Rhino viruses typically cause common colds. In a test of the effectiveness of echinacea, 43 of the 49 subjects treated with echinacea developed minovirus infections, In a placebo group, 80 of the 96 subjects developed minovirus 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.

Identify the test statistic.
\[
z=0.70
\]
(Round to two decimal places as needed.)
Identify the P-value.
P-value $=0.483$
(Round to three decimal places as needed.)
What is the conclusion based on the hypothesis test?
The $\mathrm{P}$-value is greater than the significance level of $\alpha=0.05, s 0$ fail to reject the null hypothesis. There is not sufficient evidence to support the claim that echinacea treatment has an effect:
b. Test the claim by constructing an appropriate confidence interval.

The $95 \%$ confidence interval is $\square< \left(p_{1}-p_{2}\right)< \square$
(Round to three decimal places as needed.)

Step 1 ：Given that the test statistic is \(z=0.70\) and the P-value is \(0.483\).

Step 2 ：Since the P-value is greater than the significance level of \(\alpha=0.05\), we fail to reject the null hypothesis. There is not sufficient evidence to support the claim that echinacea treatment has an effect.

Step 3 ：To test the claim by constructing an appropriate confidence interval, we need to calculate the difference in proportions \(p1 - p2\) and then construct a 95% confidence interval around this difference.

Step 4 ：The proportions \(p1\) and \(p2\) are the proportions of subjects who developed minovirus infections in the echinacea and placebo groups, respectively. These can be calculated as follows: \(p1 = 43 / 49\) and \(p2 = 80 / 96\).

Step 5 ：The difference in proportions is then \(p1 - p2\).

Step 6 ：The standard error for the difference in proportions can be calculated using the formula: \(SE = \sqrt{(p1 * (1 - p1) / n1) + (p2 * (1 - p2) / n2)}\) where \(n1\) and \(n2\) are the sizes of the echinacea and placebo groups, respectively.

Step 7 ：The 95% confidence interval can then be calculated as follows: \(CI = (p1 - p2) ± (z * SE)\) where \(z\) is the z-score for a 95% confidence interval, which is approximately 1.96.

Step 8 ：Calculating these values, we get \(p1 = 0.878\), \(p2 = 0.833\), \(diff = 0.044\), \(SE = 0.060\), \(CI_{lower} = -0.074\), and \(CI_{upper} = 0.162\).

Step 9 ：\(\boxed{\text{Final Answer: The 95% confidence interval is } -0.074