### Statistical Problem: Nurses and Fainting at the Sight of Blood**Problem Statement**: Many people assume that nurses are less likely than others to "feel faint" or "get sick" at the sight of blood. Suppose it is known that 30% of Americans will feel faint or get sick at the sight of blood. A random sample of 500 nurses was obtained. Of the 500 nurses, only 125 admitted to ever feeling faint or getting sick at the sight of blood. At the 10% significance level, can you conclude that nurses are less likely than other Americans to feel faint or get sick at the sight of blood?**Details**:- **Population proportion** (Americans who feel faint/get sick at the sight of blood): \( p = 0.30 \)- **Sample size**: \( n = 500 \)- **Number of nurses feeling faint/getting sick**: \( x = 125 \)- **Sample proportion**: \( \hat{p} = \frac{125}{500} = 0.25 \)- **Significance level**: \( \alpha = 0.10 \)**Hypotheses**:- Null Hypothesis \( (H_0) \): \( p \geq 0.30 \)- Alternative Hypothesis \( (H_a) \): \( p < 0.30 \)This problem requires performing a hypothesis test for the population proportion to determine if the proportion of nurses who feel faint or get sick at the sight of blood is significantly less than that of the general population. **Relevant Test Statistics**:To conduct the hypothesis test, we need to calculate the z-score and compare it to the critical z-value at the 10% significance level for a one-tailed test.Use the formula for the z-score of a sample proportion:\[ z = \frac{\hat{p} - p}{\sqrt{\frac{p(1 - p)}{n}}} \]Where:- \( \hat{p} \) is the sample proportion- \( p \) is the population proportion- \( n \) is the sample size**Interpretation**:Based on the calculated z-score, the conclusion will be drawn on whether the null hypothesis can be rejected in favor of the alternative hypothesis at the 10% significance level. An analysis will then be made to determine if nurses are statistically

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4. Many people assume that nurses are less likely than others to “feel faint" or "get sick" at the sight of blood. Suppose it is known that 30% of Americans will feel faint or get sick at the sight of blood. A random sample of 500 nurses was obtained. Of the 500 nurses, only 125 admitted to ever feeling faint or getting sick at the sight of blood. At the 10% significance level, can you conclude that nurses are less likely than other Americans to feel faint or get sick at the sight of blood?

4. Many people assume that nurses are less likely than others to “feel faint" or "get sick" at the sight of blood. Suppose it is known that 30% of Americans will feel faint or get sick at the sight of blood. A random sample of 500 nurses was obtained. Of the 500 nurses, only 125 admitted to ever feeling faint or getting sick at the sight of blood. At the 10% significance level, can you conclude that nurses are less likely than other Americans to feel faint or get sick at the sight of blood?

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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