00:01
For this problem, we're given a box plot and a histogram using data from the problem about local versus online insurance quotes.
00:08
What we want to know is which of these two items can help us determine if online is cheaper, the box plot or the histogram.
00:17
We also want to know why is the standard deviation smaller for the difference between the two than for either of local or online? and finally, are the conditions met for a paired t test? all right, so for number one, it says which can help us determine if online is cheaper.
00:36
For the box plot, there are two box plots standing right next to each other and showing us the mean, the quartiles, the maximum, the minimum, and comparing them.
00:46
But there really are almost no conclusions we can draw from that based on the box plot itself and the nature of this scenario.
00:54
In the box plot, there are not paired local and online quotes.
00:59
So that means that the minimum for local, the local box plot might not be from the same person as the minimum for the online.
01:10
In the histogram, however, we're looking at the difference between the two, local minus online.
01:15
So when i draw that, i mean for the histogram, not for the box plot.
01:19
So let me erase this.
01:23
For the histogram, we're taking for each person, we're going to go their local quote minus their online quote and then graph it on the histogram.
01:31
From there, we can see a little clearer if there's a difference for most people.
01:38
You can kind of see where that lines up on the histogram.
01:41
And this makes way more sense with a paired t test, because then we're looking.
01:46
Each plot on the histogram represents the price difference, as opposed to not even looking at the fact that those price quotes are paired.
02:00
So we need our answer for this one is that the histogram definitely, is going to help us more because it's including the pairs.
02:11
Part two, why is the standard deviation smaller for the price difference than for either local or online? one way to think about this is if we look at the mean local quote, it's about $799.
02:24
So that's the average local insurance quote for someone is going to be $799.
02:29
And then the average online quote is going to be $753.
02:34
So the standard deviation for the mean, or sorry, for the online and the local prices is going to be a lot larger because then we're taking a look at the difference.
02:44
And the difference just by nature is going to be a smaller number.
02:48
For example, if i had a standard deviation of, let's say, $80, right, $80 here, that wouldn't be too far off, right? it's only fluctuating a little bit.
03:00
It's going from $879 down to $719 for the local mean...