A random sample of 180 men indicated that 50 were smokers, and a random sample of 150 women surveyed indicated that 39 smoked. Construct a 98% confidence interval for the true difference in proportions of male and female smokers. The image presents a statistical exercise focused on calculating proportions and their complements for a given dataset involving men and women. Here's a structured transcription suited for an educational website:---**c) Find the value of each statistic.****Express as a decimal rounded to four decimal places**- **Proportion One (Men):** - Select an answer from a dropdown menu - An input box follows to write the calculated proportion *(Calculate using a TI-84 calculator)*- **Proportion Two (Women):** - Select an answer from a dropdown menu - An input box follows to write the calculated proportion *(Calculate using a TI-84 calculator)*\[ \hat{q}_1 = 1 - \hat{p}_1 = 1 - \text{(Men's Proportion)} = \] - Input box for calculation related to men\[ \hat{q}_2 = 1 - \hat{p}_2 = 1 - \text{(Women's Proportion)} = \] - Input box for calculation related to women- **Sample Size One (Men):** - Select an answer from a dropdown menu - An input box follows to write the sample size- **Sample Size Two (Women):** - Select an answer from a dropdown menu - An input box follows to write the sample size**Round answer(s) to two decimal places**- \( z (\alpha/2) \): - Select an answer from a dropdown menu - Multiple input boxes follow, suggesting multiple calculations or values needed- Second line with similar setup for another z-score calculation related to \( \alpha/2 \).---This page utilizes dropdowns for selecting predetermined statistical values and input boxes for entering calculated results, designed for instructional purposes using a TI-84 calculator.

Given; p1=50180=0.28p2=39150=0.26Level of significance=0.02 Confidence interval is given by- (p1-p2)±Zp1(1-p1)n1+p1(1-p2)n2 Z value from the table is 2.33.Substituting all the values, we get; (0.28-0.26)±2.33×0.28(1-0.28)180+0.26(1-0.26)1500.02±2.33×0.00112+0.001280.02±2.33×0.048980.02±0.1141 Hence the interval is (-0.0941,0.1341).