Question

Required information A chemical reaction is run 12 times, and the temperature x, (in °C) and the yield y (in percent of a theoretical maximum) is recorded each time. The following summary statistics are recorded: 7=65.0, y = 29.03, 1-1 (; - 2)2 = 6032.0, 2-1 (y; – 5)2 = 835.42, 1-1 (; – 7) (yi - y) = 1988.5 Let Bo represent the hypothetical yield at a temperature of O°C, and let By represent the increase in yleld caused by an Increase in temperature of 1°C. Assume that assumptions 1 through 4 for errors in linear models hold. Find a 95% confidence interval for the mean yleld at a temperature of 40°C. Round the answers to three decimal places. The 95% confidence Interval is ( 16.731 ).

Answer 1

Solution:

Given that: x = 65.0 CS1 29.03 - 12 i-1 I! COCA-5)? = 6032.0 [:?, cy: -9j* =.835.42 E" (x-3)(y -ỹ) - 1,88-5 Now, y - Bo + B15C Linear integration Equation Bi ["Coci-3) (4-9) [..(X:-572 => 1988.5 6032 0:3297 Bo - 9-8,5 -> 29.03 -0.3297 *65 => 7.5995 Therefore, The Linear equation 15, : 7.5995 + 0.3297 १

n-2 835.42 lo -> 9.14 ĝ+++ 1954 Prediction in terval > [1398, 42.973] Here, sc = 40°C :: ġ - 7.5995 +0.3297 * 40 20.7875 for MSE Ely:-9) 2 * Prediction interval formular ſeột82 t* with of - n-2=10 and 2=0:05 {ie 954. Level} = 2.228 sý - $+ (x* -F)? 6032 => 3.9519 fy 15.6175 * Prediction Interval for Yoc is) => 20.7875 +2.028 X 15.6175 +83.54 ► 20.7875 # 22.1859 → 6.398, 42.973) Σ (x - 32 + (40-6532 => 9.14 9.145