A pharmaceutical firm has been investigating the possibility of having hospital personnel supplied with small disposable vials that can be used to perform many of the standard laboratory analyses. For a particular analysis, such as blood sugar, the technician would insert a measured amount of blood into an appropriate vial and observe its color when thoroughly mixed with the chemical already stored in the vial. By comparing the optical density of the combined fluid to a color-coded chart, the technician would have a reading on the blood sugar level of the patient. Obviously, the system must be tightly controlled to ensure that the vials are correctly sealed with the proper amount of chemical prior to shipment to the hospital laboratories. In a random sample of 100 vials from a batch of several thousand vials, all 100 vials had the correct amount of chemical and were properly sealed.
a. Estimate the proportion of defective vials in the batch.
b. Construct a 99% confidence interval for the proportion of defective vials in the batch.
c. Using your confidence interval from (b), test the pharmaceutical firm’s claim that there are less than 1% defective vials per batch. What is the a level of your test?
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