A statistical program is recommended. Data showing the values of several pitching statistics for a random sample of 20 pitchers from the American League of Major League Baseball is provided.

MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
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A statistical program is recommended.
Data showing the values of several pitching statistics for a random sample of 20 pitchers from the American League of Major League Baseball is provided.
Player
so/IP HR/IP
R/IP
Team
L
ERA
Verlander, J
DET
24
5
2.40
1.00
0.10
0.29
Beckett, J
BOS
13
7
2.89
0.91
0.11
0.34
Wilson, C
TEX
16 7
2.94
0.92
0.07
0.40
Sabathia, C
NYY
19 8
3.00
0.97
0.07
0.37
Haren, D
LAA
16 10 3.17
0.81
0.08
0.38
McCarthy, B
OAK
9
9
3.32
0.72
0.06
0.43
Santana, E
LAA
11
12
3.38
0.78
0.11
0.42
Lester, J
BOS
15
9
3.47
0.95
0.10
0.40
Hernandez, F
SEA
14
14
3.47
0.95
0.08
0.42
Buehrle, M
CWs
13
9
3.59
0.53
0.10
0.45
Pineda, M
SEA
9
10
3.74
1.01
0.11
0.44
Colon, B
NYY
8
8 10 4.00
0.82
0.13
0.52
Tomlin, J
CLE
12 7
4.25
0.54
0.15
0.48
Pavano, C
MIN
9
13
4.30
0.46
0.10
0.55
Danks, J
CWS
8
12 4.33
0.79
0.11
0.52
Guthrie, J
BAL
9
17
4.33
0.63
0.13
0.54
Lewis, C
TEX
14
10
4.40
0.84
0.17
0.51
Scherzer, M
DET
15
9
4.43
0.89
0.15
0.52
Davis, W
TB
11
10
4.45
0.57
0.13
0.52
Porcello, R
DET
14
9
4.75
0.57
0.10
0.57
An estimated regression equation was developed to predict the average number of runs given up per inning pitched (R/IP) given the average number of strikeouts per inning pitched (SO/IP) and the average number of home runs per inning pitched (HR/IP).
R/IP = 0.5365 - 0.2483 SO/IP + 1.032 HR/IP
Transcribed Image Text:A statistical program is recommended. Data showing the values of several pitching statistics for a random sample of 20 pitchers from the American League of Major League Baseball is provided. Player so/IP HR/IP R/IP Team L ERA Verlander, J DET 24 5 2.40 1.00 0.10 0.29 Beckett, J BOS 13 7 2.89 0.91 0.11 0.34 Wilson, C TEX 16 7 2.94 0.92 0.07 0.40 Sabathia, C NYY 19 8 3.00 0.97 0.07 0.37 Haren, D LAA 16 10 3.17 0.81 0.08 0.38 McCarthy, B OAK 9 9 3.32 0.72 0.06 0.43 Santana, E LAA 11 12 3.38 0.78 0.11 0.42 Lester, J BOS 15 9 3.47 0.95 0.10 0.40 Hernandez, F SEA 14 14 3.47 0.95 0.08 0.42 Buehrle, M CWs 13 9 3.59 0.53 0.10 0.45 Pineda, M SEA 9 10 3.74 1.01 0.11 0.44 Colon, B NYY 8 8 10 4.00 0.82 0.13 0.52 Tomlin, J CLE 12 7 4.25 0.54 0.15 0.48 Pavano, C MIN 9 13 4.30 0.46 0.10 0.55 Danks, J CWS 8 12 4.33 0.79 0.11 0.52 Guthrie, J BAL 9 17 4.33 0.63 0.13 0.54 Lewis, C TEX 14 10 4.40 0.84 0.17 0.51 Scherzer, M DET 15 9 4.43 0.89 0.15 0.52 Davis, W TB 11 10 4.45 0.57 0.13 0.52 Porcello, R DET 14 9 4.75 0.57 0.10 0.57 An estimated regression equation was developed to predict the average number of runs given up per inning pitched (R/IP) given the average number of strikeouts per inning pitched (SO/IP) and the average number of home runs per inning pitched (HR/IP). R/IP = 0.5365 - 0.2483 SO/IP + 1.032 HR/IP
(a) Use the F test to determine the overall significance of the relationship.
State the null and alternative hypotheses.
O H,: B, - B2 = 0
H: All the parameters are not equal to zero.
O Ho: One or more of the parameters is not equal to zero.
H: B, = 82 = 0
O Ho: Bo - 0
H: 80 = 0
O H;: Bo *0
H: Bo = 0
O Ho: B, = 82 = 0
H: One or more of the parameters is not equal to zero.
Calculate the test statistic. (Round your answer to two decimal places.)
Calculate the p-value. (Round your answer to three decimal places.)
p-value =
What is your conclusion at the 0.05 level of significance?
O Reject H,. There is sufficient evidence to conclude that there is a significant overall relationship.
O Reject H,. There is insufficient evidence to conclude that there is a significant overall relationship.
O Do not reject H.. There is sufficient evidence to conclude that there is a significant overall relationship.
O Do not reject H.. There is insufficient evidence to conclude that there is a significant overall relationship.
(b) Use the t test to determine the significance of SO/IP.
State the null and alternative hypotheses.
O Ho: B, 2 0
H: B, < 0
O Ho: B, - 0
H: B, + 0
O Ho: B, s0
H: B, > 0
O H;: B, + 0
H: 8, = 0
O Ho: B = 0
H: B, > 0
Find the value of the test statistic for 8,. (Round your answer to two decimal places.)
Find the p-value for 8,. (Round your answer to three decimal places.)
p-value =
Transcribed Image Text:(a) Use the F test to determine the overall significance of the relationship. State the null and alternative hypotheses. O H,: B, - B2 = 0 H: All the parameters are not equal to zero. O Ho: One or more of the parameters is not equal to zero. H: B, = 82 = 0 O Ho: Bo - 0 H: 80 = 0 O H;: Bo *0 H: Bo = 0 O Ho: B, = 82 = 0 H: One or more of the parameters is not equal to zero. Calculate the test statistic. (Round your answer to two decimal places.) Calculate the p-value. (Round your answer to three decimal places.) p-value = What is your conclusion at the 0.05 level of significance? O Reject H,. There is sufficient evidence to conclude that there is a significant overall relationship. O Reject H,. There is insufficient evidence to conclude that there is a significant overall relationship. O Do not reject H.. There is sufficient evidence to conclude that there is a significant overall relationship. O Do not reject H.. There is insufficient evidence to conclude that there is a significant overall relationship. (b) Use the t test to determine the significance of SO/IP. State the null and alternative hypotheses. O Ho: B, 2 0 H: B, < 0 O Ho: B, - 0 H: B, + 0 O Ho: B, s0 H: B, > 0 O H;: B, + 0 H: 8, = 0 O Ho: B = 0 H: B, > 0 Find the value of the test statistic for 8,. (Round your answer to two decimal places.) Find the p-value for 8,. (Round your answer to three decimal places.) p-value =
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