00:01
In a sample of 500 canadians, so that would be our sample size, 275 said that they would rather retire in the united states than in canada.
00:13
And our goal here is to construct a 95 % confidence interval of the true proportion of canadians who would like to retire to the united states.
00:25
So from there, the first thing we're going to do is we're going to find our sample proportion, our p hat.
00:33
And we'll find that by taking x over n or favorable over possible 275 out of 500.
00:41
So that would equate to 0 .55.
00:45
Next, what we're going to do is we're going to find our margin of error.
00:49
And to find our margin of error, we're going to need a critical z score, and then we're going to multiply it by p hat times one minus p hat all over n.
01:01
And and then we're going to take the square root of that value.
01:05
So let's go ahead and find our critical z.
01:08
If you think about the 95 % confidence level, that's talking about the middle 95 % of this bell -shaped curve.
01:18
So if the middle 95 % is there, that means there's 5 % left to be split evenly between the two tails, so each tail would be 0 .025.
01:30
And the critical z's will be the boundaries of that interval.
01:37
Now, the fastest, most efficient way is to find the left critical z by using inverse norm on a graph and calculator.
01:47
And to use the inverse norm function, you need to provide the area that's to the left of that location, followed by the mean and the standard deviation.
01:57
So in our scenario, we're going to do inverse norm, the area to.
02:01
To the left of this boundary is 0 .025...