Question

In: Statistics and Probability

A certain retail store bases its staffing on the number of customers that arrive during certain...

A certain retail store bases its staffing on the number of customers that arrive during certain time slots. Based on prior experience this store expects 32% of its customers between 8:00 am and 12:00 pm; 21% of its customers between 12:00 pm and 4:00 pm; 35% of its customers between 4:00 pm and 8:00 pm; and 12% of its customers between 8:00 pm and midnight. On a certain day, the store had 214, 198, 276, and 134 customers in those time slots, respectively. Should the store change its staffing? (Consider an alpha of 0.05.)

Solution:

Ho: The expected values match the observed values
Ha: The expected values do not match the observed values assign(“exp”,c(32,21,35,12)) assign(“obs”,c(214,198,276,134))
sum((obs-exp)^2/exp) = 5426.773
1-pchisq(5426.773,3) = 0
p < alpha, therefore RHo: the store should change its staffing.

What was wrong with this solution?

Solutions

Expert Solution

The following table is obtained:

Categories Observed Expected (fo-fe)2/fe
Category 1 214 822*0.32=263.04 (214-263.04)2/263.04 = 9.143
Category 2 198 822*0.21=172.62 (198-172.62)2/172.62 = 3.732
Category 3 276 822*0.35=287.7 (276-287.7)2/287.7 = 0.476
Category 4 134 822*0.12=98.64 (134-98.64)2/98.64 = 12.676
Sum = 822 822 26.026

(5) Conclusion

It is concluded that the null hypothesis Ho is rejected. Therefore, there is  enough evidence to claim that  the store change its staffing at the α=0.05 significance level.


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