00:02
If we have a sample size of 250 and a sample proportion of 0 .80, is the sample size large enough to use the large sample approximation to construct a confidence interval for p? yes, it is large enough.
00:20
In general, the large sample approximation is considered valid when both n times p, which is 250 times 0 .80, and that is 200, and n times 1 minus p, which is 250 times 0 .2, is 50, are both greater than or equal to 5.
00:58
So it's valid.
01:01
To construct a 95 % confidence interval for p, we can use the formula confidence interval is equal to the sample proportion plus or minus the critical z times the square root of p times 1 minus p over n.
01:17
And so it's going to be 0 .8 plus or minus the critical z at this at 95 % is 1 .96 times the square root of 0 .8 times 1 minus 0 .8 over n, which is 250.
01:33
The lower boundary, i'll go to two places, 0 .8 minus 1 .96 times the square root of 0 .8 times 0 .2 over 250 is 0 .75...