MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN: 9781119256830
Author: Amos Gilat
Publisher: John Wiley & Sons Inc
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Concept explainers

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Regression Analysis
Regression analysis is a statistical method in which it estimates the relationship between a dependent variable and one or more independent variable. In simple terms dependent variable is called as outcome variable and independent variable is called as p…
Question

What am I doing wrong on 5.24? 
i keep getting .92 for the answer for p-hat.
please write the answer out the long way this time. Thanks.

 

 

**5.22 Getting Enough Sleep** 400 students were randomly sampled from a large university, and 289 students said they did not get enough sleep. Conduct a hypothesis test to check whether this represents a statistically significant difference from 70% and use a significance level of 0.01. --- **5.23 Working Backwards, Part I** You are given the following hypotheses: - \(H_0: p = 0.3\) - \(H_A: p \neq 0.3\) We know the sample size is 90. For what sample proportion would the p-value be equal to 0.067? Assume that all conditions necessary for inference are satisfied. --- **5.24 Working Backwards, Part II** You are given the following hypotheses: - \(H_0: p = 0.9\) - \(H_A: p \neq 0.9\) We know that the sample size is 90. For what sample proportion would the p-value be equal to 0.017? Assume that all conditions necessary for inference are satisfied. --- **5.25 Testing for Fibromyalgia** A patient named Diana was diagnosed with fibromyalgia, a long-term syndrome of body pain, and was prescribed anti-depressants. Being the skeptical type, Diana was suspicious of being on anti-depressants and initially believed that anti-depressants would help only a couple of her symptoms. However, after a few months on the medication, she decides that the anti-depressants are working, because she feels like her symptoms are in fact getting better. (a) Write the hypotheses in words for Diana's skeptical position when she started taking the anti-depressants. (b) What is a Type 1 Error in this context?
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Transcribed Image Text:**5.22 Getting Enough Sleep** 400 students were randomly sampled from a large university, and 289 students said they did not get enough sleep. Conduct a hypothesis test to check whether this represents a statistically significant difference from 70% and use a significance level of 0.01. --- **5.23 Working Backwards, Part I** You are given the following hypotheses: - \(H_0: p = 0.3\) - \(H_A: p \neq 0.3\) We know the sample size is 90. For what sample proportion would the p-value be equal to 0.067? Assume that all conditions necessary for inference are satisfied. --- **5.24 Working Backwards, Part II** You are given the following hypotheses: - \(H_0: p = 0.9\) - \(H_A: p \neq 0.9\) We know that the sample size is 90. For what sample proportion would the p-value be equal to 0.017? Assume that all conditions necessary for inference are satisfied. --- **5.25 Testing for Fibromyalgia** A patient named Diana was diagnosed with fibromyalgia, a long-term syndrome of body pain, and was prescribed anti-depressants. Being the skeptical type, Diana was suspicious of being on anti-depressants and initially believed that anti-depressants would help only a couple of her symptoms. However, after a few months on the medication, she decides that the anti-depressants are working, because she feels like her symptoms are in fact getting better. (a) Write the hypotheses in words for Diana's skeptical position when she started taking the anti-depressants. (b) What is a Type 1 Error in this context?
**5.24 Working Backwards, Part II** **Step 1:** - Given test is a two-tail test. - Population proportion is \( p = 0.9 \). - Sample size is \( n = 1429 \). **Hypotheses:** - Null hypothesis (\( H_0 \)): \( p = 0.9 \) - Alternative hypothesis (\( H_a \)): \( p \neq 0.9 \) **Step 2:** - Significance level \( p = 0.05 \)? **Calculate Sample Proportion (\( \hat{p} \)):** 1. **P-value:** - \( p = 0.01 \) for a two-tailed test. - \( Z = \pm 2.58 \) for 99% confidence interval. 2. **Standard Error (SE):** \[ SE = \sqrt{\frac{p(1-p)}{n}} = \sqrt{\frac{0.9(1-0.9)}{1429}} = 0.0079 \] 3. **Calculate \( \hat{p} \):** - Use formula for Z-score: \[ Z = \frac{\hat{p} - p}{SE} \] \[ 2.58 = \frac{\hat{p} - 0.9}{0.0079} \] \[ \hat{p} - 0.9 = 2.58 \times 0.0079 \] \[ \hat{p} = 0.9 + 0.0204 = 0.92 \] **Conclusion:** - The sample proportion (\( \hat{p} \)) is calculated to be \( 0.92 \).
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Transcribed Image Text:**5.24 Working Backwards, Part II** **Step 1:** - Given test is a two-tail test. - Population proportion is \( p = 0.9 \). - Sample size is \( n = 1429 \). **Hypotheses:** - Null hypothesis (\( H_0 \)): \( p = 0.9 \) - Alternative hypothesis (\( H_a \)): \( p \neq 0.9 \) **Step 2:** - Significance level \( p = 0.05 \)? **Calculate Sample Proportion (\( \hat{p} \)):** 1. **P-value:** - \( p = 0.01 \) for a two-tailed test. - \( Z = \pm 2.58 \) for 99% confidence interval. 2. **Standard Error (SE):** \[ SE = \sqrt{\frac{p(1-p)}{n}} = \sqrt{\frac{0.9(1-0.9)}{1429}} = 0.0079 \] 3. **Calculate \( \hat{p} \):** - Use formula for Z-score: \[ Z = \frac{\hat{p} - p}{SE} \] \[ 2.58 = \frac{\hat{p} - 0.9}{0.0079} \] \[ \hat{p} - 0.9 = 2.58 \times 0.0079 \] \[ \hat{p} = 0.9 + 0.0204 = 0.92 \] **Conclusion:** - The sample proportion (\( \hat{p} \)) is calculated to be \( 0.92 \).
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