Rhino viruses typically cause common colds. In a test of the effectiveness of echinacea, 42 of the 48 subjects treated with echinacea developed rhinovirus infections. In a placebo group, 95 of the 111 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 A. Ho: P1 #P2 O B. Ho: P1= P2 O C. Ho: P1 = P2 H1: P1 P2 H1: P1< P2 H1: P1 # P2 O F. Ho: P1 = P2 H1: P1 > P2 D. Ho P12P2 O E. Ho: P1SP2 H1 P1 P2 H1: P1 P2 (F Ide P-va (Rou

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**Hypothesis Testing for Echinacea Efficacy**

Rhinoviruses typically cause common colds. In a test of the effectiveness of echinacea, 42 of the 48 subjects treated with echinacea developed rhinovirus infections. In a placebo group, 95 of the 111 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?

- **A.**
  - \(H_0: p_1 \neq p_2\)
  - \(H_1: p_1 = p_2\)

- **B.**
  - \(H_0: p_1 \geq p_2\)
  - \(H_1: p_1 < p_2\)

- **C.**
  - \(H_0: p_1 = p_2\)
  - \(H_1: p_1 \neq p_2\)

- **D.**
  - \(H_0: p_1 = p_2\)
  - \(H_1: p_1 > p_2\)

- **E.**
  - \(H_0: p_1 \leq p_2\)
  - \(H_1: p_1 > p_2\)

- **F.**
  - \(H_0: p_1 > p_2\)
  - \(H_1: p_1 \leq p_2\)
Transcribed Image Text:**Hypothesis Testing for Echinacea Efficacy** Rhinoviruses typically cause common colds. In a test of the effectiveness of echinacea, 42 of the 48 subjects treated with echinacea developed rhinovirus infections. In a placebo group, 95 of the 111 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? - **A.** - \(H_0: p_1 \neq p_2\) - \(H_1: p_1 = p_2\) - **B.** - \(H_0: p_1 \geq p_2\) - \(H_1: p_1 < p_2\) - **C.** - \(H_0: p_1 = p_2\) - \(H_1: p_1 \neq p_2\) - **D.** - \(H_0: p_1 = p_2\) - \(H_1: p_1 > p_2\) - **E.** - \(H_0: p_1 \leq p_2\) - \(H_1: p_1 > p_2\) - **F.** - \(H_0: p_1 > p_2\) - \(H_1: p_1 \leq p_2\)
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