Do teachers find their work rewarding and satisfying? An article reports the res

Question

Do teachers find their work rewarding and satisfying? An article reports the results of a survey of 394 elementary school teachers and 264 high school teachers. Of the elementary school teachers 225 said they were very satisfied with their jobs whereas 124 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 P_elementary - p_high school. Round your answers to four decimal places.) 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 above the upper bound. 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. We are

Explanation / Answer

Step-1

Total no. elementary school teachers n1=394

Satisfied teachers s1=225

Sample proportion p1 =s1/n1 =225/394 =0.5711

                                    q1 =1-p1 =1-0.571 =0.4289

Step-2

Total no. of high school teachers n2=264

Satisfied teachers s2 =124

Sample proportion p2 =s2/n2 =124/264 =0.4697

                                                q2 =1-p2 =1-0.470 =0.5303

Step-3

Level of significance =0.05

                        z =z/2 =1.9600

Step-3

Lower limit = (p1 –p2) –z* sqrt(p1q1/n1 + p2q2/n2)

                        =(0.5711-0.4697) – 1.9600[(0.5711*0.4289 /394   + 0.4697*0.5303 /264)]

                        = 0.1014 - 0.0775

=0.0239

Upper limit =(p1 –p2) + z* sqrt(p1q1/n1 + p2q2/n2)

                        =(0.5711-0.4697) + 1.9600[(0.5711*0.4289 /394   + 0.4697*0.5303 /264)]

                        = 0.1014 + 0.0775

=0.1789

since 0.0239 <0.05 < 0.1789

We are 95% confident that the difference between the proportion of elementary school teachers who are satisfied and high school teachers who are satisfied falls between these values

Related Questions

Navigate

• Browse (All)
• Browse D
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.