An Inspector Inspects a Shipment of Medications to Determine the Efficacy

Multiple Choice

An inspector inspects a shipment of medications to determine the efficacy in terms of the proportion p in the shipment that failed to retain full potency after 60 days of production. Unless there is clear evidence that this proportion is less than 0.05, she will reject the shipment. To reach a decision, she will test the following hypotheses using the large-sample test for a population proportion:
H₀: p = 0.05, H_a: p < 0.05
To do so, she selects a simple random sample of 200 pills. Suppose that 8 of the pills have failed to retain their full potency. Which of the following assumptions for inference about a proportion using a hypothesis test are violated in this scenario?

A) The data are an SRS from the population of interest.
B) The population is at least 10 times as large as the sample.
C) n is so large that both np₀ and n(1 - p₀) are 10 or more, where p₀ is the proportion with major defects if the null hypothesis is true.
D) There appear to be no violations.