This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
Here's the solution for calculating the standard error of the proportion. Step 1: Identify the given values. The total number of people surveyed is n = 80. The number of people who like the coffee brand is x = 30. Step 2: Calculate the sample proportion (p). p = (x)/(n) = (30)/(80) = 0.375 Step 3: Calculate the complement of the sample proportion (1 - p). 1 - p = 1 - 0.375 = 0.625 Step 4: Calculate the standard error of the proportion (SE_p). The formula for the standard error of the proportion is: SE_p = sqrt(p)(1-p)n Substitute the values: SE_p = sqrt((0.375 × 0.625)/(80)) SE_p = sqrt((0.234375)/(80)) SE_p = sqrt(0.0029296875) SE_p ≈ 0.05412659 Rounding to four decimal places, the standard error of the proportion is 0.0541. Comparing this to the given options, the correct option is 0.0541. That's 2 down. 3 left today — send the next one.