Question

Use the following information to answer the questions below:

Recently, the National Center for Education Statistics reported a study of a random sample of 1990 public school teachers whose first year teaching was in 2007-2008. The study found that 5 years later (in 2013) 17% of the teachers had left the profession. However, amongst the 1580 teachers who were assigned a mentor in their first year of teaching 14% had left the profession compared with 29% of the 410 teachers who did not have a mentor in their first year.

If the standard error of the difference between the proportions is 2.5% (0.025), what would be the 95% confidence interval for the difference between the proportions of mentored and un-mentored teachers who left the profession before 2013:

Group of answer choices

15% ± 1.3%

15% ± 2.5%

15% ± 8.3%

15% ± 5.0%

Answer 1

We have

p​​​​​​1​​​​​^ = 0.29 and p​​​​2^ = 0.14

S.E( p1^ - p2^) = 0.025

The 95% confidence interval for difference in population proportions is

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

Where E = Z​​​​​​a/2* S.E( p1^ - p2^)

For a = 0.05 , Z​​​​​​a/2 = Z​​​​​​0.025 = 1.96

E = 1.96*0.025 = 0.05

(0.29 - 0.14) - 0.05 < p1 - p2 < (0.29 - 0.14) + 0.05

0.15 - 0.05 < p1 - p2 < 0.15 + 0.05

The 95% confidence interval for difference in population proportions is

15% +/- 5%