Question 135377
A vending machine company that dispenses coffee into cups must fill the cups with 7.8oz of liquid. Before selling the vending machine to a college or business, the company tests the machine to be sure it is dispensing an average amount of 7.8oz of coffee. A sample of 6 amounts is shown below. The amount of coffee is assumed to be normally distributed with a standard deviation of 0.10 oz. At the .10 level of significance, does the machine dispense as expected? 
Treat as a small sample. 
7.81 7.77 7.89 7.83 7.75 7.79
Ho: u = 7.8
Ha; u is not 7.8
x-bar = 7.8067 ; s=0.04967
Critical value for 2-tail t-test for alpha=10% and df=5: t =1.476
Test statistic: t(7.8067) = (7.8067-7.8)/[0.04967/sqrt(6)] = 0.3304
Conclusion: Since test stat is not in the reject interval, Fail to 
reject Ho. The test provides statistical evidence that the machine
dispenses as expected.
Stan H.