A data set includes data from 500 random tornadoes. The display from technology available below results from using the tornado lengths (miles) to test the claim that the mean tornado length is greater than 2.2 miles. Use a 0.05 significance level. Use the display to identify the null and alternative hypotheses, test statistic, and P-value. State the final conclusion that addresses the original claim.

MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
icon
Related questions
Topic Video
Question

A data set includes data from 500 random tornadoes. The display from technology available below results from using the tornado lengths (miles) to test the claim that the mean tornado length is greater than 2.2 miles. Use a 0.05 significance level. Use the display to identify the null and alternative hypotheses, test statistic, and P-value.

State the final conclusion that addresses the original claim.

### Hypothesis Test Results

**μ**: Mean of variable

- **Null Hypothesis (H₀)**: μ = 2.2
- **Alternative Hypothesis (H₁)**: μ > 2.2

#### Test Summary for Variable: Length

| Variable | Sample Mean | Std. Err. | DF  | T-Stat  | P-value |
|----------|--------------|-----------|-----|---------|---------|
| Length   | 2.38563      | 0.251663  | 499 | 0.737613| 0.2305  |

**Explanation of the Table:**

1. **Variable**: The attribute being tested, which in this case is "Length".
2. **Sample Mean**: The average value of the sample, which is 2.38563.
3. **Standard Error (Std. Err.)**: The standard deviation of the sample mean, which is 0.251663.
4. **Degrees of Freedom (DF)**: The number of independent values or quantities which can be assigned to a statistical distribution, which is 499.
5. **T-Statistic (T-Stat)**: The test statistic value for the hypothesis test, calculated to be 0.737613.
6. **P-value**: The probability of observing the test results under the null hypothesis, which is 0.2305 in this case.

**Conclusion:**
Given the P-value (0.2305) is greater than a common significance level (e.g., 0.05), we do not have enough evidence to reject the null hypothesis. Therefore, we cannot conclude that the mean length is greater than 2.2.
Transcribed Image Text:### Hypothesis Test Results **μ**: Mean of variable - **Null Hypothesis (H₀)**: μ = 2.2 - **Alternative Hypothesis (H₁)**: μ > 2.2 #### Test Summary for Variable: Length | Variable | Sample Mean | Std. Err. | DF | T-Stat | P-value | |----------|--------------|-----------|-----|---------|---------| | Length | 2.38563 | 0.251663 | 499 | 0.737613| 0.2305 | **Explanation of the Table:** 1. **Variable**: The attribute being tested, which in this case is "Length". 2. **Sample Mean**: The average value of the sample, which is 2.38563. 3. **Standard Error (Std. Err.)**: The standard deviation of the sample mean, which is 0.251663. 4. **Degrees of Freedom (DF)**: The number of independent values or quantities which can be assigned to a statistical distribution, which is 499. 5. **T-Statistic (T-Stat)**: The test statistic value for the hypothesis test, calculated to be 0.737613. 6. **P-value**: The probability of observing the test results under the null hypothesis, which is 0.2305 in this case. **Conclusion:** Given the P-value (0.2305) is greater than a common significance level (e.g., 0.05), we do not have enough evidence to reject the null hypothesis. Therefore, we cannot conclude that the mean length is greater than 2.2.
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 2 steps

Blurred answer
Knowledge Booster
Hypothesis Tests and Confidence Intervals for Means
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.
Similar questions
Recommended textbooks for you
MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
Probability and Statistics for Engineering and th…
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 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…
Elementary Statistics: Picturing the World (7th E…
Statistics
ISBN:
9780134683416
Author:
Ron Larson, Betsy Farber
Publisher:
PEARSON
The Basic Practice of Statistics
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
Introduction to the Practice of Statistics
Statistics
ISBN:
9781319013387
Author:
David S. Moore, George P. McCabe, Bruce A. Craig
Publisher:
W. H. Freeman