5) An important part of any dispensing process is statistical quality control. A

Question

5) An important part of any dispensing process is statistical quality control. At the X-Inn, machines are set to dispense 600 ml of soda into every customer's glass. Over time, however, the machine can get "out of control" and dispense too much soda or too little. The machine needs adjustment if the mean amount dispensed is different than 600 ml. At a random point in time each clock hour, the owner dispenses and checks a glass of dispensed soda and determines the actual volume of soda dispensed. One day the volumes of the dispensed soda were: 600.15, 599.92, 599.85, 599.92, 599.81, 600.14, 600.04, 599.98 Is there sufficient evidence to conclude that the dispensing machine needs some adjustment?

Explanation / Answer

Below are the null and alternate hypothesis
H0: mu = 600
H1: mu not equals to 600

From the given data,
mean = 599.97625
std. dev. = 0.125918057

test statistics, t = (599.97625 - 600)/(0.1259/sqrt(8)) = -0.5336

p-value = 0.6102

As p-value is greater than significance level of 0.05, we fail to reject null hypothesis.

There are not sufficient evidence to conclude that the dispensing machine needs some adjustments.

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