Question

ECHINACEA TO PREVENT COMMON COLDS Rhinovirus typically cause common colds. In a study to prevent common colds, subjects are divided into two groups. In group #1, 45 subjects were treated with echinacea and 38 of them developed rhinovirus infections. In group #2, 103 subjects were given a placebo and 88 of them developed rhinovirus infections. Use a

ECHINACEA TO PREVENT COMMON COLDS
Rhinovirus typically cause common colds. In a study to prevent common colds, subjects are divided into two groups. In group #1, 45 subjects were treated with echinacea and 38 of them developed rhinovirus infections. In group #2, 103 subjects were given a placebo and 88 of them developed rhinovirus infections. Use a 0.05 significance level to test the claim that people taking echinacea develop less rhinovirus infections than people who do not take echinacea.
Use the following steps:
Step 1. Write the Claim, Null Hypothesis and Alternative Hypothesis in symbols.
Step 2. Identify α
Step 3. Check and identify the requirements for this test.
Step 4. State the type of test (right-tail, left-tail, or two-tail test) and use the given test statistic to find the P-value (use the provided Standard Normal Distribution table, aka z-table, without rounding)
Test statistic z=-0.16
Step 5. State your decision to either reject or fail to reject the null hypothesis and why.
Step 6. Consider the claim and your decision and state the conclusion in the context of the problem.
Step 7. Considering your conclusion from part 6, does echinacea seem to be effective in preventing the common colds? Why or why not?

Answer 1

The hypothesis test does not provide enough evidence to support the claim that echinacea prevents common colds. Therefore, echinacea does not seem to be effective in preventing the common cold.

Step-by-step explanation:

Step 1: Write the Claim, Null Hypothesis, and Alternative Hypothesis in symbols. The Claim is that people taking echinacea develop less rhinovirus infections than people who do not take echinacea. The Null Hypothesis (H0) is that the proportion of people developing rhinovirus infections is the same for both groups. The Alternative Hypothesis (Ha) is that the proportion of people developing rhinovirus infections is different for the two groups.

Step 2: Identify α. The significance level α is given as 0.05.

Step 3: Check and identify the requirements for this test. The requirements for this test are met since the sample sizes for both groups are greater than 30.

Step 4: State the type of test and use the given test statistic to find the P-value. Since the Alternative Hypothesis is two-tailed, we will use a two-tail test. The test statistic z = -0.16. Using a z-table, we find the P-value for z = -0.16 is approximately 0.8757.

Step 5: State your decision to either reject or fail to reject the null hypothesis. Since the P-value (0.8757) is greater than the significance level (0.05), we fail to reject the null hypothesis.

Step 6: Consider the claim and your decision and state the conclusion. Based on the results of the hypothesis test, there is not enough evidence to support the claim that people taking echinacea develop less rhinovirus infections than people who do not take echinacea.

Step 7: Considering your conclusion from part 6, does echinacea seem to be effective in preventing the common cold? No, echinacea does not seem to be effective in preventing the common cold based on the results of this study.