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 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 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. - H0: β0 = 0 Ha: β0 ≠ 0H0: β1 = β2 = 0 Ha: All the parameters are not equal to zero. H0: β0 ≠ 0 Ha: β0 = 0H0: One or more of the parameters is not equal to zero. Ha: β1 = β2 = 0H0: β1 = β2 = 0 Ha: 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? Reject H0. There is insufficient evidence to conclude that there is a significant overall relationship.Reject H0. There is sufficient evidence to conclude that there is a significant overall relationship. Do not reject H0. There is sufficient evidence to conclude that there is a significant overall relationship.Do not reject H0. 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. H0: β1 = 0 Ha: β1 > 0H0: β1 ≥ 0 Ha: β1 < 0 H0: β1 = 0 Ha: β1 ≠ 0H0: β1 ≤ 0 Ha: β1 > 0H0: β1 ≠ 0 Ha: β1 = 0 Find the value of the test statistic for β1. (Round your answer to two decimal places.) Find the p-value for β1. (Round your answer to three decimal places.) p-value = What is your conclusion at the 0.05 level of significance? Do not reject H0. There is sufficient evidence to conclude that SO/IP is a significant factor.Reject H0. There is insufficient evidence to conclude that SO/IP is a significant factor. Reject H0. There is sufficient evidence to conclude that SO/IP is a significant factor.Do not reject H0. There is insufficient 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. H0: β2 = 0 Ha: β2 ≠ 0H0: β2 = 0 Ha: β2 > 0 H0: β2 ≥ 0 Ha: β2 < 0H0: β2 ≠ 0 Ha: β2 = 0H0: β2 ≤ 0 Ha: β2 > 0 Find the value of the test statistic for β2. (Round your answer to two decimal places.) Find the p-value for β2. (Round your answer to three decimal places.) p-value = What is your conclusion at the 0.05 level of significance? Reject H0. There is insufficient evidence to conclude that HR/IP is a significant factor.Do not reject H0. There is insufficient evidence to conclude that HR/IP is a significant factor. Reject H0. There is sufficient evidence to conclude that HR/IP is a significant factor.Do not reject H0. There is sufficient evidence to conclude that HR/IP is a significant factor.

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 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 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. - H0: β0 = 0 Ha: β0 ≠ 0H0: β1 = β2 = 0 Ha: All the parameters are not equal to zero. H0: β0 ≠ 0 Ha: β0 = 0H0: One or more of the parameters is not equal to zero. Ha: β1 = β2 = 0H0: β1 = β2 = 0 Ha: 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? Reject H0. There is insufficient evidence to conclude that there is a significant overall relationship.Reject H0. There is sufficient evidence to conclude that there is a significant overall relationship. Do not reject H0. There is sufficient evidence to conclude that there is a significant overall relationship.Do not reject H0. 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. H0: β1 = 0 Ha: β1 > 0H0: β1 ≥ 0 Ha: β1 < 0 H0: β1 = 0 Ha: β1 ≠ 0H0: β1 ≤ 0 Ha: β1 > 0H0: β1 ≠ 0 Ha: β1 = 0 Find the value of the test statistic for β1. (Round your answer to two decimal places.) Find the p-value for β1. (Round your answer to three decimal places.) p-value = What is your conclusion at the 0.05 level of significance? Do not reject H0. There is sufficient evidence to conclude that SO/IP is a significant factor.Reject H0. There is insufficient evidence to conclude that SO/IP is a significant factor. Reject H0. There is sufficient evidence to conclude that SO/IP is a significant factor.Do not reject H0. There is insufficient 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. H0: β2 = 0 Ha: β2 ≠ 0H0: β2 = 0 Ha: β2 > 0 H0: β2 ≥ 0 Ha: β2 < 0H0: β2 ≠ 0 Ha: β2 = 0H0: β2 ≤ 0 Ha: β2 > 0 Find the value of the test statistic for β2. (Round your answer to two decimal places.) Find the p-value for β2. (Round your answer to three decimal places.) p-value = What is your conclusion at the 0.05 level of significance? Reject H0. There is insufficient evidence to conclude that HR/IP is a significant factor.Do not reject H0. There is insufficient evidence to conclude that HR/IP is a significant factor. Reject H0. There is sufficient evidence to conclude that HR/IP is a significant factor.Do not reject H0. There is sufficient evidence to conclude that HR/IP is a significant factor.

