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
In: Nursing
Key Family Heating and Air Conditioning Inc. employs Andy Clark and Frank John to make service calls to repair furnaces and air-conditioning units in homes. A. Key, the owners would like to know whether there is a difference in the mean number of service calls they make per day. A random sample of 40 days last year showed the following:
| Days (n) | Sample Mean |
Population Standard Deviation |
|
| A. Clark | 40 | 4.77 | 1.05 |
| F. John | 50 | 5.02 | 1.23 |
At the .05 significance level, is there a difference in the mean number of calls per day between the two employees?
a. State the hypotheses
b. Determine the critical value =
c State the decision rule: Reject H0 if
d. Calculate the test statistic =
e. Make a decision:
In: Statistics and Probability
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 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 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 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 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 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
Thanks for your speedy response!! Timed 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: 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: β0 ≠
0
Ha: β0 = 0H0:
β1 = β2 = 0
Ha: All the parameters are not equal to
zero.H0: β0 = 0
Ha: β0 ≠ 0
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. 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.
(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.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.
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: Math