Confidence Interval VS Sample size correct

brk1yn

A larger sample size decreases the width of the confidence interval. Is this correct? Why?

Flok

Look at the formula.
X + reliability * std / root N
And play around with the variables. If you have a large N, your Root N is larger and std/root N is smaller. All else being equal, you have a smaller interval.

suyash1989

Great…I was confused with “alfa and beta errors decrease with large sample size”…..As alfa is also equal to level of significance…So if alfa decreases confidence interval should increase… which is on the contrary with this formula here….what am i missing?

orang3eph

Look at it this way
90% Confidence = 10 % Alpha = 1.65 reliability
99% Confidence = 1% Alpha = 2.58 reliability
Using the same methods as I mentioned above, see how the formula reacts.
If Alpha (Level of Sig) decreases, your reliability level is higher… Therefore, your interval is larger. Which also makes sense…
I dont see the contrary
X = 10
Standard error = 5
@ 95%
10 + 1.65 * 5
10  1.65 * 5
@ 99%
10 + 2.58 *5
10  2.58*5

you can see at 99% (1 level of significance), the interval is larger.