Question

5.) The reputations (and hence sales) of many businesses can be severely damaged by shipments of manufactured items that contain a large percentage of defectives. For example, a manufacturer of alkaline batteries may want to be reasonably certain that fewer than 5% of its batteries are defective. Suppose 300 batteries are randomly selected from a very large shipment; each is tested and 10 defective batteries are found.

1. Check the assumptions for constructing a confidence interval

2. Construct a 95% confidence interval

3. Interpret the confidence interval

4. If 5% or more are defective then the reputation of this manufacturer will be impacted. Based on your confidence interval, does the manufacturer have to worry? Why?

Answer 1

Given that Sample size =n=300

The no.of deffective batteries in the sample =x=10

The Proportion of defective batteries=P=0.05

The sample proportion

a) The sample is unbiased

b)The tabulated value at 95% confidence interval

The confidence interval

Hence 95% confidence interval of defective batteries are 0.3866,0.28

The manufacturer is worried because the defective batteries are found between 0.3866,0.28.