Question

A given poll states “54% of fifth graders read at or above the fifth-grade-level.” If there is a stated margin of error of +/- 2.5%, what is the 95% confidence interval for this statistic?

Answer 1

The z-score fo a 95% confidence interval is 1.96
Confidence interval of a statistic is given by
$C.I.= proportion \pm 1.96(2.5) \\ =54 \pm 4.9 = (54-4.9, 54+4.9) = (49.1, 58.9)$
Therefore, we are 95% confident that the proportion of fifth graders who read at or above the fifth grade level is between 49.1 and 58.9.