00:01
So in this question we have a table giving delivery time versus computer -assisted ordering, and the computer -assisted ordering can be either no or yes, and then we have totals.
00:22
The delivery time can be below average, equal, or above average, and for no the row is 4, 12, 8, and then the total is 24.
00:42
For yes we have 10, 4, 2, a total of 16, and then for the column totals we have 14, 16, 10, and 40.
01:02
Now what we want to do is test the hypothesis that delivery time is independent of computer -assisted ordering.
01:11
So alpha is 0 .05 and we're testing independence, so the null is that the ordering is independent of time, and the alternate is that there is a dependence.
01:41
Now what are our expected values? the expected values are the totals for the row times the total for the column divided by the grand total for each particular cell.
01:53
So for this cell we have 24 times 14 divided by 40, which is 8 .4.
02:06
For this one it's 24 times 16 divided by 40, which is 9 .6.
02:13
And for the last one 24 times 10 divided by 40, which is 6.
02:18
For this one we have 16 times 14 divided by 40, which is 5 .6.
02:29
For this we have 16 times 16 over 40, or 6 .4.
02:34
And for this one we have 16 times 10 over 40, which is 4.
02:42
Now we can calculate chi -squared, although the chi -squared test is actually not appropriate in this case because this expected number here is less than 5, but we'll come back to that...