Q6. ### Hypothesis Testing: Identifying Key Values and Drawing Conclusions---**Step 1: Identify the Test Statistic**Given:\[ z = \square \]*(Round to two decimal places as needed.)*---**Step 2: Identify the P-value**Given:\[ \text{P-value} = \square \]*(Round to three decimal places as needed.)*---**Step 3: Conclusion Based on the Hypothesis Test****Statement**: The P-value is \(\boxed{\text{less than}}\) the significance level of \( \alpha = 0.01 \), so \(\boxed{\text{reject}}\) the null hypothesis. There \(\boxed{\text{is not}}\) sufficient evidence to support the claim that echinacea treatment has an effect.---**Step 4: Test the Claim by Constructing a Confidence Interval****Given**:The 99% confidence interval is:\[ \square < (p_1 - p_2 ) < \square \]*(Round to three decimal places as needed.)*---**Step 5: Conclusion Based on the Confidence Interval**\[ \square < (p_1 - p_2 ) < \square \]*(Round to three decimal places as needed.)*---Explanation:1. **Identify the Test Statistic and P-Value**: Start by calculating the z-value and the corresponding P-value from your data set. Ensure that these values are rounded to the required decimal places.2. **Hypothesis Test Conclusion**: Compare your P-value to the alpha level (significance level, \( \alpha = 0.01 \)). If the P-value is less than 0.01, you reject the null hypothesis, indicating insufficient evidence to support the claim that echinacea treatment has an effect.3. **Confidence Interval Construction**: Construct a 99% confidence interval for the difference in proportions (\( p_1 - p_2 \)). Use this interval to further support your hypothesis test conclusions, once again, rounding values to three decimal places as needed.Creating clear steps and ensuring the correct rounding of values are essential in statistical testing and data interpretation, crucial for validating claims or hypotheses.--- ### Analyzing the Effectiveness of Echinacea on Rhinovirus Infections**Objective:**To assess whether echinacea has an effect on rhinovirus infections by comparing the infection rates of subjects treated with echinacea to those treated with a placebo.**Background:**Rhino viruses typically cause common colds. In a test of the effectiveness of echinacea, 45 of the 51 subjects treated with echinacea developed rhinovirus infections. In a placebo group, 83 of the 96 subjects developed rhinovirus infections. A significance level of 0.05 is used to test the claim.**Hypothesis Testing:****(a) Formulating the Hypotheses**Consider the first sample (Sample 1) to be the subjects treated with echinacea, and the second sample (Sample 2) to be the subjects treated with a placebo. The goal is to establish the null (H0) and alternative (H1) hypotheses for the hypothesis test.**Options for Hypotheses:**- **Option A:** \[ \text{H}_0: p_1 \leq p_2 \\ \text{H}_1: p_1 \neq p_2 \]- **Option B:** \[ \text{H}_0: p_1 \neq p_2 \\ \text{H}_1: p_1 = p_2 \]- **Option C:** \[ \text{H}_0: p_1 = p_2 \\ \text{H}_1: p_1 < p_2 \]- **Option D:** \[ \text{H}_0: p_1 \geq p_2 \\ \text{H}_1: p_1 \neq p_2 \]- **Option E:** \[ \text{H}_0: p_1 = p_2 \\ \text{H}_1: p_1 \neq p_2 \]- **Option F:** \[ \text{H}_0: p_1 = p_2 \\ \text{H}_1: p_1 > p_2 \]By analyzing these options, researchers can select the appropriate null and

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Identify the test statistic. Z= (Round to two decimal places as needed.) Identify the P-value. P-value= (Round to three decimal places as needed.) What is the conclusion based on the hypothesis test? reject the null The P-value is less than the significance level of a = 0.01, so greater than fail to reject hypothesis. There is not sufficient evidence to support the claim that echinacea treatment is has an effect. b. Test the claim by constructing an appropriate confidence interval. The 99% confidence interval is <(p₁-p₂) <. (Round to three decimal nlaces as needed) (Round to three decimal places as needed.) What is the conclusion based on the confidence interval?