Question

Customer Distribution by Weekday: A drop-in auto repair shop staffs the same number of mechanics on every weekday (weekends are not counted here). One of the mechanics thinks this is a bad idea because he suspects the number of customers is not evenly distributed across these days. For a sample of 289 customers, the counts by weekday are given in the table.

Number of Customers by Day (n = 289)

	Monday	Tuesday	Wednesday	Thursday	Friday
Count	43	48	57	75	66

The Test: Test the claim that the number of customers is not evenly distributed across the five weekdays. Test this claim at the 0.01 significance level.

(a) The table below is used to calculate the test statistic. Complete the missing cells.
Round your answers to the same number of decimal places as other entries for that column.

	Week	Observed	Assumed	Expected
i	Day	Frequency (Oi)	Probability (pi)	Frequency Ei	(Oi − Ei)2 Ei
1	Monday	?	0.2	57.8	3.790
2	Tuesday	48	?	57.8	1.662
3	Wednesday	57	0.2	?	0.011
4	Thursday	75	0.2	57.8	?
5	Friday	66	0.2	57.8	1.163
Σ		n = 289			χ2 = ?

(b) What is the value for the degrees of freedom?  

(c) What is the critical value of  χ^{2 (}Use the answer found in the χ²-table or round to 3 decimal places.)
t_α =  

(d) What is the conclusion regarding the null hypothesis?

reject H₀

fail to reject H₀     

(e) Choose the appropriate concluding statement.

We have proven that the number of customers is evenly distributed across the five weekdays.

The data supports the claim that the number of customers is not evenly distributed across the five weekdays.    

There is not enough data to support the claim that the number of customers is not evenly distributed across the five weekdays.

Answer 1

a)

Week	Observed	Assumed	Expected
i	Day	Frequency (Oi)	Probability (pi)	Frequency Ei	(Oi − Ei)2
					Ei
1	Monday	43	0.2	57.8	3.790
2	Tuesday	48	0.2	57.8	1.662
3	Wednesday	57	0.2	57.8	0.011
4	Thursday	75	0.2	57.8	5.118
5	Friday	66	0.2	57.8	1.163
Σ		n = 289			χ2 =11.744

b)

degrees of freedom =5-1=4

c)

critical value of  χ² =13.277

d)

fail to reject H₀

_e) There is not enough data to support the claim that the number of customers is not evenly distributed across the five weekdays.