3. A research study found that 83.3% of pool water samples taken from public swimming pools in Bologna, Italy contained mycobacteria. Although it is rare for these mycobacteria to cause diseases in humans, those with weakened immune systems may be at risk.
Suppose that Jerry is an environmental scientist who wants to determine if the proportion of public swimming pools in Georgia that contain mycobacteria is lower than the proportion of pools in Bologna. Jerry selects 55 public pools in Georgia at random and analyzes water samples from each pool. He then uses a one-sample z-test for a proportion to assess whether his hypothesis is correct.
Because Jerry's conclusion is based on a sample of the population, there is a possibility that his conclusion will be incorrect. In the following table, the column headings list the two possible realities and the row headings list the two possible outcomes of the z-test. Each cell of the table represents a specific relationship between reality and the conclusion of the test. Place a label in each cell describing whether the scenario represents the correct conclusion or a specific type of error.