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Question

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	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

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.

- H₀: β₀ = 0
H_a: β₀ ≠ 0H₀: β₁ = β₂ = 0
H_a: All the parameters are not equal to zero. H₀: β₀ ≠ 0
H_a: β₀ = 0H₀: One or more of the parameters is not equal to zero.
H_a: β₁ = β₂ = 0H₀: β₁ = β₂ = 0
H_a: 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?

Reject H₀. There is insufficient evidence to conclude that there is a significant overall relationship.Reject H₀. There is sufficient evidence to conclude that there is a significant overall relationship. Do not reject H₀. There is sufficient evidence to conclude that there is a significant overall relationship.Do not reject H₀. 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.

H₀: β₁ = 0
H_a: β₁ > 0H₀: β₁ ≥ 0
H_a: β₁ < 0 H₀: β₁ = 0
H_a: β₁ ≠ 0H₀: β₁ ≤ 0
H_a: β₁ > 0H₀: β₁ ≠ 0
H_a: β₁ = 0

Find the value of the test statistic for β₁. (Round your answer to two decimal places.)

Find the p-value for β₁. (Round your answer to three decimal places.)

p-value =

What is your conclusion at the 0.05 level of significance?

Do not reject H₀. There is sufficient evidence to conclude that SO/IP is a significant factor.Reject H₀. There is insufficient evidence to conclude that SO/IP is a significant factor. Reject H₀. There is sufficient evidence to conclude that SO/IP is a significant factor.Do not reject H₀. There is insufficient 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.

H₀: β₂ = 0
H_a: β₂ ≠ 0H₀: β₂ = 0
H_a: β₂ > 0 H₀: β₂ ≥ 0
H_a: β₂ < 0H₀: β₂ ≠ 0
H_a: β₂ = 0H₀: β₂ ≤ 0
H_a: β₂ > 0

Find the value of the test statistic for β₂. (Round your answer to two decimal places.)

Find the p-value for β₂. (Round your answer to three decimal places.)

p-value =

What is your conclusion at the 0.05 level of significance?

Reject H₀. There is insufficient evidence to conclude that HR/IP is a significant factor.Do not reject H₀. There is insufficient evidence to conclude that HR/IP is a significant factor. Reject H₀. There is sufficient evidence to conclude that HR/IP is a significant factor.Do not reject H₀. There is sufficient evidence to conclude that HR/IP is a significant factor.

State the null and alternative hypotheses.
O Họ: B1 = 0
H: B, > 0
O Ho: Bq zO
H: B1 < 0
O Ho: B1 = 0
H: B, = 0
a
O Ho: B, s0
H: B, > 0
O Ho: B, + 0
H: B, = 0
Find the value of the test statistic for B,. (Round your answer to two decimal places.)
Find the p-value for B,. (Round your answer to three decimal places.)
p-value =
What is your conclusion at the 0.05 level of significance?
O Do not reject H,. There is sufficient evidence to conclude that SsO/IP is a significant factor.
Reject H,. There is insufficient evidence to conclude that SO/IP is a significant factor.
Reject H,. There is sufficient evidence to conclude that so/IP is a significant factor.
Do not reject H,. There is insufficient 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.

(a) Use the F test to determine the overall significance of the relationship.
State the null and alternative hypotheses.
O Ho: Bo = 0
H3: Bo = 0
O Ho: B1 = B2 = 0
H: All the parameters are not equal to zero.
O Ho: Bo *0
H: Bo = 0
O Ho: One or more of the parameters is not equal to zero.
Hg: Bz = B2 = 0
O Ho: B1 = B2 = 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 Ho: There is insufficient evidence to conclude that there is a significant overall relationship.
O Reject H. There is sufficient 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 Ho. There is insufficient evidence to conclude that there is a significant overall relationship.

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