A data set includes wait times (minutes) for the Tower of Terror ride at Walt Disney World's Hollywood Studios theme park at 5:00 PM. Using 37 of the times to test the claim that the mean of all such wait times is more than 30 minutes, the accompanying Excel display is obtained. Test the given claim by using the display provided from Excel. Use a 0.05 significance level. 1. Identify the null and alternative hypotheses. 2. Identify the test statistic. 3. Identify the P-
A data set includes wait times (minutes) for the Tower of Terror ride at Walt Disney World's Hollywood Studios theme park at 5:00 PM. Using 37 of the times to test the claim that the mean of all such wait times is more than 30 minutes, the accompanying Excel display is obtained. Test the given claim by using the display provided from Excel. Use a 0.05 significance level. 1. Identify the null and alternative hypotheses. 2. Identify the test statistic. 3. Identify the P-
MATLAB: An Introduction with Applications
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ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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A data set includes wait times (minutes) for the Tower of Terror ride at Walt Disney World's Hollywood Studios theme park at 5:00 PM. Using 37 of the times to test the claim that the mean of all such wait times is more than 30 minutes, the accompanying Excel display is obtained. Test the given claim by using the display provided from Excel. Use a 0.05 significance level.
1. Identify the null and alternative hypotheses.
2. Identify the test statistic.
3. Identify the P-value.
4. State the conclusion about the null hypothesis, as well as the final conclusion that addresses the original claim.
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Transcribed Image Text:The image displays a table labeled "Excel Display" with the following statistical data:
- **Difference**: 3
- **t (Observed value)**: 0.939
- **t (Critical value)**: 1.688
- **DF (Degrees of Freedom)**: 36
- **p-value (one-tailed)**: 0.177
- **alpha**: 0.05
This table likely represents the results of a t-test, which compares the means of two groups to determine if they are statistically different from each other. The "Difference" indicates the mean difference between the groups. The "t (Observed value)" is the calculated t-statistic from the data, and the "t (Critical value)" is the threshold for significance. "DF" represents the degrees of freedom in the analysis. The "p-value (one-tailed)" suggests the probability of observing the data, assuming the null hypothesis is true. An "alpha" level of 0.05 is the standard significance level, indicating a 5% risk of concluding that a difference exists when there is none.
![**Understanding Hypothesis Testing in Statistics**
When conducting statistical analyses, it’s vital to understand how to state and interpret the conclusions about the null hypothesis.
### Scenario:
In this exercise, we'll determine whether the mean time of all taxi cab rides in New York City yellow cabs during Friday mornings is less than 15 minutes.
Here is the statement you need to address:
**State the conclusion about the null hypothesis, as well as the final conclusion that addresses the original claim:**
- **[Dropdown: Reject/Do not reject]** the null hypothesis. There **[Dropdown: is/is not]** sufficient evidence at the 0.05 significance level to **[Dropdown: support/refute]** the claim that the mean time of all taxi cab rides in New York City yellow cabs during Friday morning is less than 15 minutes.
### Explanation:
1. **Null Hypothesis (H₀):** This typically suggests no effect or no difference. In this context, it states that the mean taxi ride time is not less than 15 minutes.
2. **Alternative Hypothesis (H₁):** This is what you aim to support, suggesting the mean time is less than 15 minutes.
3. **Significance Level (α = 0.05):** This threshold determines the probability of rejecting a true null hypothesis (Type I error). A common choice is 5%.
4. **Conclusion Options:**
- **Reject the Null Hypothesis:** There is sufficient evidence to support the claim.
- **Do not Reject the Null Hypothesis:** There is not sufficient evidence to support the claim.
Understanding these concepts helps in interpreting statistical data and making informed decisions based on evidence.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3f3a5825-1402-407e-b54f-9cd8c5f3eee1%2F447b33d0-0490-4874-85a7-b4c76f1ab92f%2Fk02np3_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Understanding Hypothesis Testing in Statistics**
When conducting statistical analyses, it’s vital to understand how to state and interpret the conclusions about the null hypothesis.
### Scenario:
In this exercise, we'll determine whether the mean time of all taxi cab rides in New York City yellow cabs during Friday mornings is less than 15 minutes.
Here is the statement you need to address:
**State the conclusion about the null hypothesis, as well as the final conclusion that addresses the original claim:**
- **[Dropdown: Reject/Do not reject]** the null hypothesis. There **[Dropdown: is/is not]** sufficient evidence at the 0.05 significance level to **[Dropdown: support/refute]** the claim that the mean time of all taxi cab rides in New York City yellow cabs during Friday morning is less than 15 minutes.
### Explanation:
1. **Null Hypothesis (H₀):** This typically suggests no effect or no difference. In this context, it states that the mean taxi ride time is not less than 15 minutes.
2. **Alternative Hypothesis (H₁):** This is what you aim to support, suggesting the mean time is less than 15 minutes.
3. **Significance Level (α = 0.05):** This threshold determines the probability of rejecting a true null hypothesis (Type I error). A common choice is 5%.
4. **Conclusion Options:**
- **Reject the Null Hypothesis:** There is sufficient evidence to support the claim.
- **Do not Reject the Null Hypothesis:** There is not sufficient evidence to support the claim.
Understanding these concepts helps in interpreting statistical data and making informed decisions based on evidence.
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