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Acetic acid in cheese should be 0.8% or less. A specialty creamery selects a random sample of 5 cheeses from their inventory and measures the acetic acid level in each. From past investigation, they believe that the distribution of acetic acid levels in their cheeses is normally distributed with population standard deviation 0.1%. They want to know if the average acetic acid in their cheeses is less than the standard of 0.8%. The measured acetic acid percentages are 0.81, 0.63, 0.66, 0.86, 0.75. (Note that 0.81 is 0.81%, not 81%.)
a. Calculate the z-statistic.
Estimating the value of the population mean on the basis of the sample mean alone produces a(n):
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