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(a) To estimate the mean amount of time children spend in physical activities daily, a researcher randomly selects 8 children and records the number of hours they spend in physical activities in one day. The numbers of hours are: 4.1, 1.2, 4.6, 2.4, 3.2, 1.8, 2.4, and 0.7. Obtain a 95% confidence interval of the mean number of hours that children spend in physical activities.
(b) It is found that the average lifespan of 100 smart phones is 23.5 months with a standard deviation of 10.2 months. Construct the 99% confidence interval for the mean lifespan of all smart phones. State the assumption(s) made.
(c) A machine produces DVD discs. The diameters of these DVD discs vary, and the standard deviation is 0.01 centimeter. How large a sample should be taken if we wish to have 95% confidence that our sample mean will not differ from the true mean by more than 0.001 centimeter?
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