Confidence Intervals

[Srd2000]

Hello All, with confidence intervals the equation you use is p +/- z sqrt(p(1-p)/n) and for a 95% confidence, why does z=1.96 even though 95% is two standard deviations (z=2)?  Thanks!

[VanillaRice]

2 standard deviations is really an approximation, it is more accurate to say that 95% of values lie between z=-1.96 and z=1.96.

Hope this helps

[MathMethdz99-R]

2 standard deviations is really an approximation, it is more accurate to say that 95% of values lie between z=-1.96 and z=1.96.

Hope this helps

for our working out, is it okay to use 1.96 or should we use the non rounded value? i was thinking of just writing the 1.96 during my working out(if worth more than one mark) then using the 1-Prop Z Interval on the CAS to find the interval, would that be okay?

[LifeisaConstantStruggle]

that would be cool tho (it's good that you use your calculator to its full extent AND write appropriate working, I normally do 1.96... with some ellipses at the side of it). For 95% confidence intervals it is quite important to read the question. Eg: in Specialist exam 1 last year students were asked to calculate the 95% confidence interval with an integer multiple, so instead of 1.96 you have to use 2, otherwise 1.96 is fine in exam 1/1-Prop z interval should be used in exam 2 (normally these questions are a mark so don't worry).

[jazzycab]

for our working out, is it okay to use 1.96 or should we use the non rounded value? i was thinking of just writing the 1.96 during my working out(if worth more than one mark) then using the 1-Prop Z Interval on the CAS to find the interval, would that be okay?

Directly from the study design:
...in particular the 95% confidence interval as an example of such an interval where z ≈ 1.96

So 1.96 is fine

[MathMethdz99-R]

that would be cool tho (it's good that you use your calculator to its full extent AND write appropriate working, I normally do 1.96... with some ellipses at the side of it). For 95% confidence intervals it is quite important to read the question. Eg: in Specialist exam 1 last year students were asked to calculate the 95% confidence interval with an integer multiple, so instead of 1.96 you have to use 2, otherwise 1.96 is fine in exam 1/1-Prop z interval should be used in exam 2 (normally these questions are a mark so don't worry).

i remember that question yeah! nice way to incorporate it in exam 1.. anyways thanks for the response!