00:01
This is the full -length problem.
00:01
First of all, in question a, i have to test the hypothesis whether the distribution is correct, whether the distribution is representative of the population of the us residents.
00:14
Hdo is that the sample is representative, ha suggests that the sample is not representative.
00:30
And here, let's make the table with the expected values and the observed values.
00:36
So let's first take the observed values in the same order as they are given in the table 83, 121, 193, 103.
00:47
And here each expected value is 500 times the percentage.
00:51
So, for example, for the first group, which is northeast, that's 500 times 0 .18, that is 90.
00:59
Then it's 110, 185, and the last one is 115.
01:05
Now i can find chi -squared.
01:08
That's the sum of the observed minus expected squared divided by its expected frequencies and here that equals to 3 .24 so let's add more decimals okay i want to do it like this now let's find the number of degrees of freedom that's 4 minus 1 which is 3 and now let's find the key value 3557 so which is greater than 0 .1 so it means that i fail to reject a 0 it means that the sample is representative that's the first part of this test in the second part of this test i have to determine the following link.
02:37
Here i have to determine whether this two associated or not.
02:40
So h0 is a derisional association, ha is a deris association.
02:53
And now let's use an online calculator for chi -squared test for independence...