Quality control is an important aspect of the manufacturing

Quality control is an important aspect of the manufacturing process. At a local company, dispensing machines are manufactured to dispense 600 ml of soda into a bottle. Over time, the dispensing machines can lose precision and dispense too much or too little soda. When this occurs, the machine will require an adjustment. The machine needs an adjustment if the mean amount of soda dispensed is different than 600 ml.

The owner of a dispensing machine believes her machine has lost precision. She measures he amount of soda dispensed at 8 random times throughout the day. The amounts are listed below.

600.10, 599.91, 599.84, 599.89, 599.82, 600.11, 600.02, 599.91

The sample mean, x_bar, and the sample standard deviation, s, are calculated.

x_bar = 599.95 and s = 0.1126

1a) For the hypotheses, choose the appropriate equality or inequality symbol from this table below:

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Ho: µ _________ 600    Please select the number corresponding to the appropriate symbol.

Ha: µ _________ 600    Please select the number corresponding to the appropriate symbol.

1b) Assume the conditions for approximately normal are met.

Calculate the P-value (use of technology is recommended)

P-value = _________ (Round to three decimal places.)

Based on this P-value and testing at 0.05 level of significance, we _________ (1 = have enough, 2 = do not have enough) evidence and we, therefore, __________ (1 = reject, 2 = fail to reject) the null hypothesis that the average soda dispensed is 600 ml.

Use of this MS Excel Template may be helpful:

Solution

Formulating the null and alternative hypotheses,          
          
Ho:   u   =   600
Ha:    u   =/   600 [PART 1A]
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As we can see, this is a    two   tailed test.  
          
Thus, getting the critical t,          
df = n - 1 =    7      
tcrit =    +/-   2.364624252  
          
Getting the test statistic, as          
          
X = sample mean =    599.95      
uo = hypothesized mean =    600      
n = sample size =    8      
s = standard deviation =    0.1126      
          
Thus, t = (X - uo) * sqrt(n) / s =    -1.255962311      
          
Also, the p value is          
          
p =    0.249 [ANSWER 1B]

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Based on this P-value and testing at 0.05 level of significance, we 2 = do not have enough evidence and we, therefore, 2 = fail to reject the null hypothesis that the average soda dispensed is 600 ml.