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.

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Description: 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. Us

The test hypotheses are: Null hypothesis: H0: μ = 2.2. Alternative hypothesis: HA: μ > 2.2

Answered: A data set includes data from 500…

MATLAB: An Introduction with Applications

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ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

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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.

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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