Hi Shear Corporation of Torrance California has very specific procedures for testing the quality of its product, Hi Set metal fasteners. One of the product characteristics that is monitored is surface texture. Company inspectors draw a random sample of a given size from each large production lot and check to determine the proportion of the units in the sample that have too rough a surface texture. The sample result is then used to estimate the proportion of units in the full lot that have too rough a surface texture (source: hi shear. com/).
a. If Hi Shear quality inspectors want to build a 95% confidence interval estimate of the proportion of fasteners in a large production lot that have too rough a surface, how large a sample should they select to ensure that the 95% confidence interval is no wider than + .035? Assume the inspectors have no prior information about the likely percentage of fasteners in the lot that are too rough.
b. Recompute the appropriate sample size in part a if the inspectors know from past experience with similar lots that the proportion of fasteners in the lot that are too rough is about .07.