Question

# The restaurant owner wants to find out what the peak demand periods are, during the hours...

The restaurant owner wants to find out what the peak demand periods are, during the hours of operation, in order to be better prepared to serve his customers.

He thinks that, on average, 60% of the daily customers come between 6:00pm and 8:59pm (equally distributed in that time) and the remaining 40% of customers come at other times during the operating hours (again equally distributed).

He wants to verify if that is true or not, so he asked his staff to write down during one week the number of customers that come into the restaurant at a given hour each day. His staff gave him the following data:

Time Day 1 Day 2 Day 3 Day 4 Day 5 Day 6 Day 7
5:00pm-5:59pm 15 19 21 20 12 15 15
6:00pm-6:59pm 30 23 24 25 28 29 26
7:00pm-7:59pm 36 29 39 35 39 30 32
8:00pm-8:59pm 29 33 23 29 24 32 27
9:00pm-9:59pm 21 20 12 19 18 14 20
10:00pm-10:59pm 12 12 15 12 10 15 14
11:00pm-11:59pm 8 7 9 10 12 12

9

Help the manager figure out if his instincts are correct or not. Use a Chi-Squared test to see if the observed distribution is similar to the expected. Use the average demand for a given time as your observed value.

What is the p-value of your Chi-Square test?

Test Statistics

The number of degrees of freedom is df = 7 - 1 = 6

P-value corresponding to df = 6 and Chi-Squared statistic = 4 is 0.6767 (Obtained using online calculator. Screenshot attached)

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