**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

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ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

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Types of Bias

Statistics is the study of data collection, organization, analysis, interpretation, and presentation. Statistical bias is a characteristic of a statistical technique or its findings in which the expected value deviates from the actual root quantitative parameter being estimated. According to the actual definition of bias, it refers to the tendency of a statistic to overestimate or underestimate a parameter.

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