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 390 elementary school teachers and 267 high school teachers. the elementary school said they were very satisfied with their jobs, whereas 123 of the high school teachers were very satisfied Estimate the difference between the proportion of all elementary school teachers who are satisfied and all high with their work (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 between these values. 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. 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. 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. You may need to use the appropriate table in the Appendix of Tables to answer this question.

Explanation / Answer

Formula for confidence interval:

(p1^ -p2^) (-/+) E (p1-p2)

p1^ = x1 /n1 = 227 / 390 = 0.5820513

p2^ = x2/n2 = 123 / 267 = 0.4606742

E (p1-2) = zc * sqrt ( ( p1^*(1-p1^))/n1) + ((p2^*(1-p2^))/n2))

               = 1.96 *sqrt ((0.5820513*(1-0.5820513))/390)+((0.4606742*(1-0.4606742))/267))

               = 0.07727

zc is the critical value for 5% level of significance from normal table as 1.96

p1^ - p2^ = 0.5820513 - 0.4606742 = 0.12138

(p1^ -p2^) (-/+) E (p1-p2)

0.12138 (-/+)0.07727

0.0441 and 0.1987

Answer: 0.0441 and 0.1987

If we use all steps in excel then we get the answer as 0.0441 and 0.1986

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. (The first option)

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