Question: A coffee-dispensing machine is supposed to deliver 8 ounces of liquid into each cup, but a consumer believes that the actual amount is less. We know that the contents dispensed are normally distributed with a standard deviation of 0.9 ounces. The consumer obtains a sample of 36 cups of dispensed coffee, and finds that the mean content is 7.75 ounces.

1. Is this sufficient evidence to conclude that, on average, the machine is under filling the coffee cups? Show all parts of the indicated test; report all values to 4-decimal places.
2. Are the results significant at the 0.05 level? Why?
3. Are the results significant at the 0.01 level? Why?

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