A local school board member randomly sampled private and public high school teachers in his district to compare the proportions of National Board Certified (NBC) teachers in the faculty. The results were:
Private Schools | Public Schools
Sample size, n: 80 | 52
Proportion of NBC teachers, p-hat: .175 | .150
Blank #1: Give a point estimate for the difference in the proportion of all teachers in public schools and the proportion of all teachers in private schools who are National Board Certified. Report your answer with three decimals. Call Private schools 1 and Public schools 2 in proceeding with analysis.
The 90% confidence interval for the difference, using these data is (-0.078, 0.128) Fill in the blanks to properly interpret the interval in context.
_______% (blank #2) confident that the true proportion of private school teachers that are NBC is anywhere from 7.8% __________ (blank #3) than to 12.8% __________ (blank #4) than the true proportion of public school teachers who are NBC.
If you were now to perform a significance test, you would ___________ (blank #5: reject or not reject) H0: p1 = p2? You should be able to answer this from looking at your interval only.
Answer for blank # 1: 0.025
Answer for blank # 2: 90
Answer for blank # 3: greater
Answer for blank # 4: less
Answer for blank # 5: not reject