In a study done at the National Institute of Science and Technology (Steel et al. 1980), asbestos

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In a study done at the National Institute of Science and Technology (Steel et al. 1980), asbestos fibers on filters were counted as part of a project to develop measurement standards for asbestos concentration. Asbestos dissolved in water was spread on a filter, and punches of 3-mm diameter were taken from the filter and mounted on a transmission electron microscope. An operator counted the number of fibers in each of 23 grid squares, yielding the following summary statistics: ????̅ = 24.91, s = 5.48. Assume the fiber count can be approximated by a normal distribution.

a) Write a set of hypotheses to test if the mean asbestos concentration is greater than 18 fibersper grid.

b) Describe what a Type I error would be in this situation.

c) Describe what a Type II error would be in this situation.