Find the test statistic and the P-value **Understanding Hypothesis Testing for Predicting Geyser Eruptions**Park officials make predictions of times to the next eruption of a particular geyser and collect data for the errors (in minutes) in those predictions. The display below results from using the prediction errors to test the claim that the mean prediction error is equal to zero. The process requires using a 0.05 significance level. **Key Components to be Examined:**1. Identification of the null and alternative hypotheses.2. Calculation of the test statistic.3. Determination of the P-value.4. Final conclusion that addresses the original claim based on the above results.**Display Analysis:***Assuming all conditions for conducting a hypothesis test are met, we need to determine the null and alternative hypotheses.*### Hypothesis Identification:#### A. - **Null Hypothesis (H₀):** μ = 0 minutes- **Alternative Hypothesis (H₁):** μ < 0 minutes#### B.- **Null Hypothesis (H₀):** μ = 0 minutes- **Alternative Hypothesis (H₁):** μ > 0 minutes#### C.- **Null Hypothesis (H₀):** μ = 0 minutes- **Alternative Hypothesis (H₁):** μ ≠ 0 minutes#### D.- **Null Hypothesis (H₀):** μ = 0 minutes- **Alternative Hypothesis (H₁):** μ ≠ 0 minutes**Explanation of Options:**One of the options (A, B, C, or D) needs to be selected based on the context provided. These hypotheses will facilitate understanding if the prediction errors significantly differ from zero and in what direction (positive or negative) they differ, contributing to a better understanding of the prediction's accuracy.**Conclusion:**The correct form of null and alternative hypotheses needs to be selected and verified through calculations of test statistics and P-value. Based on these results, the accuracy of the original predictions can be assessed accordingly. ### Statistical Analysis ResultsThis section explains the results of a statistical hypothesis test. Below are the key values and their interpretations:- **Difference:** -0.496 - This value represents the difference between the sample mean and the population mean or between two sample means.- **t (Observed value):** -7.82 - The t value indicates how many standard deviations the observed difference is from the null hypothesis. - **|t| (Critical value):** 1.984 - This is the critical value for the t distribution at a certain confidence level, typically corresponding to a 95% confidence interval for a two-tailed test. If the absolute value of the observed t-value exceeds this critical value, the null hypothesis is rejected.- **DF (Degrees of Freedom):** 99 - Degrees of freedom refer to the number of independent values or quantities that can vary in the final calculation of a statistic.- **p-value (Two-tailed):** < 0.0001 - The p-value indicates the probability of obtaining the observed results, or more extreme, assuming the null hypothesis is true. A p-value less than 0.05 (the alpha level) suggests that the observed data is statistically significant, leading to the rejection of the null hypothesis.- **alpha:** 0.05 - The alpha level represents the threshold for statistical significance. Commonly set at 0.05, this value denotes a 5% risk of concluding that a difference exists when there is no actual difference.#### Interpretation:In this analysis, the observed t-value (-7.82) is much greater in magnitude than the critical value (1.984), and the p-value is less than 0.0001, which is below the alpha threshold of 0.05. This means the difference observed is statistically significant, and the null hypothesis can be rejected.--- This data provides important insights into the statistical test procedures and results, laying a foundation for interpreting and understanding hypothesis testing in research.

Name: Find the test statistic and the P-value **Understanding Hypothesis Tes
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Description: Find the test statistic and the P-value **Understanding Hypothesis Testing for Predicting Geyser Eruptions**Park officials make predictions of times to the next eruption of a particular geyser and collect data for the errors (in minutes) in those pre

From the given output, the test statistic value is –7.82. The degrees of freedom is given as 99.

Math

Statistics

Park officials make predictions of times to the next eruption of a particular geyser, and collect data for the errors (minutes) in those predictions. The display from technology available below results from using the prediction errors to test the claim that the mean prediction error is equal to zero. Comment on the accuracy of the predictions. 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.

Park officials make predictions of times to the next eruption of a particular geyser, and collect data for the errors (minutes) in those predictions. The display from technology available below results from using the prediction errors to test the claim that the mean prediction error is equal to zero. Comment on the accuracy of the predictions. 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.

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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