00:01
Hello.
00:03
So we're going to start up with this question by first finding our sample proportion given by x divided by n.
00:12
So that's going to be 120 divided by 400.
00:17
We get 0 .3.
00:20
So that's our first step.
00:23
Our next step is to get our standard error that is given by the square root of p hat into 1 minus p hat divided by n.
00:38
Going to have 0 .3 times 1 minus 0 .3 divided by n which is 400 standard error is going to be 0 .2 excuse me as 0 .0 229.
01:04
Next step we get our margin of error which is e that's margin of error that is given by the z value at alpha over 2 times the standard so how do we get a z value? we use alpha to get our z value.
01:28
So that's one minus confidence level.
01:30
Our confidence level here is 90%.
01:34
That is 0 .9.
01:35
So we get 0 .1.
01:38
Divide by 2, you have 0 .05.
01:44
The corresponding z value is 1 .645.
01:50
Margin of error e is going to be 1 .645 times 0 .0229 so 1 .645 times 0 .029 margin of error e is going to be 0 .377 finally we can set up our 90 % confidence in a while which is going to be p .0377.
02:23
Finally we can set up our 90 % confidence interval which is going to be p hat plus or minus e so that's point three plus or minus point zero uh three so let's look at point three minus 0 .0377 we're going to have point uh let me double check our decimal place here so let's do four so we have point 2623 then if we add up we're going to have point 3377 okay this is our 90 % confidence in about the second part of the question is asking for the sample size and given by the z value at alpha over 2 divided by the margin of error all squared times the p value into one minus the p value okay so now we have everything...