**Hypothesis Testing for the Effectiveness of Echinacea on Rhinovirus Infections**Rhino viruses typically cause common colds. In a study examining the effectiveness of echinacea, 36 out of 42 subjects treated with echinacea developed rhinovirus infections. In a placebo group, 97 out of 110 subjects developed rhinovirus infections. We will conduct a hypothesis test at a significance level of 0.01 to determine if echinacea has an effect on rhinovirus infections.### a. Hypothesis Test**Null and Alternative Hypotheses:**Consider the first sample to be subjects treated with echinacea and the second sample to be subjects treated with a placebo. Select the correct null (H₀) and alternative (H₁) hypotheses:- A. \(H₀: p_1 \neq p_2\), \(H₁: p_1 = p_2\)- B. \(H₀: p_1 = p_2\), \(H₁: p_1 \neq p_2\)- C. \(H₀: p_1 \leq p_2\), \(H₁: p_1 \neq p_2\)- D. \(H₀: p_1 \geq p_2\), \(H₁: p_1 \neq p_2\)- E. \(H₀: p_1 = p_2\), \(H₁: p_1 < p_2\)- F. \(H₀: p_1 = p_2\), \(H₁: p_1 > p_2\)**Identify the test statistic:**\[z = \text{(Round to two decimal places as needed.)}\]**Identify the P-value:**\[\text{P-value} = \text{(Round to three decimal places as needed.)}\]**Conclusion:**- The P-value is [ ] the significance level of \( \alpha = 0.01 \), so [ ] the null hypothesis.- There [ ] sufficient evidence to support the claim that echinacea treatment has an effect.### b. Confidence IntervalTest the claim by constructing an appropriate confidence interval.**The 99% Confidence Interval:**\[< (p_1 - p_2) < ### Confidence Interval Analysis#### Understanding the Conclusion Based on the Confidence IntervalThe analysis focuses on determining whether echinacea treatment has an effect based on the confidence interval:- **Statement:** Because the confidence interval limits [dropdown option] 0, there [dropdown option] appear to be a significant difference between the two proportions. There [dropdown option] evidence to support the claim that echinacea treatment has an effect.#### Effects of Echinacea on Infection RateBased on the given results, determine if echinacea affects the infection rate:- **Option A:** Echinacea does not appear to have a significant effect on the infection rate.- **Option B:** Echinacea does appear to have a significant effect on the infection rate. There is evidence that it increases the infection rate.- **Option C:** Echinacea does appear to have a significant effect on the infection rate. There is evidence that it lowers the infection rate.- **Option D:** The results are inconclusive. This exercise helps understand the statistical significance of an echinacea treatment analysis through confidence intervals and decision-making based on available evidence.

Name: **Hypothesis Testing for the Effectiveness of Echinacea on Rhinovirus
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Description: **Hypothesis Testing for the Effectiveness of Echinacea on Rhinovirus Infections**Rhino viruses typically cause common colds. In a study examining the effectiveness of echinacea, 36 out of 42 subjects treated with echinacea developed rhinovirus infe

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hino viruses typically cause common colds. In a test of the effectiveness of echinacea, 36 of the 42 subjects treated with echinacea developed rhinovirus infections. In a placebo gr 7 of the 110 subjects developed rhinovirus infections. Use a 0.01 significance level to test the claim that echinacea has an effect on rhinovirus infections. Complete parts (a) through elow. Test the claim using a hypothesis test. onsider the first sample to be the sample of subjects treated with echinacea and the second sample to be the sample of subjects treated with a placebo. What are the null and ternative hypotheses for the hypothesis test? DA. Ho: P1 #P2 O B. Ho: P1 = P2 H:P, #P2 OC. Ho: P1 sP2 H:P, #P2 H1: P, = P2 O D. Ho: P1 2 P2 H: P, #P2 O E. Ho: P1 = P2 H: Pq P2 lentify the test statistic.

hino viruses typically cause common colds. In a test of the effectiveness of echinacea, 36 of the 42 subjects treated with echinacea developed rhinovirus infections. In a placebo gr 7 of the 110 subjects developed rhinovirus infections. Use a 0.01 significance level to test the claim that echinacea has an effect on rhinovirus infections. Complete parts (a) through elow. Test the claim using a hypothesis test. onsider the first sample to be the sample of subjects treated with echinacea and the second sample to be the sample of subjects treated with a placebo. What are the null and ternative hypotheses for the hypothesis test? DA. Ho: P1 #P2 O B. Ho: P1 = P2 H:P, #P2 OC. Ho: P1 sP2 H:P, #P2 H1: P, = P2 O D. Ho: P1 2 P2 H: P, #P2 O E. Ho: P1 = P2 H: Pq P2 lentify the test statistic.

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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