Confidence Interval on the Difference Between Proportions (3 of 4)
Finally, the value of z for the 99% confidence interval is
computed using a
z table; it is 2.58. The
lower limit of the confidence interval is simply:
p
_{1} 
p
_{2}  (z) (estimated
)
= 0.65  0.41  (2.58)(0.067) = 0.07
The upper limit is:
= 0.65  0.41 + (2.58)(0.067) =0.41
The 99% confidence interval is therefore:
0.07 ≤ π
_{1}  π
_{2} ≤ 0.41.
This indicates that the
proportion of psychology majors that can solve the problem is from 0.07 to 0.41
higher than the proportion of physics majors that can solve it.
Summary of Computations

Compute p_{1}  p_{2}.
 Find z for confidence interval using a z
table.
 with the formula: