X5 Bus-Mfg X6 Passenger X7 135 120 200 40 427 759 10 880 481 387 326 861 122 156 887 686 490 370 464 875 883 57 482 704 989 731 75 162 732 751 600 948 358 833 692 61 9 314 396 365 329 503 505 466 359 546 427 474 382 422 433 474 558 561 357 329 497 459 355 489 436 455 514 503 380 432 478 406 471 444 493 452 461 496 469 442 414 459 457 462 7 10 10 10 7 8 5 9 3 8 9 10 10 12 8 3 10 8 3 9 2 7 11 8 9 6 6 3 9 2 10 9 6 8 8 9 4 11 2 6 853 883 822 865 751 870 780 857 818 869 848 845 885 838 760 741 859 826 806 858 785 828 980 857 803 819 821 798 815 757 1008 831 849 839 812 809 864 859 815 799 Diesel Diesel Diesel Gasoline Gasoline Diesel Gasoline Gasoline Gasoline Gasoline Diesel Gasoline Gasoline Diesel Diesel Diesel Gasoline Gasoline Gasoline Diesel Gasoline Diesel Gasoline Diesel Diesel Diesel Diesel Gasoline Diesel Diesel Diesel Diesel Diesel Diesel Diesel Diesel Gasoline Diesel Diesel Diesel Bluebird Keiser Bluebird Bluebird Keiser Keiser Keiser Keiser Keiser Bluebird Bluebird Bluebird Bluebird Thompson Bluebird Bluebird Bluebird Keiser Bluebird Bluebird Bluebird Bluebird Bluebird Bluebird Keiser Bluebird Bluebird Keiser Keiser Keiser Bluebird Keiser Bluebird Thompson Bluebird Keiser Keiser Thompson Thompson Keiser 55 Passenger 42 Passenger 55 Passenger 55 Passenger 55 Passenger 55 Passenger 14 Passenger 55 Passenger 6 Passenger 55 Passenger 55 Passenger 55 Passenger 55 Passenger 55 Passenger 6 Passenger 55 Passenger 55 Passenger 55 Passenger 55 Passenger 55 Passenger 55 Passenger 55 Passenger 55 Passenger 55 Passenger 55 Passenger 42 Passenger 55 Passenger 55 Passenger 42 Passenger 14 Passenger 55 Passenger 42 Passenger 55 Passenger 55 Passenger 55 Passenger 55 Passenger 55 Passenger 6 Passenger 55 Passenger 55 Passenger 398 43 500 279 693 884 977 38 725 982 724 603 168 45 754 39 671 418 984 953 507 540 695 193 321 918 101 714 678 768 29 554 767 699 954 705 660 520 814 353 570 439 369 390 469 381 501 432 392 441 448 468 467 478 515 411 504 504 392 423 410 529 477 540 450 390 424 433 428 494 396 458 493 475 476 403 337 492 426 449 9 9 5 2 9 9 7 6 5 1 8 4 7 6 14 6 8 9 8 10 7 4 2 11 6 5 4 7 7 7 6 4 6 9 10 4 6 10 4 4 844 832 842 792 775 882 874 837 774 823 790 800 827 830 895 804 866 842 851 835 866 846 802 847 856 799 827 817 842 815 784 817 816 816 827 806 819 836 757 817 Diesel Gasoline Gasoline Diesel Gasoline Diesel Diesel Gasoline Diesel Diesel Diesel Diesel Gasoline Diesel Diesel Gasoline Gasoline Diesel Diesel Diesel Diesel Gasoline Diesel Diesel Diesel Diesel Diesel Diesel Diesel Diesel Gasoline Diesel Diesel Gasoline Diesel Diesel Gasoline Diesel Diesel Gasoline Thompson Bluebird Bluebird Bluebird Keiser Bluebird Bluebird Keiser Bluebird Bluebird Keiser Keiser Thompson Keiser Keiser Bluebird Thompson Bluebird Bluebird Bluebird Bluebird Bluebird Bluebird Thompson Bluebird Bluebird Bluebird Bluebird Keiser Bluebird Bluebird Bluebird Keiser Bluebird Bluebird Keiser Bluebird Bluebird Bluebird Keiser 14 Passenger 55 Passenger 55 Passenger 55 Passenger 55 Passenger 55 Passenger 55 Passenger 14 Passenger 55 Passenger 55 Passenger 42 Passenger 14 Passenger 55 Passenger 55 Passenger 14 Passenger 55 Passenger 55 Passenger 55 Passenger 55 Passenger 55 Passenger 55 Passenger 55 Passenger 55 Passenger 55 Passenger 6 Passenger 55 Passenger 55 Passenger 42 Passenger 55 Passenger 42 Passenger 55 Passenger 14 Passenger 55 Passenger 55 Passenger 42 Passenger 42 Passenger 55 Passenger 55 Passenger 55 Passenger 55 Passenger Balance 1756 748 1501 1831 1622 1886 740 1593 1169 2125 1554 1474 1913 1218 1006 2215 137 167 343 2557 2276 1494 2144 1995 1053 1526 1120 1838 1746 1616 1958 634 580 1320 1675 789 1735 1784 1326 2051 1044 1885 1790 765 1645 32 1266 890 2204 2409 1338 ATM Services 13 9 10 10 14 17 6 10 6 18 12 12 6 10 12 20 7 5 7 20 15 11 17 10 8 8 8 7 11 10 6 2 4 4 6 8 12 11 16 14 7 10 11 4 6 2 11 7 14 16 14 4 2 1 4 6 3 3 8 4 6 6 7 5 3 4 3 2 4 2 7 4 2 3 7 4 4 6 5 2 4 2 7 1 5 7 4 7 5 8 4 5 6 4 3 9 0 7 1 5 8 4 Debit Interest 0 1 0 0 0 0 0 1 0 0 1 1 0 1 0 1 0 0 0 1 1 0 0 0 1 0 1 1 0 1 1 1 0 1 1 0 0 0 0 1 1 1 0 0 0 0 0 0 0 0 1 1 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 1 0 1 0 0 0 0 0 0 1 0 0 0 0 1 1 0 1 0 0 1 0 0 0 City 2 1 1 3 4 1 3 1 4 2 3 1 1 1 1 4 3 4 1 4 3 1 3 2 3 2 3 3 2 2 2 4 1 1 2 4 3 1 3 4 1 2 3 4 4 3 4 1 2 2 2 2076 1708 2138 2375 1455 1487 1125 1989 2156 12 13 18 12 9 8 6 12 14 5 3 5 4 5 4 4 3 5 1 1 0 0 1 1 1 0 1 0 0 1 0 1 0 0 1 0 2 1 4 2 3 4 2 2 2 For problems requiring computations, please ensure that your Excel file includes the associated cell computations and/or statistics output. This information is needed in order to receive full credit on these problems. Chapter 13 – Problem 63 Chapter 13 – Problem 64 Chapter 14 – Problem 35 Chapter 14 – Case A – Century National Bank
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Regression Statistics
Multiple R 0,670871
R Square
0,450067
0,409332
Standard Error0,49352
Observations
30
ANOVA
df
Regression
Residual
Total

