Thanks for your speedy response!! Timed problem.

Data showing the values of several pitching statistics for arandom sample of 20 pitchers from the American League of MajorLeague 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 theaverage number of runs given up per inning pitched (R/IP) given theaverage number of strikeouts per inning pitched (SO/IP) and theaverage 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 ofthe relationship.

State the null and alternative hypotheses.

H₀: ?₁ = ?₂ = 0
H_a: One or more of the parameters is not equalto zero.H₀: One or more of the parameters isnot equal to zero.
H_a: ?₁ = ?₂ =0    H₀: ?₀ ?0
H_a: ?₀ = 0H₀:?₁ = ?₂ = 0
H_a: All the parameters are not equal tozero.H₀: ?₀ = 0
H_a: ?₀ ? 0

Calculate the test statistic. (Round your answer to two decimalplaces.)

Calculate the p-value. (Round your answer to threedecimal places.)

p-value =

What is your conclusion at the 0.05 level of significance?

Do not reject H₀. There is insufficientevidence to conclude that there is a significant overallrelationship.Reject H₀. There is insufficientevidence to conclude that there is a significant overallrelationship.    Do not rejectH₀. There is sufficient evidence to concludethat there is a significant overall relationship.RejectH₀. There is sufficient evidence to concludethat there is a significant overall relationship.

(b)

Use the t test to determine the significance ofSO/IP.

State the null and alternative hypotheses.

H₀: ?₁ ? 0
H_a: ?₁ > 0H₀:?₁ ? 0
H_a: ?₁ <0    H₀: ?₁ =0
H_a: ?₁ > 0H₀:?₁ ? 0
H_a: ?₁ = 0H₀:?₁ = 0
H_a: ?₁ ? 0

Find the value of the test statistic for ?₁. (Roundyour answer to two decimal places.)

Find the p-value for ?₁. (Round your answerto three decimal places.)

p-value =

What is your conclusion at the 0.05 level of significance?

Reject H₀. There is sufficient evidence toconclude that SO/IP is a significant factor.Do not rejectH₀. There is sufficient evidence to concludethat SO/IP is a significant factor.    Do notreject H₀. There is insufficient evidence toconclude that SO/IP is a significant factor.RejectH₀. There is insufficient evidence to concludethat SO/IP is a significant factor.

Use the t test to determine the significance ofHR/IP.

State the null and alternative hypotheses.

H₀: ?₂ ? 0
H_a: ?₂ > 0H₀:?₂ = 0
H_a: ?₂ ?0    H₀: ?₂ ?0
H_a: ?₂ = 0H₀:?₂ ? 0
H_a: ?₂ < 0H₀:?₂ = 0
H_a: ?₂ > 0

Find the value of the test statistic for ?₂. (Roundyour answer to two decimal places.)

Find the p-value for ?₂. (Round your answerto three decimal places.)

p-value =

What is your conclusion at the 0.05 level of significance?

Reject H₀. There is insufficient evidence toconclude that HR/IP is a significant factor.RejectH₀. There is sufficient evidence to concludethat HR/IP is a significant factor.    Do notreject H₀. There is insufficient evidence toconclude that HR/IP is a significant factor.Do not rejectH₀. There is sufficient evidence to concludethat HR/IP is a significant factor.