A manufacturer of LED 3D televisions claims that only 8% of all its televisions require service during the one-year warranty period. In order to investigate this claim, a consumer protection agency takes a random sample of 200 households that purchased one of the company’s televisions.
(a) Let ˆ
Prepresent the sample proportion of televisions that require service during the warranty period. Assuming that the company’s claim is true, what is the approximate sampling distribution of ˆ
(b) Approximate the probability that at least 10% of televisions in the sample will require service during the warranty period.
(c) The sample actually revealed that 24 of the 200 households required their television to be serviced during the warranty period. Construct a 95% confidence interval for the proportion of all LED 3D televisions manufactured by this company that are serviced under warranty. Interpret the result.
(d) Suppose the consumer protection agency wishes the confidence interval in part (c) to be accurate to within 2%. What sample size would you recommend they use? You may use the information in part (c) to estimate the population proportion, p.