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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).
(a)
Use the F test to determine the overall significance of the relationship.
State the null and alternative hypotheses.
H
0
:
1
=
2
= 0
H
a
: One or more of the parameters is not equal to zero.
H
0
:
0
= 0
H
a
:
0
0
H
0
:
1
=
2
= 0
H
a
: All the parameters are not equal to zero.
H
0
:
0
0
H
a
:
0
= 0
H
0
: One or more of the parameters is not equal to zero.
H
a
:
1
=
2
= 0
Calculate the test statistic. (Round your answer to two decimal places.)
t stat =
Calculate the p-value. (Round your answer to three decimal places.)
p-value =
What is your conclusion at the 0.05 level of significance?
Do not reject H
0
. There is insufficient evidence to conclude that there is a significant overall
relationship.
Do not reject H
0
. There is sufficient evidence to conclude that there is a significant overall
relationship.
Reject H
0
. There is sufficient evidence to conclude that there is a significant overall relationship.
Reject H
0
. 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.
H
0
:
1
= 0
H
a
:
1
> 0
H
0
:
1
0
H
a
:
1
< 0
H
0
:
1
0
H
a
:
1
= 0
H
0
:
1
0
H
a
:
1
> 0
H
0
:
1
= 0
H
a
:
1
0
Find the value of the test statistic for
1
. (Round your answer to two decimal places.)
t stat =
Find the p-value for
1
. (Round your answer to three decimal places.)
p-value =
What is your conclusion at the 0.05 level of significance?
Reject H
0
. There is insufficient evidence to conclude that SO/IP is a significant factor.
Do not reject H
0
. There is insufficient evidence to conclude that SO/IP is a significant factor.
Reject H
0
. There is sufficient evidence to conclude that SO/IP is a significant factor.
Do not reject H
0
. There is sufficient evidence to conclude that SO/IP is a significant factor.
Use the t test to determine the significance of HR/IP.
State the null and alternative hypotheses.
H
0
:
2
0
H
a
:
2
> 0
H
0
:
2
0
H
a
:
2
= 0
H
0
:
2
0
H
a
:
2
< 0
H
0
:
2
= 0
H
a
:
2
0
H
0
:
2
= 0
H
a
:
2
> 0
Find the value of the test statistic for
2
. (Round your answer to two decimal places.)
t stat =
Find the p-value for
2
. (Round your answer to three decimal places.)
p-value =
What is your conclusion at the 0.05 level of significance?
Do not reject H
0
. There is sufficient evidence to conclude that HR/IP is a significant factor.
Reject H
0
. There is insufficient evidence to conclude that HR/IP is a significant factor.
Reject H
0
. There is sufficient evidence to conclude that HR/IP is a significant factor.
Do not reject H
0
. There is insufficient evidence to conclude that HR/IP is a significant factor.
Player Team W L ERA SO/IP HR/IP R/IP
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 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

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  • 1. 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). (a) Use the F test to determine the overall significance of the relationship. State the null and alternative hypotheses. H 0 : 1 = 2 = 0 H a : One or more of the parameters is not equal to zero. H 0 : 0 = 0 H a : 0 0 H 0 : 1 = 2 = 0 H a : All the parameters are not equal to zero. H 0 : 0 0 H a : 0 = 0 H 0 : One or more of the parameters is not equal to zero. H a : 1 = 2 = 0 Calculate the test statistic. (Round your answer to two decimal places.) t stat = Calculate the p-value. (Round your answer to three decimal places.) p-value = What is your conclusion at the 0.05 level of significance? Do not reject H 0 . There is insufficient evidence to conclude that there is a significant overall relationship. Do not reject H 0 . There is sufficient evidence to conclude that there is a significant overall relationship. Reject H 0 . There is sufficient evidence to conclude that there is a significant overall relationship. Reject H 0 . 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. H 0 : 1 = 0 H a : 1 > 0 H 0 : 1 0 H a : 1 < 0 H 0 : 1 0 H a : 1 = 0 H 0 : 1 0 H a : 1 > 0 H 0 : 1 = 0 H a : 1 0 Find the value of the test statistic for 1 . (Round your answer to two decimal places.) t stat =
  • 2. Find the p-value for 1 . (Round your answer to three decimal places.) p-value = What is your conclusion at the 0.05 level of significance? Reject H 0 . There is insufficient evidence to conclude that SO/IP is a significant factor. Do not reject H 0 . There is insufficient evidence to conclude that SO/IP is a significant factor. Reject H 0 . There is sufficient evidence to conclude that SO/IP is a significant factor. Do not reject H 0 . There is sufficient evidence to conclude that SO/IP is a significant factor. Use the t test to determine the significance of HR/IP. State the null and alternative hypotheses. H 0 : 2 0 H a : 2 > 0 H 0 : 2 0 H a : 2 = 0 H 0 : 2 0 H a : 2 < 0 H 0 : 2 = 0 H a : 2 0 H 0 : 2 = 0 H a : 2 > 0 Find the value of the test statistic for 2 . (Round your answer to two decimal places.) t stat = Find the p-value for 2 . (Round your answer to three decimal places.) p-value = What is your conclusion at the 0.05 level of significance? Do not reject H 0 . There is sufficient evidence to conclude that HR/IP is a significant factor. Reject H 0 . There is insufficient evidence to conclude that HR/IP is a significant factor. Reject H 0 . There is sufficient evidence to conclude that HR/IP is a significant factor. Do not reject H 0 . There is insufficient evidence to conclude that HR/IP is a significant factor. Player Team W L ERA SO/IP HR/IP R/IP 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
  • 3. 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 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