Verizon Mobile has just received a large shipment of rechargeable phone batterie

Question

Verizon Mobile has just received a large shipment of rechargeable phone batteries. In the past, 4% of the batteries in these shipments have had voltage leaks. You take a sample of 200 batteries and test each battery to determine the sample proportion of batteries in the sample with voltage leaks. The number of batteries with voltage leaks in the sample is 10.

a. Using the sample data, construct a 95% confidence interval estimate of the population proportion of batteries with voltage leaks. Does 4% lie within the confidence interval?

b. If the proportion of faulty batteries is shown to be greater than 4%, at the a = 5% significance level, Verizon will reject the shipment. Based upon the random sample, do you accept or reject the shipment of batteries? Explain you reasoning. [This question requires that you conduct a hypothesis test.]

Explanation / Answer

Ans:

Given that

sample proportion=10/200=0.05

sample size,n=200

a)95% confidence interval for p

=0.05+/-1.96*sqrt(0.05*0.95/200)

=0.05+/-0.03

=(0.02, 0.08)

Yes,confidence interval includes 0.04.

b)

H0:p<=0.04

Ha:p>0.04

z=(0.05-0.04)/sqrt(0.04*0.96/200)

z=0.722

p-value=P(z>0.722)=0.2352

As,p-value>0.05,we fail to reject H0 and we can conclude that p<=0.04,so verizon will not reject the shipment.

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