Question

You have been assigned to test the hypothesis that the average number of cars waiting in line during the early morning differs between Starbucks, PJ’s, and Aura Coffee. The following data show the number of cars in line during randomly selected times in the early morning at all three coffee shops:

Number of cars waiting in line
	Coffee shop
Time	Starbucks	PJ’s	Aura Coffee
7:00	9	8	5
7:30	12	6	3
8:00	8	5	2
8:30	6	2	3
9:00	10	3	4

Perform a one-way ANOVA using Alpha (α) = 0.05 to determine if a difference exists in the average number of cars waiting in line at the drive-thru during the early morning among these shops. Please type answer in word and include how you solved it and work in the word document.

Answer 1

Hypothesis:

Ho: $\mu$ 1 = $\mu$ 2 = $\mu$ 3 or  There is No significant difference exists in the average number of cars waiting in line at the drive-thru during the early morning among these shops.

Ha: There is significant difference exists in the average number of cars waiting in line at the drive-thru during the early morning among these shops.

CALCULATION:

Number of Treatment, t = 3 n = 15

T₁ (sum of Starbucks) = 45, T2(Sum of PJ's) = 24, T3(Sum of Aura coffee) = 17

G = Grand Total = 86

CF = Correction Factor = G²/N = 86² / 15 = 493.07

TSS=Yij? – CF

= (9)² + (8)² + ......................+ (4)² - 493.07

TSS = 132.9

-- SSTR Ξ Ti2 - CF 1=1

SSTR = (1 / 5) * [(45)² + (24)² + (17)²] - 493.07

SSTR = 84.9

SSE = TSS - SSTR

= 132.9 - 84.9

SSE = 48

MSSTR = SSTR/t-1 = 84.9 / 3-1 = 42.5

MSSE = SSE / n-t = 48 / 12 = 4

F = MSSTR / MSSE = 42.5 / 4 = 10.6

Ftabulate = F$\alpha$,(t-1,n-t) = F_0.05,(2,12) = 3.8853 .................Using F table

ANOVA TABLE:

Source of Variation	SS	df	MS	F
Between Groups	84.9	t-1=3-1=2	42.5	10.6
Within Groups	48.0	n-t=15-3=12	4.0
Total	132.9	n-1=15-1=14

Conclusion:

Test statistic > Critical value, i.e. 10.6 > 3.8853, That is Reject Ho at 5% level of significance.

Therefore, There is significant difference exists in the average number of cars waiting in line at the drive-thru during the early morning among these shops.