A particular TV manufacturer claims that its sets have such high reliability tha

Question

A particular TV manufacturer claims that its sets have such high reliability that 90% of these sets last at least five years without needing a single repair. In order to test this claim, a consumer group randomly selects 100 customers who have owned this particular set for five years. Of these 100 consumers, 80 say their TV did not need any repairs, whereas 20 said their TV needed at least one repair. (a) Find a 95% confidence interval for the proportion of this particular TV that last at least five years without needing a single repair. Interpret this interval. (b) Does the interval developed in part (a) above provide convincing evidence that the company's reliability claim is valid? Explain. (c) Suppose the TV company wanted the estimate to be within 4 percentage points of the true proportion, How many more samples should the consumer group take to meet this criteria?

Explanation / Answer

a) here estimated proportion p=80/100=0.80

here n=100 ; therefore std error =(p(1-p)/n)1/2 =0.04

for 95% CI ; z=1.96

therefore 95% confidence interval =estimated proportion -/+ z*std error =0.8 -/+ 1.96*0.04 =0.7216 ; 0.8784

above interval gives 95% confident to contain true proportion of TV sets that did not need even a single repair with in 5 years,

b) as above interval contain all values below 90% ; therefore it provide convincing evidence to reject company's relaibility claim

c)

here estinated p=0.8

margin of error E =0.04

for 95% CI ; z=1.96

therefore sample size =p(1-p)*(Z/E)2 =385

hence (385-100) =285 more samples are required.

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

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