00:01
In letter a, we need to compare, in this case, compute, sorry, the expectation of p hat, which is the sample proportion, which is given by the population proportion.
00:13
In our case, this is equal to 08.
00:16
We also need to compute what is the standard deviation of the sample proportion, the sample distribution of the p hat.
00:25
So this is given by the square root of p 1 minus p divided by n.
00:32
So p is 0 .8.
00:34
1 minus p 0 .2, divide this by 200, which is the number of observations that we are considering.
00:41
So 200 here, this is 0 .8, and this here is 0 .2.
00:47
You are going to find that this is 0 .0283.
00:52
In letter b, considering this distribution, we need to compute what is the probability that b hat will be within 0 .04 from the population proportion.
01:07
So this is the same as computing this probability here.
01:12
And we can find this probability using a z table.
01:18
So the only thing that we need to do here is in this case, basically, we just need to divide this here by the standard deviation from the p -hat distribution.
01:33
So 0 .02 -83.
01:37
0 .02 -83 and 0 .0 .083.
01:43
When we do this, now we are in a standard normal distribution and we can use the z table.
01:48
So this here will be 14134.
01:53
Now i'm going to use the letter z to express that we are in our standard normal distribution.
02:00
And now to compute this, we can use a z table.
02:04
So using a z table, you're going to find that this is 0 .84 to 5.
02:09
Now we let us see.
02:11
Let's update the sample distribution of the sample proportion.
02:17
But now because we have a higher number of samples or observations in the sample...