**Hyperhidrosis Treatment Study**Hyperhidrosis is a stressful medical condition characterized by chronic excessive sweating. Botox was approved for the treatment of hyperhidrosis in adults in 2004. A clinical trial examined the effectiveness of Botox for excessive armpit sweating in teenagers aged 12 to 17 years. Participants received either a Botox injection or a placebo injection (a simple saline solution) and were examined four weeks later to see if their sweating had been reduced. Here are the study's findings:| | Reduced | Not Reduced | Total ||------------------|---------|-------------|-------|| Botox | 70 | 30 | 100 || Placebo | 68 | 132 | 200 || Total | 138 | 162 | 300 |**Statistical Analysis**Construct an 80% confidence interval for \( p_1 - p_2 \), where \( p_1 \) denotes the proportion of teenagers who experienced a reduction in sweating in the Botox group and \( p_2 \) denotes the proportion of teenagers who experienced a reduction in sweating in the placebo group. Round your answers to three decimal places and use four decimal places for any interim calculations.*Hint:* Think about the formula for the confidence interval. How do we find \( z_{cv} \)?**Confidence Interval:** ( [ ], [ ] )We are 80% confident that there [is/is not] a difference in the proportion of teenagers with hyperhidrosis who experienced a reduction in sweating.

Obtain the 80% confidence interval for the difference in the proportion of teenagers with hyperhidrosis who experienced a reduction in sweating. The 80% confidence interval for the difference in the proportion of teenagers with hyperhidrosis who experienced a reduction in sweating is obtained below as follows: The formula for the confidence interval is, Use EXCEL Procedure for finding the critical value of z. Follow the instruction to obtain the critical value of z: Open EXCEL Go to Formula bar. In formula bar enter the function as“=NORMINV” Enter the probability as 0.90 Enter the mean as 0 and the Standard deviation as 1. Click enter EXCEL output: From the EXCEL output, the critical value of z at the 80% confidence level is 1.282 The 80% confidence interval for the difference in the proportion of teenagers with hyperhidrosis who experienced a reduction in sweating is between (0.287,0.433). Since, the confidence interval do not contains 0, it can be concluded that there is difference between proportions. We are 80% confident that there is a difference in the proportion of teenagers with hyperhidrosis who experienced a reduction is sweating.