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# Question 8 of 10 A class survey in a large class for first-year college students asked, "About how many hours do you study in a typical week?" The mean response of the 466 students was $\bar{x}=15$ hours. Suppose that we know that the study time follows a Normal distribution with standard deviation $\sigma=7$ hours in the population of all first-year students at this university. (a) What is the $99 \%$ confidence interval for the population mean? (Enter your answers rounded three decimal places.) lower bound: upper bound: (b) What condition must be met for your confidence interval to be valid? The mean must be greater than 10 to satisfy conditions for inference. The confidence interval must contain 0 to satisfy conditions for inference. The 466 students in this class must be a random sample of all of the first-year students at this university to satisfy conditions for inference. The 466 students in this class must be a matched pairs sample of all of the first-year students at this university to satisfy conditions for inference.

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