### Understanding Confidence Intervals and Hypothesis Testing**Concept:**The three confidence intervals shown below represent three samplings. The objective is to decide whether each confidence interval indicates that you should reject the null hypothesis $ H_0 $. The null hypothesis in this case is $ H_0: p \leq 0.24 $.### Graphs Explanation:1. **Hypothesis Range Representation:** - A horizontal bar indicates the value range where $ p \leq 0.24 $ (up to 0.24 on the scale).2. **Confidence Interval Graphs:** - **Interval (a):** The confidence interval (CI) ranges from $ 0.25 < p < 0.26 $. - **Interval (b):** The confidence interval (CI) ranges from $ 0.21 < p < 0.23 $. - **Interval (c):** The confidence interval (CI) ranges from $ 0.225 < p < 0.265 $.### Questions and Answers:#### (a) Choose the correct answer below:- **A. Fail to reject $ H_0 $. The confidence interval includes values less than 0.24.**- **B. Reject $ H_0 $. The confidence interval is located to the right of 0.24.**- **C. Reject $ H_0 $. The confidence interval includes values less than 0.24.**- **D. Fail to reject $ H_0 $. The confidence interval is located to the right of 0.24.**#### (b) Choose the correct answer below:- **A. Fail to reject $ H_0 $. The confidence interval includes values greater than 0.24.**- **B. Fail to reject $ H_0 $. The confidence interval includes values less than 0.24.**- **C. Reject $ H_0 $. The confidence interval includes values greater than 0.24.**- **D. Reject $ H_0 $. The confidence interval includes values less than 0.24.**### Explanation:1. **Decision for Interval (a):** - The interval $ 0.25 < p < 0.26 $ lies entirely to the right of 0.24. - You should **reject $ H_0 $** because the ## Understanding Confidence Intervals and Hypothesis TestingThe three confidence intervals displayed represent three distinct samplings. Your task is to determine whether each confidence interval suggests rejecting the null hypothesis $H_0$. Please justify your reasoning.### Hypothesis$H_0$: $p \leq 0.24$### Graphical RepresentationThere are three intervals labeled (a), (b), and (c):- **Interval (a)**: $0.25 < p < 0.26$- **Interval (b)**: $0.21 < p < 0.23$- **Interval (c)**: $0.225 < p < 0.265$The intervals are marked on a continuous scale from 0.21 to 0.27.**Choice Section**#### (b) Choose the correct answer below for Interval (a):- $ \circ $ **A.** Fail to reject $H_0$. The confidence interval includes values greater than 0.24.- $ \circ $ **B.** Fail to reject $H_0$. The confidence interval includes values less than 0.24.- $ \circ $ **C.** Reject $H_0$. The confidence interval includes values greater than 0.24.- $ \circ $ **D.** Reject $H_0$. The confidence interval includes values less than 0.24.#### (c) Choose the correct answer below for Intervals (b) & (c):- $ \circ $ **A.** Reject $H_0$. The confidence interval includes values less than 0.24.- $ \circ $ **B.** Fail to reject $H_0$. The confidence interval includes values less than 0.24.- $ \circ $ **C.** Fail to reject $H_0$. The confidence interval includes values greater than 0.24.- $ \circ $ **D.** Reject $H_0$. The confidence interval includes values greater than 0.24.### ExplanationTo determine whether to reject or fail to reject $H_0$, observe where the intervals lie in relation to the null hypothesis boundary $p = 0.24$:1. **Interval (a)**: \(0.25 < p < 0.

Here the Null Hypothesis given is : Null : H0 : p ≤ 0.24 We know that Null and Alternate Hypothesis…

Answered: 0.25 | bartleby

Math

Statistics

0.25

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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