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 the P-value of her test?

Question

Quizplus · Accepted Answer

We use the large-sample test for a population proportion.
Sample proportion = 8/200 = 0.04
Standard error = sqrt((0.05*(1-0.05))/200) = 0.0224
Test statistic = (0.04 - 0.05)/0.0224 = -0.4464
P-value=P(Z<-0.4464)=0.2582
Since the P-value is greater than the significance level of 0.05, we fail to reject the null hypothesis. Therefore, there is not enough evidence to conclude that the proportion of medications that failed to retain their full potency after 60 days is less than 0.05.

An Inspector Inspects a Shipment of Medications to Determine the Efficacy