Question

Do teachers find their work rewarding and satisfying? An article reports the results of a survey of 394 elementary school teachers and 269 high school teachers. Of the elementary school teachers, 222 said they were very satisfied with their jobs, whereas 128 of the high school teachers were very satisfied with their work. Estimate the difference between the proportion of all elementary school teachers who are satisfied and all high school teachers who are satisfied by calculating a 95% CI. (Use Pelementary - Phigh school Round your answers to four decimal places.) N USE SALT Interpret your 95% confidence interval. We are 95% confident that the difference between the proportions of elementary school teachers who are satisfied and high school teachers who are satisfied falls between these values. o We are 95% confident that the difference between the proportions of elementary school teachers who are satisfied and high school teachers who are satisfied falls above the upper bound. o We are 95% confident that the difference between the proportions of elementary school teachers who are satisfied and high school teachers who are satisfied falls below the lower bound. o We are 95% confident that the difference between the proportions of elementary school teachers who are satisfied and high school teachers who are satisfied falls outside these values. You may need to use the appropriate table in the Appendix of Tables Fill to answer this question. Need Help? Read it Talk to a Tutor

Answer 1

こ 0.563 = St1.96 0.565 CH-05652 +0.476 (+-0,67622 Solutions For elementary school teachersy Sample size CM]= 394 Forvocerable cases fx] = 222 for bigh school teachers, doemple size CH2) = 269 Fovoureeble cases (X2) = 128 The sample proportion tor elementary school teachers isg = X 222 394 & the sample propostion for bigh school teachera ja, X£ = 128 = 0.476 H2 269 Here, gs we have to find 95% C.I. ... Theretoreg. a = 0.05 & "The critical value is, Zc = 31-812 =):96 The 95% C.I is, CI. NI Ha Pat ze P (2-Ê 2 it ct-fie) M2 C.I. = (0.563-0.476-1.96* 10.563(2-0.563 +0.476C4-0LAS, 269 CS$canned with CamScanner 394 2 ER HI 394 269

Hooabib PHIR ''. CiIi= coio1, 0:165) Yol Bain Theretoolg the 95%. contidence interval too the difference between the proportion of all elementary school teachers ribo are satistied & cell high school teachers by boere sahá tieel js. ( Pelementary - Phigh school) is 0.01<p<0.165 ulovlnsitio sro Which indicates that we are gsto consident that the free difference betineen the elementary school teachers who are satisfied and high school teacher alho are satisfied falls between the co.01, 0.165) values Cinterval). CScanned with CamScanner