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.

orchestra answered 1 year ago

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