00:02
Okay, we're told that the mean cost of a meal for two in a mid -range restaurant in city a is $45.
00:11
And we're going to compare that to prices for a comparable meal in hong kong.
00:16
And so we have some data for 42 meals for two in hong kong.
00:21
And the data is listed here.
00:24
And we're going to make a 95 % confidence interval about the mean price of a meal for two in hong kong.
00:33
So the first part asks us to find the margin of error for the estimated mean cost in dollars.
00:40
So the way we do this is we use this formula for our interval.
00:44
It's going to be x bar plus minus t, knowing the degrees of the alpha level and, of course, our degrees of freedom.
00:52
We'll talk about that in a second.
00:54
And then we have our sample standard deviation divided by the square root of the sample size.
01:01
So x bar is the mean of the sample.
01:04
Let's add them up, divide by how many there are.
01:07
So it's through 2 .66.
01:10
This t value is, we have to note the degrees of freedom.
01:15
So it's a 95 % confidence interval.
01:17
So the alpha here is 0 .05, because that's what makes the 95 % 100%.
01:25
But we divided by 2 because we're looking at each on each tail of our distribution.
01:29
Because if you think about our student's t distribution, we're going to have two t values that are, well, the same absolute value of them, so that's positive and negative.
01:41
So set the error to the left of the negative is 0 .025.
01:45
The area to the right of t of the positive one is 0 .025.
01:50
And then the error in the middle is the 0 .95.
01:54
And there's our 95 % interval right there.
01:58
All right.
01:59
So there's that.
02:03
So let me give it to this.
02:08
Now, this piece here, t times s over the square of n, this is the margin of error.
02:19
So we find the t value, you do a table lookup or a spreadsheet and you get this, 2 .0195.
02:26
That's the t value.
02:28
The standard deviation is the sample standard deviation.
02:32
It's here, 6 .827, and then, of course, ends 42.
02:37
So the margin of error is 2 .127.
02:44
And just, you know, i use the full precision of my spreadsheet here, so round accordingly...