A particular TV manufacturer claims that it\'s have such high reliability that 9

Question

A particular TV manufacturer claims that it's have such high reliability that 90% of these sets 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 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

here phat =80/100=0.8

hence std error =(p(1-p)/n)1/2 =0.04

also for 95% CI, z=1.96

hence confidence interval =point estimate -/+ z*std error =0.7216 ; 0.8784

above interval provide 95% probability to contain true proportion of TV which do not need repair.

b)Above interval provide that company claim is not valid as interval does not contain 90% as valid interval value.

c) margin of error E=0.04

p=0.8

hence sample size =p(1-p)(Z/E)2 =~385

please reply for doubnt

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