Question 4: The mean lifdetime of a sample of 100 fluorescent light bulbs produced by a company is computed to be 1570 hours with a standard deviation Of 120 hours. a) Test the hypothesis that the mean lifetime is at most 1600 hours. (probability of type I error =0.05). b) How large a sample of light bulbs must we take in order to be 99.73% confident that the margin of error for the mean will be within 0.2 if the standard deviation is known to be 0.042?
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3) Our light bulb manufacturer wants to estimate how long his new LED light bulbs will last. He takes a random sample of 40 such bulbs and determines that the sample mean is 45500 hours with a standard deviation of 1200 hours. (a) Determine a 96% confidence interval for the true mean life of these bulbs. (b) If we approximate the population mean life of these bulbs by the sample mean, what is the maximum possible error we would (with 96% confidence). (c) If we want the error in (b) to be less than 150 hours, how large a sample must we take?
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Our light bulb manufacturer wants to estimate how long his new LED light bulbs will last. He takes a random sample of 40 such bulbs and determines that the sample mean is 45500 hours with a standard deviation of 1200 hours. (a) Determine a 96% confidence interval for the true mean life of these bulbs. (b) If we approximate the population mean life of these bulbs by the sample mean, what is the maximum possible error we would (with 96% confidence). (c) If we want the error in (b) to be less than 150 hours, how large a sample must we take?
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