Two competing internet routers, A and B, are being compared for the transmission speeds they can achieve for a random selection of transmitted files. The company which produces router A claims that its transmission speed exceeds that of router B. To compare, 1000 randomly selected file transmissions are monitored for each router. The sample mean and sample standard deviation of the transmission speed for router A was determined to be 10.04 and 0.987 GB/sec, respectively, while the same parameters for router B were 8.972 and 1.032 GB/sec, respectively. a) Is it reasonable to assume that the true standard deviations are known? Why or why not? b) Construct a 95% confidence interval on the mean transmission speed for router A. c) Construct a 95% confidence interval on the mean transmission speed for router B.
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Two competing internet routers, A and B, are being compared for the transmission speeds they can achieve for a random selection of transmitted files. The company which produces router A claims that its transmission speed exceeds that of router B. To compare, 1000 randomly selected file transmissions are monitored for each router. The sample mean and sample standard deviation of the transmission speed for router A was determined to be 10.04 and 0.987 GB/sec, respectively, while the same parameters for router B were 8.972 and 1.032 GB/sec, respectively.
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a) Is it reasonable to assume that the true standard deviations are known? Why or why not?
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b) Construct a 95% confidence interval on the mean transmission speed for router A.
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c) Construct a 95% confidence interval on the mean transmission speed for router B.
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d) By constructing a 95% confidence interval on the difference between the means, would you say that the claim made by the company producing router A is reasonable?
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