17 **Hypothesis Testing with Tornado Data**A data set includes information from 500 random tornadoes. The display from the available technology results from using the tornado lengths (in miles) to test the claim that the mean tornado length is greater than 2.4 miles. A significance level of 0.05 is used. Identifying the null and alternative hypotheses, the test statistic, the P-value, and stating the final conclusion are essential steps in addressing the original claim.---### Hypothesis FormulationAssuming all conditions for conducting a hypothesis test are met, the task is to select the correct null and alternative hypotheses:- **Option A:** Null Hypothesis (H₀): μ = 2.4 miles Alternative Hypothesis (H₁): μ < 2.4 miles- **Option B:** Null Hypothesis (H₀): μ = 2.4 miles Alternative Hypothesis (H₁): μ > 2.4 miles- **Option C:** Null Hypothesis (H₀): μ = 2.4 miles Alternative Hypothesis (H₁): μ ≠ 2.4 miles- **Option D:** Null Hypothesis (H₀): μ < 2.4 miles Alternative Hypothesis (H₁): μ = 2.4 miles### Identify the Test Statistic- Round your answer to two decimal places as needed.### Identify the P-value- Round your answer to three decimal places as needed.### ConclusionState the final conclusion addressing the original claim:- **Conclusion:** \[ \text{Reject/Fail to Reject} \] H₀. There is [sufficient/insufficient] evidence to support the claim that the mean tornado length is greater than 2.4 miles. ### Display from Technology**Hypothesis Test Results:**- **μ**: Mean of variable- **H₀**: μ = 2.4- **Hₐ**: μ > 2.4| Variable | Sample Mean | Std. Err. | DF | T-Stat | P-value ||----------|-------------|-----------|-----|---------|---------|| Length | 2.59463 | 0.233786 | 499 | 0.832513| 0.2028 |**Explanation:**This table shows the results of a hypothesis test concerning the mean of a variable, referred to here as "Length." The null hypothesis \( H_0 \) suggests the mean (μ) is 2.4, while the alternative hypothesis \( H_A \) suggests the mean is greater than 2.4. Below, the table breaks down different statistical measures from the test:- **Sample Mean**: \( 2.59463 \) - The average value from the sample data.- **Std. Err.**: \( 0.233786 \) - The standard error of the sample mean.- **DF (Degrees of Freedom)**: \( 499 \) - Number of independent values in the data that can vary.- **T-Stat**: \( 0.832513 \) - The calculated t-statistic from the test.- **P-value**: \( 0.2028 \) - Probability of obtaining test results at least as extreme as the observed results, assuming that the null hypothesis is true.A P-value greater than 0.05 generally suggests there is not enough evidence to reject the null hypothesis.

Given that: Sample size, n=500 Level of significance, α=0.05 Sample mean, x¯=2.59463 Standard error, SE=0.233786State the null and alternative hypotheses: H0:μ=2.4H1:μ>2.4 This is right-tailed test. Thus, Option (B) is the correct answer. Compute the test statistic: t=x¯-μsn=x¯-μSE=2.59463-2.40.233786=0.8325≅0.83 The value of test statistic is 0.83.Obtain the degrees of freedom: df=n-1=500-1=499 Determine the critical value at 499 degrees of freedom by using the following excel function: The required p-value is 0.203. Make Decision: Rejection rule: Reject H0 if p-value of the test statistic < significance level, α=0.05, otherwise do not reject it. ∵0.203>0.05 Conclusion: Do not reject H0. There is not sufficient evidence to support the claim that the mean tornado length is greater than 2.4 miles at 0.05 significance level.

Math

Statistics

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 2.4 miles. Use a 0.05 significance level. Identify the null and alternative hypotheses, test statistic, P-value, and state the final conclusion that addresses the original claim. ✪ Click the icon to view the display from technology. Assuming all conditions for conducting a hypothesis test are met, what are the null and alternative hypotheses? O A. Ho: μ = 2.4 miles OB. Ho: H=2.4 miles H₁: μ<2.4 miles H₁: μ> 2.4 miles OC. Ho: μ=2.4 miles H₁: μ#2.4 miles Identify the test statistic. (Round to two decimal places as needed.) Identify the P-value. (Round to three decimal places as needed.) State the final conclusion that addresses the original claim. Ho. There is O D. Ho: 2.4 miles H₁: μ=2.4 miles evidence to support the claim that the mean tornado length is greater than 2.4 miles