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. Using appropriate technology, what is a 95% plus four confidence interval for the true proportion of pills in the shipment that have failed to retain full potency based on these data?

A) 0.049 ± 0.0269
B) 0.049 ± 0.0272
C) 0.049 ± 0.0296
D) 0.049 ± 0.0299