confidence interval for difference in proportions

[statisticsisawesome]

To find the confidence interval for a difference in proportions, is the formula
(p1 hat - p2 hat) +- z * sqrt((p1 hat * q1 hat)/(n1)) + (p2hat * q2hat)/(n2))
or is it (p1 hat - p2 hat) +- z * SE
where SE = standard error
i've seen both formulas used

 

[Prof]

These two formulas for large sample confidence intervals are the same. In the first one, you have filled in what SE from the second formula is equal to which is sqrt((p1 hat * q1 hat)/(n1)) + (p2hat * q2hat)/(n2)) .

 

[statisticsisawesome]

how do we know weather to do a pooled or an unpooled test for this below question??

Carpal tunnel syndrome is a painful wrist condition that can be treated with surgery or less invasively with wrist
splints. In a study of 180 patients with the condition, half had surgery and half used wrist splints. In the surgery
group, 65 patients showed improvement after three months while 42 of those who used wrist splints improved.
Is surgery more effective than the use of wrist splints for patients with this condition?
a)
Write appropriate hypotheses.
b)
Test the hypotheses, find the P-value
and state your conclusion
in plain English
. Use α = 0.01.
c)
Create a 98% confidence interval for the difference in
proportions of patients showing improvement, and
interpret your interval.
d)
Comment on your interval in relation to your conclusion from b)