SS
MS
F
Significance F
2 5,381973 2,690987 11,04846 0,000312
27 6,576177 0,243562
29 11,95815

Coefficients
Standard Error t Stat
P-value Lower 95% Upper 95%
Intercept
-5,95268 2,004201
-2,9701 0,006182
-10,065
-1,8404
BA
36,27043 7,741811 4,685006
7,1E-05 20,38555 52,15531
ERA
-0,19441 0,184681 -1,05268 0,301817 -0,57334 0,184524

Team

Attendance

BA

ERA

Arizona Diamondbacks

2,18

0,259

3,93

Atlanta Braves

2,42

0,247

3,42

2,1

0,247

3,9

Boston Red Sox

3,04

0,26

4,7

Chicago Cubs

2,88

0,24

4,51

Chicago White Sox

1,97

0,255

4,02

Cincinnati Reds

2,35

0,251

3,34

Cleveland Indians

1,6

0,251

4,78

2,63

0,274

5,22

Detroit Tigers

3,03

0,268

3,75

Houston Astros

1,61

0,236

4,56

Kansas City Royals

1,74

0,265

4,3

Los Angeles Angels

3,06

0,274

4,02

Los Angeles Dodgers

3,32

0,252

3,34

Miami Marlins

2,22

0,244

4,09

Milwaukee Brewers
Minnesota Twins

2,83
2,78

0,259
0,26

4,22
4,77

New York Mets

2,24

0,249

4,09

New York Yankees

3,54

0,265

3,85

Oakland Athletics

1,68

0,238

3,48

3,57

0,255

3,83

Pittsburgh Pirates

2,09

0,243

3,86

2,12

0,247

4,01

San Francisco Giants

3,38

0,269

3,68

Seattle Mariners

1,72

0,234

3,76

St. Louis Cardinals

3,26

0,271

3,71

Tampa Bay Rays

1,56

0,24

3,19

Texas Rangers

3,46

0,273

3,99

2,1

0,245

4,64

2,37

0,261

3,33

Baltimore Orioles

Toronto Blue Jays
Washington Nationals

Attendance
Attendance
BA
ERA

BA
1

0,653832474

1

-0,054837543 0,143525677

Average Salary

1990

\$578.930

1991

\$891.188

1992

\$1.084.408

1993

\$1.120.254

1994

\$1.188.679

1995

\$1.071.029

1996

\$1.176.967

1997

\$1.383.578

1998

\$1.441.406

1999

\$1.720.050

2000

\$1.988.034

2001

\$2.264.403

2002

\$2.383.235

2003

\$2.555.476

2004

\$2.486.609

2005

\$2.632.655
\$2.866.544
\$2.944.556
\$3.154.845
\$3.240.206

ERA

1

2010

\$3.297.828

2011

\$3.305.393

2012

\$3.440.000

Team

Salary 2012

Attendance

X1

X5

X7

Arizona Diamondbacks

74,3

2,18

Atlanta Braves

83,3

2,42

Baltimore Orioles

81,4

2,1

173,2

3,04

Chicago Cubs

88,2

2,88

Chicago White Sox

96,9

1,97

Cincinnati Reds

82,2

2,35

Cleveland Indians

78,4

1,6

78,1

2,63

Detroit Tigers

132,3

3,03

Houston Astros

60,7

1,61

Kansas City Royals

60,9

1,74

Los Angeles Angels

154,5

3,06

Los Angeles Dodgers

95,1

3,32

Miami Marlins

118,1

2,22

Milwaukee Brewers
Minnesota Twins

97,7
94,1

2,83
2,78

New York Mets

93,4

2,24

New York Yankees

198

3,54

Oakland Athletics

55,4

1,68

174,5

3,57

Pittsburgh Pirates

63,4

2,09

55,2

2,12

San Francisco Giants

117,6

3,38

82

1,72

St. Louis Cardinals

110,3

3,26

Tampa Bay Rays

64,2

1,56

Texas Rangers

120,5

3,46

Toronto Blue Jays

75,5

2,1

Washington Nationals

81,3

2,37

Boston Red Sox

Seattle Mariners

Scatter diagram showing relationship between Salary and
Attendance
4
3,5

Attendance

3
2,5
2
Series1

1,5
1
0,5
0
0

50

100

150
Salary

200

250

Average Salary

1989

\$512.930

1990

\$578.930

1991

\$891.188

1992

\$1.084.408

1993

\$1.120.254

1994

\$1.188.679

1995

\$1.071.029

1996

\$1.176.967

1997

\$1.383.578

1998

\$1.441.406

1999

\$1.720.050

2000

\$1.988.034

2001

\$2.264.403

2002

\$2.383.235

2003

\$2.555.476

2004

\$2.486.609

2005
2006

\$2.632.655
\$2.866.544

2007

\$2.944.556

2008

\$3.154.845

2009

\$3.240.206

2010

\$3.297.828

2011

\$3.305.393

2012

\$3.440.000

SUMMARY OUTPUT
Regression Statistics
Multiple R
0,770317814
R Square
0,593389535
0,578867732
Standard Error
0,416717999
Observations
30
ANOVA
df
Regression
Residual
Total

Intercept
X Variable 1

SS
MS
F
Significance F
1 7,095841 7,095841 40,86198 6,41E-07
28 4,862309 0,173654
29 11,95815

CoefficientsStandard Error t Stat
P-value Lower 95% Upper 95%Lower 95.0%
1,178554138 0,219546 5,368153 1,01E-05 0,728835 1,628273 0,728835
0,013429923 0,002101 6,392337 6,41E-07 0,009126 0,017734 0,009126

PROBABILITY OUTPUT
Percentile
1,666666667
5
8,333333333
11,66666667
15
18,33333333
21,66666667
25
28,33333333
31,66666667
35
38,33333333
41,66666667
45
48,33333333
51,66666667
55
58,33333333
61,66666667
65
68,33333333
71,66666667

Y
1,56
1,6
1,61
1,68
1,72
1,74
1,97
2,09
2,1
2,1
2,12
2,18
2,22
2,24
2,35
2,37
2,42
2,63
2,78
2,83
2,88
3,03

75
78,33333333
81,66666667
85
88,33333333
91,66666667
95
98,33333333

3,04
3,06
3,26
3,32
3,38
3,46
3,54
3,57

Upper 95.0%
1,628273
0,017734

Regression Equation: y = 1.179 + 0.0134x
a)

Scatter Diagram
Scatter diagram showing relationship between Salary and
Attendance
4
3,5

Attendance

3
2,5
2
Series1

1,5
1
0,5
0
0

50

100

150

200

250

Salary

From the scatter diagram above, the relationship between salary and attendance although not strong is direct.
b)

Expected attendance for a team with a salary of \$80.0 million
y = 1.179 + 0.0134x
y = 1.179 + 0.0134 (80)
y = 2.251

c)

Expected addition in attendance for an additional \$30 million pay by owners
y = [1.179 + 0.0134(110)] - [1.179 + 0.0134 (80)]
y = 2.653 - 2.251
y = 0.402
Therefore the attendance will be more by 402 people.

d)

Hypothesis test to conclude that the slope of the regression line is positive at 0.05 significance level
Null hypothesis (Ho) will be that the slope is not positive while the alternative hypothesis (Hi) will be that the sl
is positive
The slope is the x-intercept.
From the regression output, the p-value for x-intercept is less than 0.05 and therefore we reject the null hypothes
Therefore, we can conclude that the slope of the regression line is indeed positive.

e)

Percentage of variations in attendance accounted for by salary
From the regression analysis output, R-squared is used to determine the variation in y-variable

accounted for by the x-variable.
Therefore 59.34% of the variation in attendance is accounted for by salary.
f)

Correlation
Attendance
Attendance
1
BA
0,65
ERA
-0,05

BA
1
0,14

ERA

1

The correlation between batting average and attendance is stronger than that between ERA and attendance
Hypothesis testing
Intercept
BA
ERA

Coefficients
Standard Error t Stat
P-value Lower 95% Upper 95%
-5,95268 2,004201
-2,9701 0,006...

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