League A teams visit League B teams, the League A pitcher must bat. So, if the DH does result in more runs, it would be expected that league A teams will score more runs in League A park than when visiting League B parks. To test this cl random sample of runs scored by league A teams with and without their DH is given in the accompanying table Complete parts a) through d) below a) Draw side-by-side boxplots of the number of runs scored by League A teams with and without their DH Choose the correct graph below OA OB. Q OC. B 10 xxx G Q Q O D. B RIMME 10 10 Does there appear to be a difference in the number of runs between these situations? OA. No because the number of runs scored in a League A park is about the same as the number of runs scored in a League B park OB. No but the number of runs scored in a League A park appear to be slightly higher than the number of runs scored in a League B park. OC. Yes because the number of runs scored in a League A park appear to have a higher median than the number of runs scored in a League B park OD. D. Yes because the number of runs scored in a League B park appear to have a higher median than the number of runs scored in a League A park Q Q Sample of Runs League A Park (with DH) 2 3 6 6 8 1 3 7 6 4 4 12 5 6 5 6 5 9 9 3 14 4 6 1 2 6 4 3 3 Full data set League B Park (without DH) 5 5 4 7 2 9 10 1 1 3 2 7 6 8 3 5 5 13 7 2 5 14 7 0 2 4 2 2 4 9 3 2
League A teams visit League B teams, the League A pitcher must bat. So, if the DH does result in more runs, it would be expected that league A teams will score more runs in League A park than when visiting League B parks. To test this cl random sample of runs scored by league A teams with and without their DH is given in the accompanying table Complete parts a) through d) below a) Draw side-by-side boxplots of the number of runs scored by League A teams with and without their DH Choose the correct graph below OA OB. Q OC. B 10 xxx G Q Q O D. B RIMME 10 10 Does there appear to be a difference in the number of runs between these situations? OA. No because the number of runs scored in a League A park is about the same as the number of runs scored in a League B park OB. No but the number of runs scored in a League A park appear to be slightly higher than the number of runs scored in a League B park. OC. Yes because the number of runs scored in a League A park appear to have a higher median than the number of runs scored in a League B park OD. D. Yes because the number of runs scored in a League B park appear to have a higher median than the number of runs scored in a League A park Q Q Sample of Runs League A Park (with DH) 2 3 6 6 8 1 3 7 6 4 4 12 5 6 5 6 5 9 9 3 14 4 6 1 2 6 4 3 3 Full data set League B Park (without DH) 5 5 4 7 2 9 10 1 1 3 2 7 6 8 3 5 5 13 7 2 5 14 7 0 2 4 2 2 4 9 3 2
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
Complete a-c
for c do we reject or accept the p-value due to sufficient or insufficient evidence?
![### Understanding Hypothesis Testing for Mean Runs in Different Ballparks
#### a) Criteria for Hypothesis Testing
In conducting a hypothesis test to determine if the mean number of runs scored differs between two types of ballparks, consider the following criteria:
- **A.** Each sample is obtained independently of the other.
- **B.** Each sample is a simple random sample.
- **C.** Each sample has the same sample size.
- **D.** Each sample size is large.
- **E.** Each sample size is small relative to the size of its population.
#### c) Hypothesis Test for Mean Runs
To test whether the mean number of runs scored in a League A park is greater than that in a League B park at the \( \alpha = 0.01 \) significance level, follow these steps:
1. **Determine Hypotheses**
Let \( \mu_A \) represent the mean number of runs scored by a League A team in a League A park, and \( \mu_B \) represent the mean number of runs scored by a League A team in a League B park.
- Null Hypothesis (\( H_0 \)): \[ \mu_A = \mu_B \]
- Alternative Hypothesis (\( H_1 \)): \[ \mu_A > \mu_B \]
2. **Find the test statistic** \( t_0 \):
\[
t_0 = \_\_\_ \quad (\text{Round to two decimal places as needed.})
\]
3. **Determine the P-value for the test**:
\[
\text{P-value} = \_\_\_ \quad (\text{Round to three decimal places as needed.})
\]
These steps will guide you in testing the hypothesis that the mean number of runs differs between the two types of parks at a specified level of significance.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9286dec2-87de-41e0-b292-cb9e24765e4b%2Fcddb98f3-e354-4a54-b38b-5906d7d79615%2F0wurt1o_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Understanding Hypothesis Testing for Mean Runs in Different Ballparks
#### a) Criteria for Hypothesis Testing
In conducting a hypothesis test to determine if the mean number of runs scored differs between two types of ballparks, consider the following criteria:
- **A.** Each sample is obtained independently of the other.
- **B.** Each sample is a simple random sample.
- **C.** Each sample has the same sample size.
- **D.** Each sample size is large.
- **E.** Each sample size is small relative to the size of its population.
#### c) Hypothesis Test for Mean Runs
To test whether the mean number of runs scored in a League A park is greater than that in a League B park at the \( \alpha = 0.01 \) significance level, follow these steps:
1. **Determine Hypotheses**
Let \( \mu_A \) represent the mean number of runs scored by a League A team in a League A park, and \( \mu_B \) represent the mean number of runs scored by a League A team in a League B park.
- Null Hypothesis (\( H_0 \)): \[ \mu_A = \mu_B \]
- Alternative Hypothesis (\( H_1 \)): \[ \mu_A > \mu_B \]
2. **Find the test statistic** \( t_0 \):
\[
t_0 = \_\_\_ \quad (\text{Round to two decimal places as needed.})
\]
3. **Determine the P-value for the test**:
\[
\text{P-value} = \_\_\_ \quad (\text{Round to three decimal places as needed.})
\]
These steps will guide you in testing the hypothesis that the mean number of runs differs between the two types of parks at a specified level of significance.
Transcribed Image Text:In this educational exercise, we explore a baseball scenario regarding the designated hitter (DH) rule in League A, specifically comparing the number of runs scored in League A parks (with DH) vs. League B parks (without DH).
### Boxplots:
Four options (A, B, C, D) present potential boxplot representations comparing the number of runs scored by League A teams with and without the DH. Each boxplot displays:
- **Box:** Represents the interquartile range (IQR)
- **Line within box:** Median number of runs
- **Whiskers:** Data variability outside the IQR
- **X (if present):** Outliers beyond expected variability
### Sample of Runs (Table):
**Data Set:**
- League A Park (with DH): 2, 1, 7, 4, 2, 3, 11, 14, 6
- League B Park (without DH): 5, 5, 4, 2, 4, 5, 13, 2, 7, 0
### Questions:
a) **Choose the Correct Boxplot**:
Identify which boxplot correctly represents the run distribution. The correct choice must accurately display the median and variability based on the provided data.
b) **Difference in Runs**:
Evaluate if there's a noticeable difference in runs between parks with and without the DH.
- Option A: No seen difference.
- Option B: League A Park shows slightly higher runs.
- Option C: League A Park has a higher median.
- Option D: League B Park shows higher median runs.
c) **Hypothesis Testing**:
Discuss using hypothesis tests to determine if the mean number of runs significantly differs between the two types of ballparks.
This exercise allows students to practice statistical interpretation using visual data representations and facilitates understanding of real-world applications of boxplots and hypothesis testing in sports analytics.
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