It was asked:
> How would you test the following hypothesis:
> A fast-food restaurant claims that 75% of their revenue is from the
> "drive-thru". Suppose you have 50 days of receipts from the
> restaurant. Each days' receipt shows the total revenue and the
> "drive-thru" revenue for that day.
and various people responded (eg):
compute the proportion from the drive through for each day, and
> then test if that were 75%. Then, instead of two numbers for each day,
> you have only one,
Yes...
> and that's the one you're interested in.
No, it isn't! The mean of the daily proportions is not in general the
same thing as the overall mean. This is closely related to Simpson's
paradox.
Drive Table Proprortion
through DT
Tue 30 10 .75
Wed 30 10 .75
Thu 30 10 .75
Fri 30 90 .25
Sat 30 90 .25
Sun 30 90 .25
___________________________
# 0.5
=======
Total 180 300 | 0.375
Note also that the original data set (if there were one) should
probably be analyzed as a time series with a 1-week cyclic component.
-Robert Dawson
.
.
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