Vesco, Inc. is the manufacturer of a popular television set brand, ColorCrisp-510. Vesco claims that 95 percent of its set last at least five years without needing a single repair. In order to test this claim, a consumer group randomly selects 400 customers who have owned a ColorCrisp-510 television set for five years. Of these 400 customers, 316 say their ColorCrisp-510 television sets did not need a repair, whereas 84 say their ColorCrisp-510 television sets did need at least one repair.
a) = 316/400 = 0.79
At 99% confidence level, the critical value is z_{0.005} = 2.58
The 99% confidence interval is
+/- z_{0.005} * sqrt((1 - )/n)
= 0.79 +/- 2.58 * sqrt(0.79(1 - 0.79)/400)
= 0.79 +/- 0.0525
= 0.7375, 0.8425
b) The hypothesized value 0.95 doesn't lie in confidence interval.
Yes, the confidence interval provide strong evidence that the percentage of all ColorCrisp -510 television sets that last at least five years without a single repair is less than the 95% claimed by Vesco, Inc.
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