00:01
There's an automobile manufacturer that wants to know the proportion of new car buyers who prefer foreign cars over domestic cars.
00:10
So we've got a sample of 1 ,164 new car buyers.
00:17
And of those sampled, there are 325 that prefer foreign over domestic.
00:26
So that means our point estimate or our sample proportion is 325 over 1 ,164.
00:38
We want to construct an 85 % confidence interval.
00:43
So that means we're talking about the center 85%.
00:48
If there's 85 % in the center, that means there's 15 % to be split between.
00:58
The two tails, making the left tail .075, and the right tail to be .075.
01:06
So in order to determine a confidence interval, we do need to find a margin of error, and the formula for margin of error is the critical z times the square root of p -hat, q -hat divided by n.
01:25
So we need the critical z scores, that bound the confidence interval.
01:31
So we need the z score on the left and we need the z score on the right.
01:36
And to find the z score, we're going to use inverse norm on a texas instruments graphing calculator.
01:45
So i'm going to bring in my graphing calculator.
01:49
And to do inverse norm, we're going to hit second, vairs, and it's number three in this menu.
01:56
Now when you use inverse norm, you have to provide the area in the left tail.
02:00
So in our picture, the area in the left tail is 0 .075, followed by the mean, well, since we're working with z scores, the mean of the z scores is zero.
02:13
And then you have to follow it up with the standard deviation.
02:16
And the standard deviation of our standard normal z scores is always one.
02:21
So that is going to get us the left boundary.
02:24
If i round that to three decimal places, i do get negative 1 .440...