**Understanding Confidence Intervals and Hypothesis Testing****Question:** The p-value for a two-sided hypothesis test of the null hypothesis \( H_0: \mu = 12 \) is 0.07. Which of the following confidence intervals would include the value 12?1. 90% Confidence Interval2. 95% Confidence Interval3. 99% Confidence Interval**Options:**a. Impossible to Determine b. **1 only** c. 2 and 3 d. 1 and 2 e. 1, 2, and 3 The correct answer, in this case, is option b, which indicates that **only the 90% confidence interval** would include the value 12 given the p-value of 0.07.**Explanation of Concepts:**- **Null Hypothesis (\( H_0 \))**: A statement that there is no effect or no difference, and it is the hypothesis that a test seeks to disprove.- **p-value**: The probability of obtaining test results at least as extreme as the observed during the test, assuming that the null hypothesis is correct. Lower p-values indicate stronger evidence against the null hypothesis.- **Confidence Interval (CI)**: A range of values that is likely to contain the population parameter with a certain level of confidence (e.g., 90%, 95%, 99%).**Detailed Steps in Interpretation:**1. **Significance Level (\( \alpha \))**: - For a **90% CI**, \( \alpha = 0.10 \) (or 10%). - For a **95% CI**, \( \alpha = 0.05 \) (or 5%). - For a **99% CI**, \( \alpha = 0.01 \) (or 1%).2. **Comparing p-value with \( \alpha \)**: - p-value (0.07) compared to \( \alpha = 0.10 \) for 90% CI: - Since 0.07 < 0.10, we do not reject \( H_0 \) at 90% confidence level, meaning 12 is included in the 90% CI. - p-value (0.07) compared to \( \alpha = 0.05 \) for 95% CI: -

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The p-value for a two-sided hypothesis test of the null hypothesis Họ: H = 12 is 0.07. Which of the following confidence intervals would include the value 12? 1. 90% Confidence Interval 2. 95% Confidence Interval 3. 99% Confidence Interval Impossible to Determine 1 only Ob. 2 and 3 Oc. 1 and 2 Od. 1, 2, and 3 Oe.

The p-value for a two-sided hypothesis test of the null hypothesis Họ: H = 12 is 0.07. Which of the following confidence intervals would include the value 12? 1. 90% Confidence Interval 2. 95% Confidence Interval 3. 99% Confidence Interval Impossible to Determine 1 only Ob. 2 and 3 Oc. 1 and 2 Od. 1, 2, and 3 Oe.

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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