Expected value and standard deviation of the sample proportion Expected value an

Question

Expected value and standard deviation of the sample proportion

Expected value and standard deviation of the sample proportion (finite population) A local computer store just received a shipment of 227 flash drives. The manager wants to estimate the number of defective flash drives in the shipment. Rather than checking every flash drive, the manager plans to take a simple random sample of size 68 in order to estimate the proportion of defective flash drives in the shipment. If the sample proportion of defective flash drives, p, is greater than 0.0147 (there is more than one defective flash drive in the sample), the manager will file a complaint and request a new shipment. Suppose that the true proportion of defective flash drives in the shipment is approximately p = 0.03. What is the expected value of the sample proportion? E(P)= Since the sample is to be drawn from a finite population, and since the sample is___________ 5% of the population size, the finite population correction factor_ needed when you calculate the standard deviation of the sampling distribution. What is the standard deviation of the sampling distribution of the sample proportion?

Explanation / Answer

Expected value of defective pieces in sample proportion, E(p)=np=68*0.03=2.04

Since the sample is more than 5% of the population size, the finite population correction factor,

fpc=sqrt[(N-n)/(N-1)]=0.83877 is needed to calculate standard deviation.

standard deviation= [n·p(1-p)]*fpc = [68*0.03*0.97]*0.83877=1.174

Related Questions

Navigate

• Browse (All)
• Browse E
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.