To test whether sales and day of the week are independent, the following random

Question

To test whether sales and day of the week are independent, the following random sample was collected:

For example, in the sample, in 30 observations it was a week day with moderate sales; in 25 observations it was a day on a week end with high sales, etc.

If sales and day of the week are independent, what would be the "expected frequency" of a week day with low sales in the above data?

(Provide one decimal position)

Explanation / Answer

If sales and day of the week are independent

All the days of the week will have the same expected sales as the probability of sales would be the same on each day irrespective of being a week day or a weekend

ie probability of sale =1/7

We have total sales on a low sales day=12+20=32

Here there would be a equal probability of low sales on a week day or week end

Hence the probability of low sales would be 0.5

Expected sales =0.5*32=16

Hence the expected frequency of a week day with low sales=16.0  

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