Rhino viruses typically cause common colds. In a test of the effectiveness of echinacea, 34 of the 41 subjects treated with echinacea developed rhinovirus infections. In a placebo group, 83 of the 97 subjects developed rhinovirus infections. Use a 0.05 significance level to test the claim that echinacea has an effect on rhinovirus infections. Complete parts (a) through (c) below. a. Test the claim using a hypothesis test. Consider 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 alternative hypotheses for the hypothesis test? O B. Ho: P1 SP2 H: P, #P2 OC. Ho: P1 = P2 H4:P1 < P2 O A. Ho P1 P2 H: P1 P2 O D. Ho: P1 2 P2 H4: P, #P2 O E. Ho: P1 #P2 H,: P, = P2 F. Ho: P1 = P2 H: P, #P2 Identify the test statistic. "Round to two decimal places as needed.)

MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
icon
Related questions
Topic Video
Question

please help me also find the p value and what the conclusion would be. Thank you!

### Hypothesis Testing: Echinacea and Rhinovirus Infections

**Background:**
Rhino viruses typically cause common colds. This study examines the effectiveness of echinacea in preventing rhinovirus infections. In a test of the effectiveness of echinacea, the following results were observed:

- Echinacea group: 34 of 41 subjects developed rhinovirus infections.
- Placebo group: 83 of 97 subjects developed rhinovirus infections.

Using a significance level of 0.05, we will test the claim that echinacea has an effect on rhinovirus infections.

**Hypothesis Test:**
We need to determine the null and alternative hypotheses for the test. The first sample is the group treated with echinacea, and the second sample is the placebo group.

- **Null Hypothesis (\(H_0\)):** \( p_1 = p_2 \)
- **Alternative Hypothesis (\(H_1\)):** \( p_1 \neq p_2 \)

In this scenario, the correct choice is F, as indicated in the image.

**Identify the Test Statistic:**
Calculate the test statistic \( z \) using the formula for the difference in proportions. It will be rounded to two decimal places as needed, but the image does not provide the exact z-value in the blank space.

This setup allows the evaluation of whether there is a statistically significant difference in the infection rates between the echinacea and placebo groups, based on the observed data.
Transcribed Image Text:### Hypothesis Testing: Echinacea and Rhinovirus Infections **Background:** Rhino viruses typically cause common colds. This study examines the effectiveness of echinacea in preventing rhinovirus infections. In a test of the effectiveness of echinacea, the following results were observed: - Echinacea group: 34 of 41 subjects developed rhinovirus infections. - Placebo group: 83 of 97 subjects developed rhinovirus infections. Using a significance level of 0.05, we will test the claim that echinacea has an effect on rhinovirus infections. **Hypothesis Test:** We need to determine the null and alternative hypotheses for the test. The first sample is the group treated with echinacea, and the second sample is the placebo group. - **Null Hypothesis (\(H_0\)):** \( p_1 = p_2 \) - **Alternative Hypothesis (\(H_1\)):** \( p_1 \neq p_2 \) In this scenario, the correct choice is F, as indicated in the image. **Identify the Test Statistic:** Calculate the test statistic \( z \) using the formula for the difference in proportions. It will be rounded to two decimal places as needed, but the image does not provide the exact z-value in the blank space. This setup allows the evaluation of whether there is a statistically significant difference in the infection rates between the echinacea and placebo groups, based on the observed data.
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 2 steps with 3 images

Blurred answer
Knowledge Booster
Research Design Formulation
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, statistics and related others by exploring similar questions and additional content below.
Recommended textbooks for you
MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
Probability and Statistics for Engineering and th…
Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning
Statistics for The Behavioral Sciences (MindTap C…
Statistics for The Behavioral Sciences (MindTap C…
Statistics
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
Elementary Statistics: Picturing the World (7th E…
Elementary Statistics: Picturing the World (7th E…
Statistics
ISBN:
9780134683416
Author:
Ron Larson, Betsy Farber
Publisher:
PEARSON
The Basic Practice of Statistics
The Basic Practice of Statistics
Statistics
ISBN:
9781319042578
Author:
David S. Moore, William I. Notz, Michael A. Fligner
Publisher:
W. H. Freeman
Introduction to the Practice of Statistics
Introduction to the Practice of Statistics
Statistics
ISBN:
9781319013387
Author:
David S. Moore, George P. McCabe, Bruce A. Craig
Publisher:
W. H. Freeman