# 50) A vending machine company wants to check three of its machines to determine if they50)are properly dispensing 12 ounces of coffee. Their data is given below.Machine AMachine CMachine B11.811.712.212.111.912.112.012.011.711.911.811.912.212.012.1Compute the test value for the coffee machines.B) 2.259 5.06D) 4.86A) 6.62

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4 views help_outlineImage Transcriptionclose50) A vending machine company wants to check three of its machines to determine if they 50) are properly dispensing 12 ounces of coffee. Their data is given below. Machine A Machine C Machine B 11.8 11.7 12.2 12.1 11.9 12.1 12.0 12.0 11.7 11.9 11.8 11.9 12.2 12.0 12.1 Compute the test value for the coffee machines. B) 2.25 9 5.06 D) 4.86 A) 6.62 fullscreen
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Step 1

Let µ1, µ2 and µ3 are the population mean of Machines A, B and C.

The hypothesis can be constructed as:

Null hypothesis, H0: µ1= µ2= µ3

Alternative hypothesis, Ha: (At least two µi’s are not equal.)

From the provided information, the number of treatments (k) = 3

Sample size (n1= n2= n3) = 5

The sample mean of all treatments can be obtained as: help_outlineImage Transcriptionclose72 ΣΧ n 11.8+12.1+12.0 +11.9 12.1 5 = 11.98 11.7 11.9 11.7+11.8+ 12.0 5 = 11.82 12.2 12.112.0+11.9+12.2 5 =12.08 fullscreen
Step 2

The total number of observations can be obtained as:

N = n1+ n2+ n3

= 5+5+5

= 15

The grand total can be obtained as: help_outlineImage Transcriptionclose=(5x11.98)+(5x11.82) + (5 x 12.08) 179.4 The square sum of all values can be obtained as: ΣΣ-(11.3) + (12.1) ++ (12.2)* =2146 fullscreen
Step 3

The total sum of square c... help_outlineImage Transcriptionclose(x) SSTΣΣx" N (179.4) -2146 15 0.376 Treatment sum of squares can be obtained as (x) 2 SSTr i. 122)) (01.sj +12.1)) (1.7)(12.0) (122- (12 (179.4) 5 5 5 15 (59.9) (59.1) (60.4)(179.4) 5 5 5 15 -2145.796-2145.624 0.172 fullscreen

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