The State Department of Weights and Measures is responsible for making sure that commercial weighing and measuring devices, such as scales, are accurate so customers and businesses are not cheated. Periodically, employees of the department go to businesses and test their scales. For example, dairy bottles milk in 1-gallon containers. Suppose that if the filling process is working correctly, the mean volume of all gallon containers is μ = 1.00 gallon with a standard deviation equal to σ = 0.10 gallon.

The department is suspicious of the accuracy of measurement if the standard for the population (μ = 1.00) does not fall within a 90% confidence interval. If the department employee selects a random sample of n = 9 dairy bottles with a mean of .95 gallons, what is the 90% confidence interval and should the department be suspicious?

a. 8.83 to 9.170; no

b. .896 to 1.004; no

c. .896 to 1.004; yes

d. 8.83 to 9.170; yes

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