Three Years Ago,a Major Hotel Chain Purchased a Large Number $\alpha$

Essay

Three years ago,a major hotel chain purchased a large number of heating and air-conditioning units from three major manufacturers,A,B and
C.The accounting department of the hotel chain kept records on their repair and replacement costs over the last 3 years.The manager of the purchasing department randomly selected 6 brand A,7 brand B,and 6 brand C heating and air-conditioning unit records.The repair and replacement costs in dollars are summarized in the following table.At $\alpha$ = .05,can it be concluded that there is a significant difference in repair costs among the three brands? $$\begin{array} { l c c } \text { Brand A } & \text { Brand B } & \text { Brand C } \\\$ 80 & \$ 100 & \$ 140 \\\$ 250 & \$ 170 & \$ 280 \\\$ 150 & \$ 430 & \$ 100 \\\$ 70 & \$ 290 & \$ 100 \\\$ 220 & \$ 370 & \$ 340 \\\$ 300 & \$ 420 & \$ 250 \\& \$ 350 &\end{array}$$ Failed to reject H₀.No significant difference in location of the distribution of cost between the three brands. $\begin{array}{lrcrcr}\text { Brand A } & \left(\mathrm{R}_{\mathrm{A}}\right) & \text { Brand B } & \left(\mathrm{R}_{\mathrm{B}}\right) & \text { Brand C } & \left(\mathrm{R}_{\mathrm{C}}\right) \\\$ 80 & (2) & \$ 100 & (4) & \$ 140 & (6) \\\$ 250 & (10.5) & \$ 170 & (8) & \$ 280 & (12) \\\$ 150 & (7) & \$ 430 & (19) & \$ 100 & (4)\\\$ 70 & (1) & \$ 290 & (13) & \$ 100 & (4) \\\$ 220 & (9) & \$ 370 & (17) & \$ 340 & (15) \\\$ 300 & (14) & \$ 420 & (18) & \$ 250 & (10.5)\\&43.5&\$350&(16)&&51.5\\&&&95\end{array}$ T_A = 43.5T_B = 95T_C = 51.5 $$\begin{array} { l } \chi _ { .05,2 } ^ { 2 } = 5.99 \\H = \frac { 12 } { ( 19 ) ( 20 ) } \left[ \frac { ( 43.5 ) ^ { 2 } } { 6 } + \frac { ( 95 ) ^ { 2 } } { 7 } + \frac { ( 51.5 ) ^ { 2 } } { 6 } \right] - 3 ( 19 + 1 ) \\H = 4.633 \\4.633 < 5.99 , \text { failed to reject } H _ { 0 }\end{array}$$ There is no significant difference in location of the distribution of cost between the three brands.