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
Related questions
Concept explainers
Continuous Probability Distributions
Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.
Normal Distribution
Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!
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
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.
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
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
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.
Transcribed Image Text: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.
Transcribed Image Text:(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.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 7 steps with 1 images
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, statistics and related others by exploring similar questions and additional content below.Recommended textbooks for you
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning
Statistics for The Behavioral Sciences (MindTap C…
Statistics
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning
Statistics for The Behavioral Sciences (MindTap C…
Statistics
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
Elementary Statistics: Picturing the World (7th E…
Statistics
ISBN:
9780134683416
Author:
Ron Larson, Betsy Farber
Publisher:
PEARSON
The Basic Practice of Statistics
Statistics
ISBN:
9781319042578
Author:
David S. Moore, William I. Notz, Michael A. Fligner
Publisher:
W. H. Freeman
Introduction to the Practice of Statistics
Statistics
ISBN:
9781319013387
Author:
David S. Moore, George P. McCabe, Bruce A. Craig
Publisher:
W. H. Freeman