Questions
Using the set of scores below, determine if the difference between the two sets of scores...

Using the set of scores below, determine if the difference between the two sets of scores is significant at alpha .05, two tailed.  Determine this through the paired t-test.  Show the 5 steps of hypothesis testing. Solve manually, by hand showing all steps. Do not use SPSS or excel.

X                     Y

            3                      8

            8                      7

            5                      6

            7                      7

            6                      6

            8                      9

In: Statistics and Probability

Since an early age, Kendall has had what most people called a “short fuse.”

Since an early age, Kendall has had what most people called a “short fuse.” Because he would always argue and start fights, it became difficult for him to make friends during his school years. In addition, nothing seemed to curb the angry response Kendall displayed when his parents tried to discipline him. Aside from his inability to control his temper, Kendall was intelligent and athletic. He made good grades and engaged in competitive sports. Social relationships remained an issue as he was controlling and impulsive.


After graduating from college, Kendall works in a pharmaceutical laboratory. Co-workers describe him as “touchy” and “easily ticked off,” but very brilliant and efficient at what he does. On one particular day, Kendall is unable to contain his anger over an incident in which a lab technician makes an error in a chemical formula. Kendall becomes so irate and angry, he throws the flask across the room narrowly missing the young technician’s head. The technician runs out of the lab screaming that “Ken has lost it this time.” Kendall is put on leave from the company and is required to enter treatment for anger management.


1. How are anger and aggression evident in Kendall’s situation?


2. In what ways might Kendall’s behavior be a conditioned response?


3. What methods might be used to help him diffuse some

In: Nursing

Reactive Anger” Since an early age, Kendall has had what most people called a “short fuse.”...

Reactive Anger”

Since an early age, Kendall has had what most people called a “short fuse.” Because he would always argue and start fights, it became difficult for him to make friends during his school years. In addition, nothing seemed to curb the angry response Kendall displayed when his parents tried to discipline him. Aside from his inability to control his temper, Kendall was intelligent and athletic. He made good grades and engaged in competitive sports. Social relationships remained an issue as he was controlling and impulsive.

After graduating from college, Kendall works in a pharmaceutical laboratory. Co-workers describe him as “touchy” and “easily ticked off,” but very brilliant and efficient at what he does. On one particular day, Kendall is unable to contain his anger over an incident in which a lab technician makes an error in a chemical formula. Kendall becomes so irate and angry, he throws the flask across the room narrowly missing the young technician’s head. The technician runs out of the lab screaming that “Ken has lost it this time.” Kendall is put on leave from the company and is required to enter treatment for anger management.

1. How are anger and aggression evident in Kendall’s situation?

2. In what ways might Kendall’s behavior be a conditioned response?

3. What methods might be used to help him diffuse some

In: Nursing

Advanced Quantitative Business Analysis. Question: Which method of forecasting would you recommend between 4 MA &...

Advanced Quantitative Business Analysis.

Question: Which method of forecasting would you recommend between 4 MA & 2 WMA? Why?

Period

Sales

4 MA

Error

|Error|

Error^2

(|Err.|/A)*100

1

110

2

115

3

125

4

120

5

125

6

120

7

130

8

115

9

110

10

130

Weights

0.65

0.35

2 WMA

In: Statistics and Probability

Excel is recommended for this problem. Data showing the values of several pitching statistics for a...

Excel is recommended for this problem.

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

(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?

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 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?

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.    

Reject H0. There is insufficient 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.

In: Statistics and Probability

A statistical program is recommended. Data showing the values of several pitching statistics for a random...

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 ≠ 0

H0: β0 ≠ 0
Ha: β0 = 0    

H0: β1 = β2 = 0
Ha: One or more of the parameters is not equal to zero.

H0: One or more of the parameters is not equal to zero.
Ha: β1 = β2 = 0

H0: β1 = β2 = 0
Ha: All the parameters are 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.

Do not reject H0. There is sufficient 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 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 < 0

H0: β1 ≠ 0
Ha: β1 = 0    

H0: β1 ≤ 0
Ha: β1 > 0

H0: β1 = 0
Ha: β1 > 0

H0: 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 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.

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 = 0

H0: β2 ≤ 0
Ha: β2 > 0    

H0: β2 = 0
Ha: β2 ≠ 0

H0: β2 = 0
Ha: β2 > 0

H0: 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.

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.

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

In: Statistics and Probability

A statistical program is recommended. Data showing the values of several pitching statistics for a random...

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: One or more of the parameters is not equal to zero.
Ha: β1 = β2 = 0

H0: β1 = β2 = 0
Ha: One or more of the parameters is not equal to zero.   

H0: β0 = 0
Ha: β0 ≠ 0

H0: β0 ≠ 0
Ha: β0 = 0

H0: β1 = β2 = 0
Ha: All the parameters are 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 sufficient evidence to conclude that there is a significant overall relationship.

Reject H0. There is insufficient 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 > 0

H0: β1 = 0
Ha: β1 ≠ 0  

  H0: β1 ≠ 0
Ha: β1 = 0

H0: β1 ≤ 0
Ha: β1 > 0

H0: 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?

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.    

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

Do not reject H0. 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.

H0: β2 ≤ 0
Ha: β2 > 0

H0: β2 = 0
Ha: β2 ≠ 0    

H0: β2 ≥ 0
Ha: β2 < 0H

0: β2 = 0
Ha: β2 > 0

H0: 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 sufficient 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.    

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

.Reject H0. There is insufficient evidence to conclude that HR/IP is a significant factor.

In: Statistics and Probability

A statistical program is recommended. Data showing the values of several pitching statistics for a random...

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

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

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?

Do not reject H0. There is sufficient 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.    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.

In: Statistics and Probability

Data showing the values of several pitching statistics for a random sample of 20 pitchers from...

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

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

(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?

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.Do not reject H0. 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.

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

In: Statistics and Probability

A statistical program is recommended. Data showing the values of several pitching statistics for a random...

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: β0 = 0
Ha: β0 ≠ 0     H0: 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.H0: β1 = β2 = 0
Ha: All the parameters are 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?

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.     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.

(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.Do not reject H0. There is insufficient 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.

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

In: Statistics and Probability