A coin-operated coffee machine made by BIG Corporation was designed to discharge a mean of 7.3 ounces of coffee per cup. BIG has good reason to believe that the mean amount of coffee dispensed by the machine, µ, is less than 7.3 ounces, and plans to do a statistical test of the claim that the machine is working as designed. Technicians gather a random sample of fill amounts and find that the mean of the sample is 6.9 ounces and that the standard deviation is 0.5 ounces.
Based on this information, complete the parts below.
What are the null hypothesis H₀ and the alternative hypothesis H₁ that should be used for the test?
H₀ :
H₁ :
Suppose that BIG decides to reject the null hypothesis. What sort of error might it be making? (choose one)
Type I
Type II
Suppose the true mean amount of coffee dispensed by the machine is 7.3 ounces.
Fill in the blanks to describe a Type I error.
A Type I error would be rejecting/failing to reject (choose one) the hypothesis that µ is less than/less than or equal to/greater than/greater than or equal to/no equal to/equal to (choose one) 7.3/6.9/0.5 (choose one) when, in fact, µ is equal to 0.5/equal to 7.3/less than 0.5/less than 6.5/less than 7.3/greater than 7.3 (choose one)